ENVIRONMENTAL ENGINEERING SCIENCEVolume 19 Number 6 2002copy Mary Ann Liebert Inc

Influence of Crossflow Membrane Filter Geometry and Shear Rate on Colloidal Fouling in Reverse Osmosis and

Nanofiltration Separations

Eric MV Hoek1 Albert S Kim2 and Menachem Elimelech3

1Department of Chemical and Environmental EngineeringUniversity of California

Riverside CA 925212Department of Civil and Environmental Engineering

University of Hawaii at ManoaHonolulu HI 96822

3Department of Chemical Engineering Environmental Engineering ProgramYale University

New Haven CT 06520

ABSTRACT

A laboratory-scale crossflow membrane filtration apparatus was designed to investigate the relative in-fluence of filter geometry and shear rate on colloidal fouling of reverse osmosis (RO) and nanofiltration(NF) membranes An expression that allows clarification of the mechanisms of flux decline due to col-loidal fouling in RO and NF separations was derived by combining the solution-diffusion model film-theory and a modified cake filtration model With this new fouling model the interplay between the saltconcentration polarization layer and a growing colloid deposit layer may be quantified The hydraulicpressure drop across a colloid deposit layer was shown to be negligible compared to cake-enhanced os-motic pressure The difference in flux decline observed in filters with different channel heights resultedfrom different cake layer thickness and thus different cake-enhanced osmotic pressure A moderate re-duction in the initial concentration polarization and cake-enhanced osmotic pressure was obtained by op-erating at a higher shear rate within a given filter However thicker cakes were produced in the filter withgreater channel height regardless of crossflow hydrodynamics which resulted in greater loss of flux Inall modes of operation for either channel height salt rejection decreased in proportion to the extent offlux decline By decreasing channel height both flux and salt rejection were enhanced by reducing allfouling mechanismsmdashsalt concentration polarization cake layer resistance and the cake-enhanced os-motic pressure

Key words reverse osmosis nanofiltration film-theory mass transfer membrane fouling colloidal foul-ing osmotic pressure concentration polarization cake resistance

357

Corresponding author University of California Department of Chemical and Environmental Engineering Riverside CA92521 Phone 909-787-7345 Fax 909-787-5696 E-mail hoekengrucredu

INTRODUCTION

THE PERFORMANCE OF REVERSE OSMOSIS (RO) andnanofiltration (NF) membranes has been studied ex-

tensively in terms of operating conditions module geom-etry and treatment train configuration (Sirkar and Rao1981 Sirkar et al 1982 Evangelista 1985 Wiley et al1985 Kataoka et al 1991 Van Der Meer and Van Dijk1997 Voros et al 1997 Zhu et al 1997 Maskan et al2000) Of considerable importance to all of these studiesis the influence of mass transfer on the buildup of re-jected ionic species at the membrane surface or concen-tration polarization (CP) High-concentration polariza-tion increases the salt concentration at the membranesurface which results in lower salt rejection and highertrans-membrane osmotic pressure and thus a reductionin performance Many past performance studies specifi-cally focused on optimizing crossflow hydrodynamicsandor membrane filter geometry to limit salt CP and theassociated loss of performance due to osmotic pressurebuildup (Sirkar and Rao 1981 Sirkar et al 1982 Evan-gelista 1985 Wiley et al 1985 Van Der Meer and VanDijk 1997 Voros et al 1997 Zhu et al 1997 Maskanet al 2000) However the use of RONF membranes inwater treatment processes is further hindered becauseeven pretreated feed waters may contain dissolved nat-ural organic matter and small colloids composed of nat-ural silica clays aggregated organics or biologic mat-ter in addition to ionic constituents (Mallevialle et al1996 Hong and Elimelech 1997 Zhu and Elimelech1997 Braghetta et al 1998 Chellam and Taylor 2001)Therefore the additional pressure drop due to biologiccolloidal or organic matter fouling must be rigorouslyincorporated into RONF performance models to accu-rately predict the transient loss of flux and associated de-cline in salt rejection

Incorporation of colloidal fouling into RONF perfor-mance models is not trivial because the fundamentalmechanisms are not well-understood What is knowncomes predominantly from research on colloidal foulingof microfiltration and ultrafiltration membranes Salt con-centration has been shown to exacerbate colloidal foul-ing for RO and NF membranes (Zhu and Elimelech1997 Braghetta et al 1998 Yiantsios and Karabelas1998) but little is known about the nature ofcolloidndashsolute interactions within the salt CP layer It wasrecently demonstrated that a growing colloid depositlayer may exacerbate concentration polarization for saltrejecting membranes and cause far more flux declinethan could be explained by the hydraulic resistance of thecolloid deposit layer alone (Hoek 2002 Hoek and Eli-melech 2002) The experimental data suggested that theprimary mechanism of fouling was hindered back-diffu-

sion of salt ions within the colloid deposit layers leadingto a ldquocake-enhanced osmotic pressurerdquo Therefore it ishypothesized that the decline in performance associatedwith colloidal fouling may be controlled by optimizingmass transfer and this is tested by investigating the rel-ative influence of crossflow membrane filter geometryand hydrodynamics

In this investigation the combined ldquosolution diffu-sionndashfilm-theoryrdquo model is used to describe the influenceof crossflow membrane filter geometry and crossflow hy-drodynamics on initial salt concentration polarizationThis solute transport-CP model is further combined witha modified cake filtration model to provide a simple an-alytical expression that allows simultaneous estimationof cake layer porosity and the cake-enhanced osmoticpressure from experimental fouling data A laboratory-scale crossflow membrane filtration apparatus was de-signed specifically to investigate the relative influence offilter geometry and crossflow hydrodynamics on col-loidal fouling of salt rejecting membranes Measurementof colloid deposit layer mass during several filtration ex-periments verified the relative insignificance of cakelayer hydraulic resistance and revealed valuable insightinto the role of channel height and shear rate in colloidalfouling of membranes

THEORETICAL

Solute transport and concentration polarization

The starting point for our mathematical description ofRONF separations is the solutionndashdiffusion model Themodel assumes that the permeation driving force is thegradient in chemical potential of the solute (Wijmans andBaker 1995) When the transport equation is expressedin terms of solvent flux (J) it is given as

J 5 A(DP 2 sDP) (1)

where A is the solvent permeability through the mem-brane DP is the applied pressure DP is the osmotic pres-sure difference between the membrane surface and thepermeate and s is the reflection coefficient The reflec-tion coefficient represents the intrinsic salt rejection bythe membrane but when intrinsic salt rejection is overca 098 which is typical for reverse osmosis separationss may be assumed equal to unity (Bhattacharjee et al2001) When intrinsic salt rejection is significantly lessthan 098 (ie nanofiltration) the reflection coefficientshould be used to more accurately predict the resultanttrans-membrane osmotic pressure (Murthy and Gupta1997) The combined product of sDP may be thought ofas the ldquoeffective trans-membranerdquo osmotic pressure dropwhich will be denoted as Dpm in this study Equation (1)

358 HOEK ET AL

serves as the starting point for the design of most mod-ern RONF separations

The rejection of ionic species results in an elevated saltconcentration near the membrane surface The high soluteconcentration at the membrane surface decays back to thebulk ionic concentration over some distance defined asthe concentration polarization (CP) layer ldquothicknessrdquo Incrossflow membrane filtration the CP layer quicklyreaches a steady state and the transverse solute fluxthrough the CP layer is constant The solvent flux (J) maythen be determined by the following one-dimensionalsteady-state mass balance across the CP layer

JC 2 D 5 JCp (2)

where C is the solute concentration D is the solute dif-fusivity Cp is the solute permeate concentration and yis the distance measured normal to and away from themembrane surface (Zydney 1997)

Integrating Equation (2) over the salt concentration po-larization layer thickness (d) with the appropriate bound-ary conditions (y 5 0 C 5 Cm y 5 d C 5 Cb) results in

J 5 ln 1 2 (3)

where Cm is the membrane surface salt concentration andCb is the bulk salt concentration This expression can berearranged to provide a direct estimation of the concen-tration polarization modulus (CmCb) from

5 (1 2 Ro) 1 Ro exp 1 2 (4)

Here Ro is the observed rejection (51 2 CpCb) and k(5Dd) is the mass transfer coefficient Alternate re-arrangement of Equation (3) allows estimation of the ef-fective trans-membrane osmotic pressure from

Dpm 5 2CbRTRo exp 1 2 (5)

where T is absolute temperature and R is the universalgas constant The constant 2 accounts for a 11 elec-trolyte solution at concentrations where vanrsquot Hoffrsquos lawis valid which is the case for the experiments performedin this investigation It is clear from Equation (5) thatDpm increases when bulk salt concentration rejectionand flux increase Further maintaining high mass trans-fer coefficient is critical for optimal operation of RONFprocesses

ldquoFilm-theoryrdquo model

Attempts to predict either the concentration polariza-tion modulus (CmCb) or the trans-membrane osmoticpressure (Dpm) have traditionally been limited to mass

Jk

Jk

CmCb

Cm 2 CpCb 2 Cp

Dd

dCdy

transfer analogies of the heat transfer correlations for de-velopment of a stagnant film layermdashsometimes referredto as ldquofilm-theoryrdquo models (Blatt et al 1970) More fun-damental models of concentration polarization exist(Song and Elimelech 1995 Elimelech and Bhattachar-jee 1998 Bhattacharjee et al 1999 2001) but film the-ory provides a simple analytical approach that works wellfor most RONF separations Therefore film theoryserves as the design basis for most modern reverse os-mosis processes

For laminar flow in a thin rectangular channel theldquofilm-theoryrdquo mass transfer coefficient (kf) may be re-lated to the Sherwood number (Sh) through the follow-ing equation

Sh 5 kf 5 162 1Re Sc 213

(6)

where Re is the Reynolds number (5udhn with u beingthe bulk crossflow velocity and n the solution kinematicviscosity) dh is the channel hydrodynamic diameter(lt2Hc with Hc being the channel height) Sc is theSchmidt number (nD) and Lc is the channel length(Porter 1972)

By expanding the individual components and rear-ranging the mass transfer coefficient is shown to dependon flow rate channel geometry and solute type via

kf 5 162 1 213

5 162 1 213

5162 1 213

(7)

Here Q is the feed flow rate Wc is the channel widthand g0 is the wall shear rate The shear rate representsthe velocity gradient (dudy) through a laminar hydrody-namic boundary layer and can be estimated directly from6QWcHc

2 in a thin rectangular channel (Davis 1992)From Equation (7) it is clear that for a given solute

mass transfer is most significantly enhanced by reducingchannel height (Hc) and to a lesser extent by increasingcrossflow It is this relationship that provides the logicalbasis for testing the relative influence of crossflow rateand channel height on colloidal fouling For this studythe preferred form of Equation (7) contains the shear rate(g0) because it captures the influences of both crossflowrate and channel height in a single term

Cake filtration model

The mechanism of flux decline associated with col-loid deposition on a membrane surface is typicallymodeled through the phenomenologic ldquocake filtrationrdquomodel which was originally developed for microfil-

g0D2

12Lc

uD2

2HcLc

QD2

2WcHc

2Lc

dbLc

dhD

CROSSFLOW MEMBRANE FILTER GEOMETRY 359

ENVIRON ENG SCI VOL 19 NO 6 2002

tration separations (Davis 1992) The transient flux isdescribed by

J(t) 5 Rm 1

DpRc(t)

(8a)

where the solvent flux J is a function of the net (or ef-fective) applied pressure Dp(5DP 2 Dpm) the mem-brane hydraulic resistance Rm (51A) and the cake layerresistance Rc (Faibish et al 1998) Flux at constant pres-sure is solely governed by the product of a constant spe-cific cake resistance (a) and transient deposit layer massper unit membrane area (Md) as

Rc(t) 5 aMd (t) 5 3 4 Md (t) (8b)

where m0 is the solvent viscosity laquo is the cake layerporosity ap is the particle radius and rp is the particledensity The specific cake resistance (the term in brack-ets) cannot be determined a priori without knowing thecake layer porosity However the following discussionleads to an analytical expression for directly estimatingcake layer porosity and cake-enhanced osmotic pressurefrom known constants and experimentally measurable pa-rameters

Cake-enhanced osmotic pressure model

In the standard cake filtration model the transientflux decline (or decline in trans-membrane pressure) isassumed to arise solely from the added hydraulic re-sistance of the cake layer However it was previouslydemonstrated that this is an unreasonable assumptionfor salt rejecting membranes because the primarymechanism of the flux decline is a transient cake-en-hanced osmotic pressure (Hoek 2002) The cake-en-hanced osmotic pressure model begins by rearrangingthe cake filtration equation into a series of pressuredrops

Dpm(t) 5 DP 2 Dpm(t) 2 Dpc(t) (9a)

where the cake-enhanced osmotic pressure is describedby

Dpm(t) 5 DP 2 J(t)Rm

2 J(t) 3 4Md (t) (9b)

The transient driving force for permeation the trans-membrane pressure (Dpm) is a function of the constantapplied pressure (DP) the transient cake-enhanced os-motic pressure (Dpm) and the transient trans-cake hy-draulic pressure (Dpc)

It is hypothesized that for thin cake layers (comparedto the film layer thickness) the cake-enhanced osmotic

45m(1 2 laquo)

rpa2plaquo3

45 m0(1 2 laquo)

rpa2plaquo

3

pressure results solely from the hindered back-diffusionof salt ions trapped within the colloid-cake layer (Hoek2002) Figure 1 illustrates this effect With no particlesdeposited (top) the solute concentration polarizationlayer quickly reaches steady state whereby solute trans-port by convection towards the membrane (minus thatwhich permeates) is balanced by solute back-transport bydiffusion As particles accumulate and form a thin cakelayer over the surface of the membrane (bottom) the dif-fusion of salt ions back into the bulk is hindered becauseof the tortuous path the ions must follow to circumnavi-gate the deposited colloids Hindered back-diffusion ofsalt ions trapped in the cake layer leads to an enhancedmembrane surface salt concentration (Cm) and thus en-hanced osmotic pressure drop across the membrane(Dpm)

The mathematical model that follows is based on threeimportant assumptions First the cake layer is thin com-pared to the salt film-layer thickness Past investigationshave shown that the tangential flow field is relatively un-affected when the cake layer is thin with respect to thechannel height (Faibish et al 1998) because the cakelayer does not occupy a significant fraction of the chan-

360 HOEK ET AL

Figure 1 Conceptual illustration of ldquocake-enhanced osmoticpressurerdquo effect In the absence of a colloid deposit layer (topfigure) the elevated concentration at the membrane surface(Cm) decays to the bulk concentration (Cb) over the salt con-centration polarization (film) layer thickness (df) The salt con-centration drops across the membrane thickness (dm) due to saltrejection For a thin deposit layer (bottom figure) the film layerthickness remains constant and the difference between df andcake thickness (dc) is ds In the presence of a colloid depositlayer the membrane surface salt concentration is enhanced(Cm) due to hindered back-diffusion of salt ions and a decreasein salt rejection results The elevated Cm will also result in el-evated permeate salt concentration Cp

nel cross section (Davis 1992) Crossflow shear rate isrelatively unaffected by the presence of the cake layerand thus the CP layer thickness remains at the film thick-ness determined prior to particle deposition Second thecolloid deposit layer does not reject salt ions so the pro-file of salt concentration above the colloid deposit layeris unchanged from that prior to cake formation Thirdthe effective diffusion coefficient for salt ions trappedwithin the colloid deposit layer can be estimated withknowledge of the cake layer porosity

A simple analytical expression for estimating the de-pendence of the hindered diffusion coefficient (D) onporosity is given by

D 5 (laquot) D (10)

where D is the solute diffusivity in the bulk laquo is theporosity and t(lt1 2 lnlaquo2) is the diffusive tortuosity(Boudreau 1996) Recent investigations have shown thatcake layer porosities for silica colloids filtered under sim-ilar physical and chemical conditions were typically inthe range of 03 to 07 (Faibish et al 1998 Yiantsiosand Karabelas 1998 Endo and Alonso 2001) The ratioof the effective diffusion coefficient to the bulk diffusioncoefficient is plotted against cake layer porosity in Fig2 Over the range of typical porosity values the effectivediffusion coefficient may be reduced to between 10 and40 of the bulk diffusion coefficient which results insignificantly enhanced salt concentration at the mem-brane surface

Next the effective mass transfer coefficient is brokendown into two partsmdashone describing mass transferthrough the colloid deposit layer and one describing masstransfer from the interface of the colloid layer back into

the bulk The resulting ldquohinderedrdquo mass transfer coeffi-cient (k) is estimated from

5 1 (11)

where dc is the colloid deposit layer thickness and ds isthe difference between the film (df) and cake layer thick-nesses Equation (11) comes directly from integratingEquation (2) separately across the cake and CP layersEven if the cake layer is very thin (dc ds) the cake-enhanced osmotic pressure may be significant becausethe hindered diffusion coefficient can be an order of mag-nitude smaller than the bulk diffusion coefficient

Because the film layer thickness was assumed con-stant the salt layer thickness over the cake is the dif-ference between the original film thickness and thecake thickness (ie ds 5 df 2 dc) Note that the cakelayer thickness can be written in terms of cake massper unit membrane area as dc 5 Md rp(1 2 laquo) (Faibishet al 1998) Rewriting Equation (11) the hinderedmass transfer coefficient expression in terms of df anddc and substituting into Equation (5) results in the fol-lowing expression for the cake-enhanced osmotic pres-sure

Dpm 5 2CbRTRo

exp3 1 1 2 24 (12)

All parameters in this equation are constant or exper-imentally measurable except cake porosity (laquo) and cake-enhanced osmotic pressure (Dpm) Setting Equation (12)equal to Equation (9b) allows direct calculation of thecake layer porosity and thus cake-enhanced osmoticpressure

MATERIALS AND METHODS

Membranes

Four commercial RONF polyamide thin-film com-posite membranes were used in this study The RO mem-branes were Hydranautics LFC1 (Oceanside CA) andTrisep X20 (Goleta CA) The NF membranes were Dow-FilmTec NF70 (Minneapolis MN) and Osmonics HL(Minnetonka MN) All membranes were stored in deion-ized water at 5degC with water replaced regularly Themembranes were characterized for relevant performanceproperties such as pure water permeability (A) and ob-served salt rejection (Ro) Salt rejection experiments wereconducted at 001 M NaCl and unadjusted pH of 68 602 which are the same feed conditions used in all foul-ing experiments All four membranes are thought to be

1D`

1 2 ln(laquo2)

D`laquo

JMd rp(1 2 laquo)

Jkf

dsD

dcD

1k

CROSSFLOW MEMBRANE FILTER GEOMETRY 361

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 2 Ratio of the cake-hindered salt diffusion coefficientto the bulk diffusion coefficient predicted by Equation (10) fora range of cake layer porosities

moderately negatively charged (215 to 225 mV) at typ-ical solution chemistries based on streaming potentialanalyses reported elsewhere (Vrijenhoek et al 2001)

Reagents and model colloids

Salt stock solutions were prepared using ACS gradeNaCl (Fisher Scientific Pittsburgh PA) dissolved indeionized water (Nanopure Infinity Ultrapure BarnsteadDubuque IA) Nissan Chemical America Corporation(Houston TX) provided the colloidal particles used inthe fouling experiments The particles were certified as010 mm (6003 mm) silica particles in an aqueous sus-pension Chemical analysis by the manufacturer indicatesthe suspension to be 407 (ww) amorphous silica witha specific gravity of 13 Based on the specific gravityand weight percent of the suspension the particle densitywas calculated to be 236 gcm3 Gravimetric analysis ofthe particle suspension revealed the particle density to be211 gcm3 which compares well with the above calcu-lation and other reported values (Faibish et al 1998)Particles were negatively charged (225 mV) at pH 68 602 and 001 M NaCl as determined from electrophoreticmobility measurements reported elsewhere (Vrijenhoeket al 2001)

Laboratory-scale crossflow membrane filters

The test apparatus was a modified version of twocommercially available stainless steel crossflow mem-brane filtration (CMF) units (Sepa CF Osmonics IncMinnetonka MN) The crossflow membrane filtrationunits are rated for operating pressures up to 6895 kPa(1000 psi) Both crossflow units have dimensions of146 and 95 cm for channel length (Lc) and width (Wc)respectively while the channel heights (Hc) are 34 mil(086 mm) and 68 mil (173 mm) respectively The twocrossflow membrane filtration units will hereafter be de-scribed simply as the ldquo34rdquo and ldquo68rdquo units thus indi-cating their respective channel heights These channeldimensions provide an effective membrane area (Am) of139 3 1022 m2 per unit and cross-sectional flow areas(Ax) of 082 3 1024 m2 for the 34 unit and 164 3 1024

m2 for the 68 unit The applied pressure (DP) was con-stant and monitored by a pressure gage (Cole-ParmerChicago IL) and flux was monitored in real time by adigital flow meter (Optiflow 1000 Humonics RanchoCordova CA) Specific modifications to the manufac-turerrsquos setup were reported elsewhere (Vrijenhoek et al2001) a schematic diagram of the experimental systemis presented in Fig 3

362 HOEK ET AL

Figure 3 Crossflow membrane filtration (CMF) apparatus used in experiments designed to simultaneously test the influenceof crossflow hydrodynamics and membrane filter geometry on colloidal fouling The two crossflow membrane filters may be fedin parallel from a common feed tank or individually

Measuring membrane hydraulic resistance

Different membrane coupons were used for each fil-tration experiment so the membrane hydraulic resis-tance was determined prior to each fouling experimentFirst deionized (DI) water was circulated at 250 psi(1724 kPa) for up to 24 h to dissociate flux decline dueto membrane compaction (and other unknown causesinherent of lab-scale recirculation systems) Flux wasmonitored continuously for the duration of the experi-ment and recorded in real time on a laboratory com-puter After DI equilibration the pressure was changedin increments of 50 psi (345 kPa) from a high of 250psi to a low of 50 psi and flux recorded at a feed flowrate of 095 liters per minute (Lpm) At each pressureflux was monitored for at least 30 min to ensure stableperformance The crossflow was then increased to 190Lpm and flux was recorded at 50 psi increments from50 to 250 psi Finally feed flow rate was set at 379Lpm and the flux was recorded at 50 psi incrementsfrom 250 psi down to 50 psi At each crossflow andpressure the average of all of the stable flux measure-ments was plotted against applied pressure The slopeof a line fitted to pure water flux vs pressure data bya least-squares linear regression provided the mem-brane hydraulic resistance As expected there was nomeasured influence of feed flow rate on pure water fluxfor any experiments but the procedure provided extradata points for the regression analysis The pH of feedwas monitored throughout the pure water flux experi-ments to ensure constant feed solution chemistry

Measuring CP modulus and initial osmoticpressure drop

After the membrane pure water hydraulic resistance(Rm) was determined concentration polarization effectscould be quantified using film-theory and the velocityvariation technique described herein An appropriatevolume of 1 M stock NaCl solution was added to thefeed tank to provide the desired experimental ionicstrength The same feed solution ionic strength (001M) was used for all filtration experiments in this studyThe sequence of varying applied pressure and feed flowrate was repeated The effective osmotic pressure dropacross the membrane (Dpm) for each velocity variationwas determined from Equation (1) with A 5 1Rm Eachcombination of pressure and flow yielded different per-meate and crossflow velocities respectively and hencethe description as the ldquovelocity variationrdquo techniqueThe experimental film-theory mass transfer coefficientwas calculated from the measured Dpm and Equation(5) and then the experimental CP modulus was calcu-lated from Equation (4) for each velocity variation The

feed solution pH was monitored throughout the salt wa-ter experiments to ensure stable feed conditions Ob-served salt rejection (Ro) was determined by measur-ing feed and permeate conductivity Conductivity wasdetermined to be linearly proportional to NaCl con-centration by performing a least-squares linear regres-sion of conductivity measurements for solutions withknown NaCl concentrations

Measuring decline in flux and salt rejection dueto colloidal fouling

After the salt water experiments were finished pres-sure and crossflow were adjusted to produce the de-sired initial flux and wall shear for the fouling exper-iment After stable performance (flux and saltrejection) was achieved for a minimum of 60 min adose of silica particles was added to the feed tank toprovide the appropriate particle feed concentrationThe concentration of 100 nm silica particles was0008 (vv) which yielded an average turbidity of532 NTU The same concentration of particles wasused in all colloidal fouling experiments performed forthis study Conductivity pH and turbidity measure-ments were made at the start end and at several pointsduring the fouling experiment to determine salt rejec-tion to ensure complete rejection of particles and toensure feed conditions were constant throughout thetest The transient flux at constant pressure was down-loaded in real time from the digital permeate flow me-ter to a laboratory computer

Measuring colloid deposit layer mass

In some experiments the mass of colloid deposit lay-ers was measured using a previously published technique(Faibish et al 1998) The feed tank volume was reducedsuch that the mass of particles dosed into the feed tankwould be measurably reduced by the mass of particlesaccumulated in the cake layer over the membrane Asmaller feed volume was used for these experiments suchthat a small but measurable decrease in feed turbidityoccurred within in the time scale of the experiment Inthese experiments only one crossflow filter was used sothat the decline in feed suspension turbidity was relatedto a single crossflow membrane filter No significant dif-ference in mass transfer parameters flux decline data orsalt rejection data was found when compared to data fromexperiments using constant feed particle concentrationfed in parallel to both crossflow membrane filters Themeasured colloid deposit layer mass was then combinedwith other relevant measured and constant parametersinto Equations (9) and (12) to determine the cake poros-ity and cake-enhanced osmotic pressure

CROSSFLOW MEMBRANE FILTER GEOMETRY 363

ENVIRON ENG SCI VOL 19 NO 6 2002

RESULTS AND DISCUSSION

Predicted and measured concentrationpolarization effects

The film-theory predicted mass transfer parameters forthe lab-scale CMF units are provided in Table 1 Thelisted volumetric feed flow rates (Q) are those used infouling experiments and the data are arranged in order of decreasing CP modulus Velocity shear rate andReynolds number all increase with increasing feed flowHowever at a given volumetric flow rate velocity is dou-bled as dh is halved so the Reynolds number is the samein either channel The wall shear rate captures both thedifference in channel geometry and crossflow and so itcan be made identical in the two units at certain cross-flow rates The mass transfer coefficients CP moduliand osmotic pressure drops predicted from the film-the-ory equations all increase in proportion to the change inshear rate again highlighting the usefulness of this pa-rameter The theoretical film layer thickness was calcu-lated from kf 5 Ddf using 1611 3 1029 m2s as the dif-fusion coefficient for NaCl and ranged from about 50 to125 mm The most important data from Table 1 are items3 and 4 The shear rate is identical so the film-theorypredicted mass transfer parameters (kf df Cm Cb andDpm) are identical

The theoretical and experimental concentration polar-ization moduli for the crossflow membrane filters areplotted against crossflow Reynolds number in Fig 4 Ex-perimentally determined salt rejection is labeled next toeach experimental data point The labels 1 to 6 corre-spond to the same item numbers in Table 1 The exper-imental osmotic pressure drop was determined at a sta-ble flux of 142 3 1025 ms (30 gfd) and combined withobserved salt rejection data in Equation (5) to calculatethe experimental mass transfer coefficient The experi-

mental CP modulus was then calculated from Equation(4) The theoretical concentration polarization modulusdata plotted in Fig 4 was calculated from Equation (4)using the experimental salt rejection values at the corre-sponding Reynolds flows and linearly interpolating (orextrapolating) salt rejection values for flow rates in be-tween (or beyond) The theoretical CP modulus was rel-atively insensitive to Ro over the range of experimentallyobserved rejection values in Fig 4 so this simple linearinterpolation should not introduce significant error

Both the predicted and experimental concentration po-larization effects are shown to be more severe in the 68unit than in the 34 unit over the entire range of flow ratesThe experimental data are in fairly good agreement withpredicted CP modulus data although the experimentaldata appear relatively flat over the range of Reynoldsnumbers This may be due in part to the fact that wall-suction (permeation) is ignored in the film-theory pre-dicted mass transfer coefficient In items 3 and 4 of Table1 the hydrodynamic conditions are predicted to yield thesame CP modulus in the two filters but experimental CPmoduli differed by about 17 This film-theory ldquoerrorrdquomay be due to entrance and side-wall effects not ac-counted for in film theory predictions as well as otherpotential unknown experimental errors

Figure 5 presents the predicted trans-cake hydraulicpressures cake-enhanced osmotic pressures and perme-ate fluxes in the 34 and 68 units for varied cake layerthickness and porosity Hydrodynamic conditions werethose described in items 1 and 4 of Table 1 Howeverbecause the mass transfer parameters are identical initems 3 and 4 the 34 unit curves displayed in Fig 5 the-oretically represent the cake-enhanced osmotic pressuresfor the 68 unit under the conditions of item 3 in Table 1

At a feed flow rate of 095 Lpm the initial trans-mem-brane osmotic pressures were about 14 and 21 psi in the

364 HOEK ET AL

Table 1 Film-theory predicted mass transfer parameters for experimental CMF units

Item CMFa Qb uc g0d Ree kf df Cm Cb

fDpm

g

no unit [Lpm] [cms] [s21] [2] [mms] [mm] [2] [psi]

1 68 095 96 334 372 13 126 30 212 68 189 192 668 745 16 100 24 173 68 379 384 1336 1489 20 79 20 144 34 095 192 1336 372 20 79 20 145 34 189 384 2671 745 26 63 17 126 34 379 769 5342 1489 32 50 15 11

Operation conditions used in the calculations are J0 5 142 3 1025 ms (30 gfd) Cb 5 001 M NaCl and Ro 5 98 aChannelheight (Hc) 5 0864 mm (34) and 173 mm (68) channel length (Lc) 5 146 mm channel width (Wc) 5 95 mm bQ 5 volumetricfeed flow rate in liters per minute (Lpm) cu 5 QAx Ax 5 channel cross-sectional area dg0 5 6uHc and is the channel wall shearrate eRe 5 udhn and is the channel crossflow Reynolds number dh 5 2Hc n 5 kinematic viscosity fconcentration polarization(CP) modulus calculated from Equation (4) geffective trans-membrane osmotic pressure calculated from Equation 5

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

INTRODUCTION

THE PERFORMANCE OF REVERSE OSMOSIS (RO) andnanofiltration (NF) membranes has been studied ex-

tensively in terms of operating conditions module geom-etry and treatment train configuration (Sirkar and Rao1981 Sirkar et al 1982 Evangelista 1985 Wiley et al1985 Kataoka et al 1991 Van Der Meer and Van Dijk1997 Voros et al 1997 Zhu et al 1997 Maskan et al2000) Of considerable importance to all of these studiesis the influence of mass transfer on the buildup of re-jected ionic species at the membrane surface or concen-tration polarization (CP) High-concentration polariza-tion increases the salt concentration at the membranesurface which results in lower salt rejection and highertrans-membrane osmotic pressure and thus a reductionin performance Many past performance studies specifi-cally focused on optimizing crossflow hydrodynamicsandor membrane filter geometry to limit salt CP and theassociated loss of performance due to osmotic pressurebuildup (Sirkar and Rao 1981 Sirkar et al 1982 Evan-gelista 1985 Wiley et al 1985 Van Der Meer and VanDijk 1997 Voros et al 1997 Zhu et al 1997 Maskanet al 2000) However the use of RONF membranes inwater treatment processes is further hindered becauseeven pretreated feed waters may contain dissolved nat-ural organic matter and small colloids composed of nat-ural silica clays aggregated organics or biologic mat-ter in addition to ionic constituents (Mallevialle et al1996 Hong and Elimelech 1997 Zhu and Elimelech1997 Braghetta et al 1998 Chellam and Taylor 2001)Therefore the additional pressure drop due to biologiccolloidal or organic matter fouling must be rigorouslyincorporated into RONF performance models to accu-rately predict the transient loss of flux and associated de-cline in salt rejection

Incorporation of colloidal fouling into RONF perfor-mance models is not trivial because the fundamentalmechanisms are not well-understood What is knowncomes predominantly from research on colloidal foulingof microfiltration and ultrafiltration membranes Salt con-centration has been shown to exacerbate colloidal foul-ing for RO and NF membranes (Zhu and Elimelech1997 Braghetta et al 1998 Yiantsios and Karabelas1998) but little is known about the nature ofcolloidndashsolute interactions within the salt CP layer It wasrecently demonstrated that a growing colloid depositlayer may exacerbate concentration polarization for saltrejecting membranes and cause far more flux declinethan could be explained by the hydraulic resistance of thecolloid deposit layer alone (Hoek 2002 Hoek and Eli-melech 2002) The experimental data suggested that theprimary mechanism of fouling was hindered back-diffu-

sion of salt ions within the colloid deposit layers leadingto a ldquocake-enhanced osmotic pressurerdquo Therefore it ishypothesized that the decline in performance associatedwith colloidal fouling may be controlled by optimizingmass transfer and this is tested by investigating the rel-ative influence of crossflow membrane filter geometryand hydrodynamics

In this investigation the combined ldquosolution diffu-sionndashfilm-theoryrdquo model is used to describe the influenceof crossflow membrane filter geometry and crossflow hy-drodynamics on initial salt concentration polarizationThis solute transport-CP model is further combined witha modified cake filtration model to provide a simple an-alytical expression that allows simultaneous estimationof cake layer porosity and the cake-enhanced osmoticpressure from experimental fouling data A laboratory-scale crossflow membrane filtration apparatus was de-signed specifically to investigate the relative influence offilter geometry and crossflow hydrodynamics on col-loidal fouling of salt rejecting membranes Measurementof colloid deposit layer mass during several filtration ex-periments verified the relative insignificance of cakelayer hydraulic resistance and revealed valuable insightinto the role of channel height and shear rate in colloidalfouling of membranes

THEORETICAL

Solute transport and concentration polarization

The starting point for our mathematical description ofRONF separations is the solutionndashdiffusion model Themodel assumes that the permeation driving force is thegradient in chemical potential of the solute (Wijmans andBaker 1995) When the transport equation is expressedin terms of solvent flux (J) it is given as

J 5 A(DP 2 sDP) (1)

where A is the solvent permeability through the mem-brane DP is the applied pressure DP is the osmotic pres-sure difference between the membrane surface and thepermeate and s is the reflection coefficient The reflec-tion coefficient represents the intrinsic salt rejection bythe membrane but when intrinsic salt rejection is overca 098 which is typical for reverse osmosis separationss may be assumed equal to unity (Bhattacharjee et al2001) When intrinsic salt rejection is significantly lessthan 098 (ie nanofiltration) the reflection coefficientshould be used to more accurately predict the resultanttrans-membrane osmotic pressure (Murthy and Gupta1997) The combined product of sDP may be thought ofas the ldquoeffective trans-membranerdquo osmotic pressure dropwhich will be denoted as Dpm in this study Equation (1)

358 HOEK ET AL

serves as the starting point for the design of most mod-ern RONF separations

The rejection of ionic species results in an elevated saltconcentration near the membrane surface The high soluteconcentration at the membrane surface decays back to thebulk ionic concentration over some distance defined asthe concentration polarization (CP) layer ldquothicknessrdquo Incrossflow membrane filtration the CP layer quicklyreaches a steady state and the transverse solute fluxthrough the CP layer is constant The solvent flux (J) maythen be determined by the following one-dimensionalsteady-state mass balance across the CP layer

JC 2 D 5 JCp (2)

where C is the solute concentration D is the solute dif-fusivity Cp is the solute permeate concentration and yis the distance measured normal to and away from themembrane surface (Zydney 1997)

Integrating Equation (2) over the salt concentration po-larization layer thickness (d) with the appropriate bound-ary conditions (y 5 0 C 5 Cm y 5 d C 5 Cb) results in

J 5 ln 1 2 (3)

where Cm is the membrane surface salt concentration andCb is the bulk salt concentration This expression can berearranged to provide a direct estimation of the concen-tration polarization modulus (CmCb) from

5 (1 2 Ro) 1 Ro exp 1 2 (4)

Here Ro is the observed rejection (51 2 CpCb) and k(5Dd) is the mass transfer coefficient Alternate re-arrangement of Equation (3) allows estimation of the ef-fective trans-membrane osmotic pressure from

Dpm 5 2CbRTRo exp 1 2 (5)

where T is absolute temperature and R is the universalgas constant The constant 2 accounts for a 11 elec-trolyte solution at concentrations where vanrsquot Hoffrsquos lawis valid which is the case for the experiments performedin this investigation It is clear from Equation (5) thatDpm increases when bulk salt concentration rejectionand flux increase Further maintaining high mass trans-fer coefficient is critical for optimal operation of RONFprocesses

ldquoFilm-theoryrdquo model

Attempts to predict either the concentration polariza-tion modulus (CmCb) or the trans-membrane osmoticpressure (Dpm) have traditionally been limited to mass

Jk

Jk

CmCb

Cm 2 CpCb 2 Cp

Dd

dCdy

transfer analogies of the heat transfer correlations for de-velopment of a stagnant film layermdashsometimes referredto as ldquofilm-theoryrdquo models (Blatt et al 1970) More fun-damental models of concentration polarization exist(Song and Elimelech 1995 Elimelech and Bhattachar-jee 1998 Bhattacharjee et al 1999 2001) but film the-ory provides a simple analytical approach that works wellfor most RONF separations Therefore film theoryserves as the design basis for most modern reverse os-mosis processes

For laminar flow in a thin rectangular channel theldquofilm-theoryrdquo mass transfer coefficient (kf) may be re-lated to the Sherwood number (Sh) through the follow-ing equation

Sh 5 kf 5 162 1Re Sc 213

(6)

where Re is the Reynolds number (5udhn with u beingthe bulk crossflow velocity and n the solution kinematicviscosity) dh is the channel hydrodynamic diameter(lt2Hc with Hc being the channel height) Sc is theSchmidt number (nD) and Lc is the channel length(Porter 1972)

By expanding the individual components and rear-ranging the mass transfer coefficient is shown to dependon flow rate channel geometry and solute type via

kf 5 162 1 213

5 162 1 213

5162 1 213

(7)

Here Q is the feed flow rate Wc is the channel widthand g0 is the wall shear rate The shear rate representsthe velocity gradient (dudy) through a laminar hydrody-namic boundary layer and can be estimated directly from6QWcHc

2 in a thin rectangular channel (Davis 1992)From Equation (7) it is clear that for a given solute

mass transfer is most significantly enhanced by reducingchannel height (Hc) and to a lesser extent by increasingcrossflow It is this relationship that provides the logicalbasis for testing the relative influence of crossflow rateand channel height on colloidal fouling For this studythe preferred form of Equation (7) contains the shear rate(g0) because it captures the influences of both crossflowrate and channel height in a single term

Cake filtration model

The mechanism of flux decline associated with col-loid deposition on a membrane surface is typicallymodeled through the phenomenologic ldquocake filtrationrdquomodel which was originally developed for microfil-

g0D2

12Lc

uD2

2HcLc

QD2

2WcHc

2Lc

dbLc

dhD

CROSSFLOW MEMBRANE FILTER GEOMETRY 359

ENVIRON ENG SCI VOL 19 NO 6 2002

tration separations (Davis 1992) The transient flux isdescribed by

J(t) 5 Rm 1

DpRc(t)

(8a)

where the solvent flux J is a function of the net (or ef-fective) applied pressure Dp(5DP 2 Dpm) the mem-brane hydraulic resistance Rm (51A) and the cake layerresistance Rc (Faibish et al 1998) Flux at constant pres-sure is solely governed by the product of a constant spe-cific cake resistance (a) and transient deposit layer massper unit membrane area (Md) as

Rc(t) 5 aMd (t) 5 3 4 Md (t) (8b)

where m0 is the solvent viscosity laquo is the cake layerporosity ap is the particle radius and rp is the particledensity The specific cake resistance (the term in brack-ets) cannot be determined a priori without knowing thecake layer porosity However the following discussionleads to an analytical expression for directly estimatingcake layer porosity and cake-enhanced osmotic pressurefrom known constants and experimentally measurable pa-rameters

Cake-enhanced osmotic pressure model

In the standard cake filtration model the transientflux decline (or decline in trans-membrane pressure) isassumed to arise solely from the added hydraulic re-sistance of the cake layer However it was previouslydemonstrated that this is an unreasonable assumptionfor salt rejecting membranes because the primarymechanism of the flux decline is a transient cake-en-hanced osmotic pressure (Hoek 2002) The cake-en-hanced osmotic pressure model begins by rearrangingthe cake filtration equation into a series of pressuredrops

Dpm(t) 5 DP 2 Dpm(t) 2 Dpc(t) (9a)

where the cake-enhanced osmotic pressure is describedby

Dpm(t) 5 DP 2 J(t)Rm

2 J(t) 3 4Md (t) (9b)

The transient driving force for permeation the trans-membrane pressure (Dpm) is a function of the constantapplied pressure (DP) the transient cake-enhanced os-motic pressure (Dpm) and the transient trans-cake hy-draulic pressure (Dpc)

It is hypothesized that for thin cake layers (comparedto the film layer thickness) the cake-enhanced osmotic

45m(1 2 laquo)

rpa2plaquo3

45 m0(1 2 laquo)

rpa2plaquo

3

pressure results solely from the hindered back-diffusionof salt ions trapped within the colloid-cake layer (Hoek2002) Figure 1 illustrates this effect With no particlesdeposited (top) the solute concentration polarizationlayer quickly reaches steady state whereby solute trans-port by convection towards the membrane (minus thatwhich permeates) is balanced by solute back-transport bydiffusion As particles accumulate and form a thin cakelayer over the surface of the membrane (bottom) the dif-fusion of salt ions back into the bulk is hindered becauseof the tortuous path the ions must follow to circumnavi-gate the deposited colloids Hindered back-diffusion ofsalt ions trapped in the cake layer leads to an enhancedmembrane surface salt concentration (Cm) and thus en-hanced osmotic pressure drop across the membrane(Dpm)

The mathematical model that follows is based on threeimportant assumptions First the cake layer is thin com-pared to the salt film-layer thickness Past investigationshave shown that the tangential flow field is relatively un-affected when the cake layer is thin with respect to thechannel height (Faibish et al 1998) because the cakelayer does not occupy a significant fraction of the chan-

360 HOEK ET AL

Figure 1 Conceptual illustration of ldquocake-enhanced osmoticpressurerdquo effect In the absence of a colloid deposit layer (topfigure) the elevated concentration at the membrane surface(Cm) decays to the bulk concentration (Cb) over the salt con-centration polarization (film) layer thickness (df) The salt con-centration drops across the membrane thickness (dm) due to saltrejection For a thin deposit layer (bottom figure) the film layerthickness remains constant and the difference between df andcake thickness (dc) is ds In the presence of a colloid depositlayer the membrane surface salt concentration is enhanced(Cm) due to hindered back-diffusion of salt ions and a decreasein salt rejection results The elevated Cm will also result in el-evated permeate salt concentration Cp

nel cross section (Davis 1992) Crossflow shear rate isrelatively unaffected by the presence of the cake layerand thus the CP layer thickness remains at the film thick-ness determined prior to particle deposition Second thecolloid deposit layer does not reject salt ions so the pro-file of salt concentration above the colloid deposit layeris unchanged from that prior to cake formation Thirdthe effective diffusion coefficient for salt ions trappedwithin the colloid deposit layer can be estimated withknowledge of the cake layer porosity

A simple analytical expression for estimating the de-pendence of the hindered diffusion coefficient (D) onporosity is given by

D 5 (laquot) D (10)

where D is the solute diffusivity in the bulk laquo is theporosity and t(lt1 2 lnlaquo2) is the diffusive tortuosity(Boudreau 1996) Recent investigations have shown thatcake layer porosities for silica colloids filtered under sim-ilar physical and chemical conditions were typically inthe range of 03 to 07 (Faibish et al 1998 Yiantsiosand Karabelas 1998 Endo and Alonso 2001) The ratioof the effective diffusion coefficient to the bulk diffusioncoefficient is plotted against cake layer porosity in Fig2 Over the range of typical porosity values the effectivediffusion coefficient may be reduced to between 10 and40 of the bulk diffusion coefficient which results insignificantly enhanced salt concentration at the mem-brane surface

Next the effective mass transfer coefficient is brokendown into two partsmdashone describing mass transferthrough the colloid deposit layer and one describing masstransfer from the interface of the colloid layer back into

the bulk The resulting ldquohinderedrdquo mass transfer coeffi-cient (k) is estimated from

5 1 (11)

where dc is the colloid deposit layer thickness and ds isthe difference between the film (df) and cake layer thick-nesses Equation (11) comes directly from integratingEquation (2) separately across the cake and CP layersEven if the cake layer is very thin (dc ds) the cake-enhanced osmotic pressure may be significant becausethe hindered diffusion coefficient can be an order of mag-nitude smaller than the bulk diffusion coefficient

Because the film layer thickness was assumed con-stant the salt layer thickness over the cake is the dif-ference between the original film thickness and thecake thickness (ie ds 5 df 2 dc) Note that the cakelayer thickness can be written in terms of cake massper unit membrane area as dc 5 Md rp(1 2 laquo) (Faibishet al 1998) Rewriting Equation (11) the hinderedmass transfer coefficient expression in terms of df anddc and substituting into Equation (5) results in the fol-lowing expression for the cake-enhanced osmotic pres-sure

Dpm 5 2CbRTRo

exp3 1 1 2 24 (12)

All parameters in this equation are constant or exper-imentally measurable except cake porosity (laquo) and cake-enhanced osmotic pressure (Dpm) Setting Equation (12)equal to Equation (9b) allows direct calculation of thecake layer porosity and thus cake-enhanced osmoticpressure

MATERIALS AND METHODS

Membranes

Four commercial RONF polyamide thin-film com-posite membranes were used in this study The RO mem-branes were Hydranautics LFC1 (Oceanside CA) andTrisep X20 (Goleta CA) The NF membranes were Dow-FilmTec NF70 (Minneapolis MN) and Osmonics HL(Minnetonka MN) All membranes were stored in deion-ized water at 5degC with water replaced regularly Themembranes were characterized for relevant performanceproperties such as pure water permeability (A) and ob-served salt rejection (Ro) Salt rejection experiments wereconducted at 001 M NaCl and unadjusted pH of 68 602 which are the same feed conditions used in all foul-ing experiments All four membranes are thought to be

1D`

1 2 ln(laquo2)

D`laquo

JMd rp(1 2 laquo)

Jkf

dsD

dcD

1k

CROSSFLOW MEMBRANE FILTER GEOMETRY 361

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 2 Ratio of the cake-hindered salt diffusion coefficientto the bulk diffusion coefficient predicted by Equation (10) fora range of cake layer porosities

moderately negatively charged (215 to 225 mV) at typ-ical solution chemistries based on streaming potentialanalyses reported elsewhere (Vrijenhoek et al 2001)

Reagents and model colloids

Salt stock solutions were prepared using ACS gradeNaCl (Fisher Scientific Pittsburgh PA) dissolved indeionized water (Nanopure Infinity Ultrapure BarnsteadDubuque IA) Nissan Chemical America Corporation(Houston TX) provided the colloidal particles used inthe fouling experiments The particles were certified as010 mm (6003 mm) silica particles in an aqueous sus-pension Chemical analysis by the manufacturer indicatesthe suspension to be 407 (ww) amorphous silica witha specific gravity of 13 Based on the specific gravityand weight percent of the suspension the particle densitywas calculated to be 236 gcm3 Gravimetric analysis ofthe particle suspension revealed the particle density to be211 gcm3 which compares well with the above calcu-lation and other reported values (Faibish et al 1998)Particles were negatively charged (225 mV) at pH 68 602 and 001 M NaCl as determined from electrophoreticmobility measurements reported elsewhere (Vrijenhoeket al 2001)

Laboratory-scale crossflow membrane filters

The test apparatus was a modified version of twocommercially available stainless steel crossflow mem-brane filtration (CMF) units (Sepa CF Osmonics IncMinnetonka MN) The crossflow membrane filtrationunits are rated for operating pressures up to 6895 kPa(1000 psi) Both crossflow units have dimensions of146 and 95 cm for channel length (Lc) and width (Wc)respectively while the channel heights (Hc) are 34 mil(086 mm) and 68 mil (173 mm) respectively The twocrossflow membrane filtration units will hereafter be de-scribed simply as the ldquo34rdquo and ldquo68rdquo units thus indi-cating their respective channel heights These channeldimensions provide an effective membrane area (Am) of139 3 1022 m2 per unit and cross-sectional flow areas(Ax) of 082 3 1024 m2 for the 34 unit and 164 3 1024

m2 for the 68 unit The applied pressure (DP) was con-stant and monitored by a pressure gage (Cole-ParmerChicago IL) and flux was monitored in real time by adigital flow meter (Optiflow 1000 Humonics RanchoCordova CA) Specific modifications to the manufac-turerrsquos setup were reported elsewhere (Vrijenhoek et al2001) a schematic diagram of the experimental systemis presented in Fig 3

362 HOEK ET AL

Figure 3 Crossflow membrane filtration (CMF) apparatus used in experiments designed to simultaneously test the influenceof crossflow hydrodynamics and membrane filter geometry on colloidal fouling The two crossflow membrane filters may be fedin parallel from a common feed tank or individually

Measuring membrane hydraulic resistance

Different membrane coupons were used for each fil-tration experiment so the membrane hydraulic resis-tance was determined prior to each fouling experimentFirst deionized (DI) water was circulated at 250 psi(1724 kPa) for up to 24 h to dissociate flux decline dueto membrane compaction (and other unknown causesinherent of lab-scale recirculation systems) Flux wasmonitored continuously for the duration of the experi-ment and recorded in real time on a laboratory com-puter After DI equilibration the pressure was changedin increments of 50 psi (345 kPa) from a high of 250psi to a low of 50 psi and flux recorded at a feed flowrate of 095 liters per minute (Lpm) At each pressureflux was monitored for at least 30 min to ensure stableperformance The crossflow was then increased to 190Lpm and flux was recorded at 50 psi increments from50 to 250 psi Finally feed flow rate was set at 379Lpm and the flux was recorded at 50 psi incrementsfrom 250 psi down to 50 psi At each crossflow andpressure the average of all of the stable flux measure-ments was plotted against applied pressure The slopeof a line fitted to pure water flux vs pressure data bya least-squares linear regression provided the mem-brane hydraulic resistance As expected there was nomeasured influence of feed flow rate on pure water fluxfor any experiments but the procedure provided extradata points for the regression analysis The pH of feedwas monitored throughout the pure water flux experi-ments to ensure constant feed solution chemistry

Measuring CP modulus and initial osmoticpressure drop

After the membrane pure water hydraulic resistance(Rm) was determined concentration polarization effectscould be quantified using film-theory and the velocityvariation technique described herein An appropriatevolume of 1 M stock NaCl solution was added to thefeed tank to provide the desired experimental ionicstrength The same feed solution ionic strength (001M) was used for all filtration experiments in this studyThe sequence of varying applied pressure and feed flowrate was repeated The effective osmotic pressure dropacross the membrane (Dpm) for each velocity variationwas determined from Equation (1) with A 5 1Rm Eachcombination of pressure and flow yielded different per-meate and crossflow velocities respectively and hencethe description as the ldquovelocity variationrdquo techniqueThe experimental film-theory mass transfer coefficientwas calculated from the measured Dpm and Equation(5) and then the experimental CP modulus was calcu-lated from Equation (4) for each velocity variation The

feed solution pH was monitored throughout the salt wa-ter experiments to ensure stable feed conditions Ob-served salt rejection (Ro) was determined by measur-ing feed and permeate conductivity Conductivity wasdetermined to be linearly proportional to NaCl con-centration by performing a least-squares linear regres-sion of conductivity measurements for solutions withknown NaCl concentrations

Measuring decline in flux and salt rejection dueto colloidal fouling

After the salt water experiments were finished pres-sure and crossflow were adjusted to produce the de-sired initial flux and wall shear for the fouling exper-iment After stable performance (flux and saltrejection) was achieved for a minimum of 60 min adose of silica particles was added to the feed tank toprovide the appropriate particle feed concentrationThe concentration of 100 nm silica particles was0008 (vv) which yielded an average turbidity of532 NTU The same concentration of particles wasused in all colloidal fouling experiments performed forthis study Conductivity pH and turbidity measure-ments were made at the start end and at several pointsduring the fouling experiment to determine salt rejec-tion to ensure complete rejection of particles and toensure feed conditions were constant throughout thetest The transient flux at constant pressure was down-loaded in real time from the digital permeate flow me-ter to a laboratory computer

Measuring colloid deposit layer mass

In some experiments the mass of colloid deposit lay-ers was measured using a previously published technique(Faibish et al 1998) The feed tank volume was reducedsuch that the mass of particles dosed into the feed tankwould be measurably reduced by the mass of particlesaccumulated in the cake layer over the membrane Asmaller feed volume was used for these experiments suchthat a small but measurable decrease in feed turbidityoccurred within in the time scale of the experiment Inthese experiments only one crossflow filter was used sothat the decline in feed suspension turbidity was relatedto a single crossflow membrane filter No significant dif-ference in mass transfer parameters flux decline data orsalt rejection data was found when compared to data fromexperiments using constant feed particle concentrationfed in parallel to both crossflow membrane filters Themeasured colloid deposit layer mass was then combinedwith other relevant measured and constant parametersinto Equations (9) and (12) to determine the cake poros-ity and cake-enhanced osmotic pressure

CROSSFLOW MEMBRANE FILTER GEOMETRY 363

ENVIRON ENG SCI VOL 19 NO 6 2002

RESULTS AND DISCUSSION

Predicted and measured concentrationpolarization effects

The film-theory predicted mass transfer parameters forthe lab-scale CMF units are provided in Table 1 Thelisted volumetric feed flow rates (Q) are those used infouling experiments and the data are arranged in order of decreasing CP modulus Velocity shear rate andReynolds number all increase with increasing feed flowHowever at a given volumetric flow rate velocity is dou-bled as dh is halved so the Reynolds number is the samein either channel The wall shear rate captures both thedifference in channel geometry and crossflow and so itcan be made identical in the two units at certain cross-flow rates The mass transfer coefficients CP moduliand osmotic pressure drops predicted from the film-the-ory equations all increase in proportion to the change inshear rate again highlighting the usefulness of this pa-rameter The theoretical film layer thickness was calcu-lated from kf 5 Ddf using 1611 3 1029 m2s as the dif-fusion coefficient for NaCl and ranged from about 50 to125 mm The most important data from Table 1 are items3 and 4 The shear rate is identical so the film-theorypredicted mass transfer parameters (kf df Cm Cb andDpm) are identical

The theoretical and experimental concentration polar-ization moduli for the crossflow membrane filters areplotted against crossflow Reynolds number in Fig 4 Ex-perimentally determined salt rejection is labeled next toeach experimental data point The labels 1 to 6 corre-spond to the same item numbers in Table 1 The exper-imental osmotic pressure drop was determined at a sta-ble flux of 142 3 1025 ms (30 gfd) and combined withobserved salt rejection data in Equation (5) to calculatethe experimental mass transfer coefficient The experi-

mental CP modulus was then calculated from Equation(4) The theoretical concentration polarization modulusdata plotted in Fig 4 was calculated from Equation (4)using the experimental salt rejection values at the corre-sponding Reynolds flows and linearly interpolating (orextrapolating) salt rejection values for flow rates in be-tween (or beyond) The theoretical CP modulus was rel-atively insensitive to Ro over the range of experimentallyobserved rejection values in Fig 4 so this simple linearinterpolation should not introduce significant error

Both the predicted and experimental concentration po-larization effects are shown to be more severe in the 68unit than in the 34 unit over the entire range of flow ratesThe experimental data are in fairly good agreement withpredicted CP modulus data although the experimentaldata appear relatively flat over the range of Reynoldsnumbers This may be due in part to the fact that wall-suction (permeation) is ignored in the film-theory pre-dicted mass transfer coefficient In items 3 and 4 of Table1 the hydrodynamic conditions are predicted to yield thesame CP modulus in the two filters but experimental CPmoduli differed by about 17 This film-theory ldquoerrorrdquomay be due to entrance and side-wall effects not ac-counted for in film theory predictions as well as otherpotential unknown experimental errors

Figure 5 presents the predicted trans-cake hydraulicpressures cake-enhanced osmotic pressures and perme-ate fluxes in the 34 and 68 units for varied cake layerthickness and porosity Hydrodynamic conditions werethose described in items 1 and 4 of Table 1 Howeverbecause the mass transfer parameters are identical initems 3 and 4 the 34 unit curves displayed in Fig 5 the-oretically represent the cake-enhanced osmotic pressuresfor the 68 unit under the conditions of item 3 in Table 1

At a feed flow rate of 095 Lpm the initial trans-mem-brane osmotic pressures were about 14 and 21 psi in the

364 HOEK ET AL

Table 1 Film-theory predicted mass transfer parameters for experimental CMF units

Item CMFa Qb uc g0d Ree kf df Cm Cb

fDpm

g

no unit [Lpm] [cms] [s21] [2] [mms] [mm] [2] [psi]

1 68 095 96 334 372 13 126 30 212 68 189 192 668 745 16 100 24 173 68 379 384 1336 1489 20 79 20 144 34 095 192 1336 372 20 79 20 145 34 189 384 2671 745 26 63 17 126 34 379 769 5342 1489 32 50 15 11

Operation conditions used in the calculations are J0 5 142 3 1025 ms (30 gfd) Cb 5 001 M NaCl and Ro 5 98 aChannelheight (Hc) 5 0864 mm (34) and 173 mm (68) channel length (Lc) 5 146 mm channel width (Wc) 5 95 mm bQ 5 volumetricfeed flow rate in liters per minute (Lpm) cu 5 QAx Ax 5 channel cross-sectional area dg0 5 6uHc and is the channel wall shearrate eRe 5 udhn and is the channel crossflow Reynolds number dh 5 2Hc n 5 kinematic viscosity fconcentration polarization(CP) modulus calculated from Equation (4) geffective trans-membrane osmotic pressure calculated from Equation 5

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

serves as the starting point for the design of most mod-ern RONF separations

The rejection of ionic species results in an elevated saltconcentration near the membrane surface The high soluteconcentration at the membrane surface decays back to thebulk ionic concentration over some distance defined asthe concentration polarization (CP) layer ldquothicknessrdquo Incrossflow membrane filtration the CP layer quicklyreaches a steady state and the transverse solute fluxthrough the CP layer is constant The solvent flux (J) maythen be determined by the following one-dimensionalsteady-state mass balance across the CP layer

JC 2 D 5 JCp (2)

where C is the solute concentration D is the solute dif-fusivity Cp is the solute permeate concentration and yis the distance measured normal to and away from themembrane surface (Zydney 1997)

Integrating Equation (2) over the salt concentration po-larization layer thickness (d) with the appropriate bound-ary conditions (y 5 0 C 5 Cm y 5 d C 5 Cb) results in

J 5 ln 1 2 (3)

where Cm is the membrane surface salt concentration andCb is the bulk salt concentration This expression can berearranged to provide a direct estimation of the concen-tration polarization modulus (CmCb) from

5 (1 2 Ro) 1 Ro exp 1 2 (4)

Here Ro is the observed rejection (51 2 CpCb) and k(5Dd) is the mass transfer coefficient Alternate re-arrangement of Equation (3) allows estimation of the ef-fective trans-membrane osmotic pressure from

Dpm 5 2CbRTRo exp 1 2 (5)

where T is absolute temperature and R is the universalgas constant The constant 2 accounts for a 11 elec-trolyte solution at concentrations where vanrsquot Hoffrsquos lawis valid which is the case for the experiments performedin this investigation It is clear from Equation (5) thatDpm increases when bulk salt concentration rejectionand flux increase Further maintaining high mass trans-fer coefficient is critical for optimal operation of RONFprocesses

ldquoFilm-theoryrdquo model

Attempts to predict either the concentration polariza-tion modulus (CmCb) or the trans-membrane osmoticpressure (Dpm) have traditionally been limited to mass

Jk

Jk

CmCb

Cm 2 CpCb 2 Cp

Dd

dCdy

transfer analogies of the heat transfer correlations for de-velopment of a stagnant film layermdashsometimes referredto as ldquofilm-theoryrdquo models (Blatt et al 1970) More fun-damental models of concentration polarization exist(Song and Elimelech 1995 Elimelech and Bhattachar-jee 1998 Bhattacharjee et al 1999 2001) but film the-ory provides a simple analytical approach that works wellfor most RONF separations Therefore film theoryserves as the design basis for most modern reverse os-mosis processes

For laminar flow in a thin rectangular channel theldquofilm-theoryrdquo mass transfer coefficient (kf) may be re-lated to the Sherwood number (Sh) through the follow-ing equation

Sh 5 kf 5 162 1Re Sc 213

(6)

where Re is the Reynolds number (5udhn with u beingthe bulk crossflow velocity and n the solution kinematicviscosity) dh is the channel hydrodynamic diameter(lt2Hc with Hc being the channel height) Sc is theSchmidt number (nD) and Lc is the channel length(Porter 1972)

By expanding the individual components and rear-ranging the mass transfer coefficient is shown to dependon flow rate channel geometry and solute type via

kf 5 162 1 213

5 162 1 213

5162 1 213

(7)

Here Q is the feed flow rate Wc is the channel widthand g0 is the wall shear rate The shear rate representsthe velocity gradient (dudy) through a laminar hydrody-namic boundary layer and can be estimated directly from6QWcHc

2 in a thin rectangular channel (Davis 1992)From Equation (7) it is clear that for a given solute

mass transfer is most significantly enhanced by reducingchannel height (Hc) and to a lesser extent by increasingcrossflow It is this relationship that provides the logicalbasis for testing the relative influence of crossflow rateand channel height on colloidal fouling For this studythe preferred form of Equation (7) contains the shear rate(g0) because it captures the influences of both crossflowrate and channel height in a single term

Cake filtration model

The mechanism of flux decline associated with col-loid deposition on a membrane surface is typicallymodeled through the phenomenologic ldquocake filtrationrdquomodel which was originally developed for microfil-

g0D2

12Lc

uD2

2HcLc

QD2

2WcHc

2Lc

dbLc

dhD

CROSSFLOW MEMBRANE FILTER GEOMETRY 359

ENVIRON ENG SCI VOL 19 NO 6 2002

tration separations (Davis 1992) The transient flux isdescribed by

J(t) 5 Rm 1

DpRc(t)

(8a)

where the solvent flux J is a function of the net (or ef-fective) applied pressure Dp(5DP 2 Dpm) the mem-brane hydraulic resistance Rm (51A) and the cake layerresistance Rc (Faibish et al 1998) Flux at constant pres-sure is solely governed by the product of a constant spe-cific cake resistance (a) and transient deposit layer massper unit membrane area (Md) as

Rc(t) 5 aMd (t) 5 3 4 Md (t) (8b)

where m0 is the solvent viscosity laquo is the cake layerporosity ap is the particle radius and rp is the particledensity The specific cake resistance (the term in brack-ets) cannot be determined a priori without knowing thecake layer porosity However the following discussionleads to an analytical expression for directly estimatingcake layer porosity and cake-enhanced osmotic pressurefrom known constants and experimentally measurable pa-rameters

Cake-enhanced osmotic pressure model

In the standard cake filtration model the transientflux decline (or decline in trans-membrane pressure) isassumed to arise solely from the added hydraulic re-sistance of the cake layer However it was previouslydemonstrated that this is an unreasonable assumptionfor salt rejecting membranes because the primarymechanism of the flux decline is a transient cake-en-hanced osmotic pressure (Hoek 2002) The cake-en-hanced osmotic pressure model begins by rearrangingthe cake filtration equation into a series of pressuredrops

Dpm(t) 5 DP 2 Dpm(t) 2 Dpc(t) (9a)

where the cake-enhanced osmotic pressure is describedby

Dpm(t) 5 DP 2 J(t)Rm

2 J(t) 3 4Md (t) (9b)

The transient driving force for permeation the trans-membrane pressure (Dpm) is a function of the constantapplied pressure (DP) the transient cake-enhanced os-motic pressure (Dpm) and the transient trans-cake hy-draulic pressure (Dpc)

It is hypothesized that for thin cake layers (comparedto the film layer thickness) the cake-enhanced osmotic

45m(1 2 laquo)

rpa2plaquo3

45 m0(1 2 laquo)

rpa2plaquo

3

pressure results solely from the hindered back-diffusionof salt ions trapped within the colloid-cake layer (Hoek2002) Figure 1 illustrates this effect With no particlesdeposited (top) the solute concentration polarizationlayer quickly reaches steady state whereby solute trans-port by convection towards the membrane (minus thatwhich permeates) is balanced by solute back-transport bydiffusion As particles accumulate and form a thin cakelayer over the surface of the membrane (bottom) the dif-fusion of salt ions back into the bulk is hindered becauseof the tortuous path the ions must follow to circumnavi-gate the deposited colloids Hindered back-diffusion ofsalt ions trapped in the cake layer leads to an enhancedmembrane surface salt concentration (Cm) and thus en-hanced osmotic pressure drop across the membrane(Dpm)

The mathematical model that follows is based on threeimportant assumptions First the cake layer is thin com-pared to the salt film-layer thickness Past investigationshave shown that the tangential flow field is relatively un-affected when the cake layer is thin with respect to thechannel height (Faibish et al 1998) because the cakelayer does not occupy a significant fraction of the chan-

360 HOEK ET AL

Figure 1 Conceptual illustration of ldquocake-enhanced osmoticpressurerdquo effect In the absence of a colloid deposit layer (topfigure) the elevated concentration at the membrane surface(Cm) decays to the bulk concentration (Cb) over the salt con-centration polarization (film) layer thickness (df) The salt con-centration drops across the membrane thickness (dm) due to saltrejection For a thin deposit layer (bottom figure) the film layerthickness remains constant and the difference between df andcake thickness (dc) is ds In the presence of a colloid depositlayer the membrane surface salt concentration is enhanced(Cm) due to hindered back-diffusion of salt ions and a decreasein salt rejection results The elevated Cm will also result in el-evated permeate salt concentration Cp

nel cross section (Davis 1992) Crossflow shear rate isrelatively unaffected by the presence of the cake layerand thus the CP layer thickness remains at the film thick-ness determined prior to particle deposition Second thecolloid deposit layer does not reject salt ions so the pro-file of salt concentration above the colloid deposit layeris unchanged from that prior to cake formation Thirdthe effective diffusion coefficient for salt ions trappedwithin the colloid deposit layer can be estimated withknowledge of the cake layer porosity

A simple analytical expression for estimating the de-pendence of the hindered diffusion coefficient (D) onporosity is given by

D 5 (laquot) D (10)

where D is the solute diffusivity in the bulk laquo is theporosity and t(lt1 2 lnlaquo2) is the diffusive tortuosity(Boudreau 1996) Recent investigations have shown thatcake layer porosities for silica colloids filtered under sim-ilar physical and chemical conditions were typically inthe range of 03 to 07 (Faibish et al 1998 Yiantsiosand Karabelas 1998 Endo and Alonso 2001) The ratioof the effective diffusion coefficient to the bulk diffusioncoefficient is plotted against cake layer porosity in Fig2 Over the range of typical porosity values the effectivediffusion coefficient may be reduced to between 10 and40 of the bulk diffusion coefficient which results insignificantly enhanced salt concentration at the mem-brane surface

Next the effective mass transfer coefficient is brokendown into two partsmdashone describing mass transferthrough the colloid deposit layer and one describing masstransfer from the interface of the colloid layer back into

the bulk The resulting ldquohinderedrdquo mass transfer coeffi-cient (k) is estimated from

5 1 (11)

where dc is the colloid deposit layer thickness and ds isthe difference between the film (df) and cake layer thick-nesses Equation (11) comes directly from integratingEquation (2) separately across the cake and CP layersEven if the cake layer is very thin (dc ds) the cake-enhanced osmotic pressure may be significant becausethe hindered diffusion coefficient can be an order of mag-nitude smaller than the bulk diffusion coefficient

Because the film layer thickness was assumed con-stant the salt layer thickness over the cake is the dif-ference between the original film thickness and thecake thickness (ie ds 5 df 2 dc) Note that the cakelayer thickness can be written in terms of cake massper unit membrane area as dc 5 Md rp(1 2 laquo) (Faibishet al 1998) Rewriting Equation (11) the hinderedmass transfer coefficient expression in terms of df anddc and substituting into Equation (5) results in the fol-lowing expression for the cake-enhanced osmotic pres-sure

Dpm 5 2CbRTRo

exp3 1 1 2 24 (12)

All parameters in this equation are constant or exper-imentally measurable except cake porosity (laquo) and cake-enhanced osmotic pressure (Dpm) Setting Equation (12)equal to Equation (9b) allows direct calculation of thecake layer porosity and thus cake-enhanced osmoticpressure

MATERIALS AND METHODS

Membranes

Four commercial RONF polyamide thin-film com-posite membranes were used in this study The RO mem-branes were Hydranautics LFC1 (Oceanside CA) andTrisep X20 (Goleta CA) The NF membranes were Dow-FilmTec NF70 (Minneapolis MN) and Osmonics HL(Minnetonka MN) All membranes were stored in deion-ized water at 5degC with water replaced regularly Themembranes were characterized for relevant performanceproperties such as pure water permeability (A) and ob-served salt rejection (Ro) Salt rejection experiments wereconducted at 001 M NaCl and unadjusted pH of 68 602 which are the same feed conditions used in all foul-ing experiments All four membranes are thought to be

1D`

1 2 ln(laquo2)

D`laquo

JMd rp(1 2 laquo)

Jkf

dsD

dcD

1k

CROSSFLOW MEMBRANE FILTER GEOMETRY 361

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 2 Ratio of the cake-hindered salt diffusion coefficientto the bulk diffusion coefficient predicted by Equation (10) fora range of cake layer porosities

moderately negatively charged (215 to 225 mV) at typ-ical solution chemistries based on streaming potentialanalyses reported elsewhere (Vrijenhoek et al 2001)

Reagents and model colloids

Salt stock solutions were prepared using ACS gradeNaCl (Fisher Scientific Pittsburgh PA) dissolved indeionized water (Nanopure Infinity Ultrapure BarnsteadDubuque IA) Nissan Chemical America Corporation(Houston TX) provided the colloidal particles used inthe fouling experiments The particles were certified as010 mm (6003 mm) silica particles in an aqueous sus-pension Chemical analysis by the manufacturer indicatesthe suspension to be 407 (ww) amorphous silica witha specific gravity of 13 Based on the specific gravityand weight percent of the suspension the particle densitywas calculated to be 236 gcm3 Gravimetric analysis ofthe particle suspension revealed the particle density to be211 gcm3 which compares well with the above calcu-lation and other reported values (Faibish et al 1998)Particles were negatively charged (225 mV) at pH 68 602 and 001 M NaCl as determined from electrophoreticmobility measurements reported elsewhere (Vrijenhoeket al 2001)

Laboratory-scale crossflow membrane filters

The test apparatus was a modified version of twocommercially available stainless steel crossflow mem-brane filtration (CMF) units (Sepa CF Osmonics IncMinnetonka MN) The crossflow membrane filtrationunits are rated for operating pressures up to 6895 kPa(1000 psi) Both crossflow units have dimensions of146 and 95 cm for channel length (Lc) and width (Wc)respectively while the channel heights (Hc) are 34 mil(086 mm) and 68 mil (173 mm) respectively The twocrossflow membrane filtration units will hereafter be de-scribed simply as the ldquo34rdquo and ldquo68rdquo units thus indi-cating their respective channel heights These channeldimensions provide an effective membrane area (Am) of139 3 1022 m2 per unit and cross-sectional flow areas(Ax) of 082 3 1024 m2 for the 34 unit and 164 3 1024

m2 for the 68 unit The applied pressure (DP) was con-stant and monitored by a pressure gage (Cole-ParmerChicago IL) and flux was monitored in real time by adigital flow meter (Optiflow 1000 Humonics RanchoCordova CA) Specific modifications to the manufac-turerrsquos setup were reported elsewhere (Vrijenhoek et al2001) a schematic diagram of the experimental systemis presented in Fig 3

362 HOEK ET AL

Figure 3 Crossflow membrane filtration (CMF) apparatus used in experiments designed to simultaneously test the influenceof crossflow hydrodynamics and membrane filter geometry on colloidal fouling The two crossflow membrane filters may be fedin parallel from a common feed tank or individually

Measuring membrane hydraulic resistance

Different membrane coupons were used for each fil-tration experiment so the membrane hydraulic resis-tance was determined prior to each fouling experimentFirst deionized (DI) water was circulated at 250 psi(1724 kPa) for up to 24 h to dissociate flux decline dueto membrane compaction (and other unknown causesinherent of lab-scale recirculation systems) Flux wasmonitored continuously for the duration of the experi-ment and recorded in real time on a laboratory com-puter After DI equilibration the pressure was changedin increments of 50 psi (345 kPa) from a high of 250psi to a low of 50 psi and flux recorded at a feed flowrate of 095 liters per minute (Lpm) At each pressureflux was monitored for at least 30 min to ensure stableperformance The crossflow was then increased to 190Lpm and flux was recorded at 50 psi increments from50 to 250 psi Finally feed flow rate was set at 379Lpm and the flux was recorded at 50 psi incrementsfrom 250 psi down to 50 psi At each crossflow andpressure the average of all of the stable flux measure-ments was plotted against applied pressure The slopeof a line fitted to pure water flux vs pressure data bya least-squares linear regression provided the mem-brane hydraulic resistance As expected there was nomeasured influence of feed flow rate on pure water fluxfor any experiments but the procedure provided extradata points for the regression analysis The pH of feedwas monitored throughout the pure water flux experi-ments to ensure constant feed solution chemistry

Measuring CP modulus and initial osmoticpressure drop

After the membrane pure water hydraulic resistance(Rm) was determined concentration polarization effectscould be quantified using film-theory and the velocityvariation technique described herein An appropriatevolume of 1 M stock NaCl solution was added to thefeed tank to provide the desired experimental ionicstrength The same feed solution ionic strength (001M) was used for all filtration experiments in this studyThe sequence of varying applied pressure and feed flowrate was repeated The effective osmotic pressure dropacross the membrane (Dpm) for each velocity variationwas determined from Equation (1) with A 5 1Rm Eachcombination of pressure and flow yielded different per-meate and crossflow velocities respectively and hencethe description as the ldquovelocity variationrdquo techniqueThe experimental film-theory mass transfer coefficientwas calculated from the measured Dpm and Equation(5) and then the experimental CP modulus was calcu-lated from Equation (4) for each velocity variation The

feed solution pH was monitored throughout the salt wa-ter experiments to ensure stable feed conditions Ob-served salt rejection (Ro) was determined by measur-ing feed and permeate conductivity Conductivity wasdetermined to be linearly proportional to NaCl con-centration by performing a least-squares linear regres-sion of conductivity measurements for solutions withknown NaCl concentrations

Measuring decline in flux and salt rejection dueto colloidal fouling

After the salt water experiments were finished pres-sure and crossflow were adjusted to produce the de-sired initial flux and wall shear for the fouling exper-iment After stable performance (flux and saltrejection) was achieved for a minimum of 60 min adose of silica particles was added to the feed tank toprovide the appropriate particle feed concentrationThe concentration of 100 nm silica particles was0008 (vv) which yielded an average turbidity of532 NTU The same concentration of particles wasused in all colloidal fouling experiments performed forthis study Conductivity pH and turbidity measure-ments were made at the start end and at several pointsduring the fouling experiment to determine salt rejec-tion to ensure complete rejection of particles and toensure feed conditions were constant throughout thetest The transient flux at constant pressure was down-loaded in real time from the digital permeate flow me-ter to a laboratory computer

Measuring colloid deposit layer mass

In some experiments the mass of colloid deposit lay-ers was measured using a previously published technique(Faibish et al 1998) The feed tank volume was reducedsuch that the mass of particles dosed into the feed tankwould be measurably reduced by the mass of particlesaccumulated in the cake layer over the membrane Asmaller feed volume was used for these experiments suchthat a small but measurable decrease in feed turbidityoccurred within in the time scale of the experiment Inthese experiments only one crossflow filter was used sothat the decline in feed suspension turbidity was relatedto a single crossflow membrane filter No significant dif-ference in mass transfer parameters flux decline data orsalt rejection data was found when compared to data fromexperiments using constant feed particle concentrationfed in parallel to both crossflow membrane filters Themeasured colloid deposit layer mass was then combinedwith other relevant measured and constant parametersinto Equations (9) and (12) to determine the cake poros-ity and cake-enhanced osmotic pressure

CROSSFLOW MEMBRANE FILTER GEOMETRY 363

ENVIRON ENG SCI VOL 19 NO 6 2002

RESULTS AND DISCUSSION

Predicted and measured concentrationpolarization effects

The film-theory predicted mass transfer parameters forthe lab-scale CMF units are provided in Table 1 Thelisted volumetric feed flow rates (Q) are those used infouling experiments and the data are arranged in order of decreasing CP modulus Velocity shear rate andReynolds number all increase with increasing feed flowHowever at a given volumetric flow rate velocity is dou-bled as dh is halved so the Reynolds number is the samein either channel The wall shear rate captures both thedifference in channel geometry and crossflow and so itcan be made identical in the two units at certain cross-flow rates The mass transfer coefficients CP moduliand osmotic pressure drops predicted from the film-the-ory equations all increase in proportion to the change inshear rate again highlighting the usefulness of this pa-rameter The theoretical film layer thickness was calcu-lated from kf 5 Ddf using 1611 3 1029 m2s as the dif-fusion coefficient for NaCl and ranged from about 50 to125 mm The most important data from Table 1 are items3 and 4 The shear rate is identical so the film-theorypredicted mass transfer parameters (kf df Cm Cb andDpm) are identical

The theoretical and experimental concentration polar-ization moduli for the crossflow membrane filters areplotted against crossflow Reynolds number in Fig 4 Ex-perimentally determined salt rejection is labeled next toeach experimental data point The labels 1 to 6 corre-spond to the same item numbers in Table 1 The exper-imental osmotic pressure drop was determined at a sta-ble flux of 142 3 1025 ms (30 gfd) and combined withobserved salt rejection data in Equation (5) to calculatethe experimental mass transfer coefficient The experi-

mental CP modulus was then calculated from Equation(4) The theoretical concentration polarization modulusdata plotted in Fig 4 was calculated from Equation (4)using the experimental salt rejection values at the corre-sponding Reynolds flows and linearly interpolating (orextrapolating) salt rejection values for flow rates in be-tween (or beyond) The theoretical CP modulus was rel-atively insensitive to Ro over the range of experimentallyobserved rejection values in Fig 4 so this simple linearinterpolation should not introduce significant error

Both the predicted and experimental concentration po-larization effects are shown to be more severe in the 68unit than in the 34 unit over the entire range of flow ratesThe experimental data are in fairly good agreement withpredicted CP modulus data although the experimentaldata appear relatively flat over the range of Reynoldsnumbers This may be due in part to the fact that wall-suction (permeation) is ignored in the film-theory pre-dicted mass transfer coefficient In items 3 and 4 of Table1 the hydrodynamic conditions are predicted to yield thesame CP modulus in the two filters but experimental CPmoduli differed by about 17 This film-theory ldquoerrorrdquomay be due to entrance and side-wall effects not ac-counted for in film theory predictions as well as otherpotential unknown experimental errors

Figure 5 presents the predicted trans-cake hydraulicpressures cake-enhanced osmotic pressures and perme-ate fluxes in the 34 and 68 units for varied cake layerthickness and porosity Hydrodynamic conditions werethose described in items 1 and 4 of Table 1 Howeverbecause the mass transfer parameters are identical initems 3 and 4 the 34 unit curves displayed in Fig 5 the-oretically represent the cake-enhanced osmotic pressuresfor the 68 unit under the conditions of item 3 in Table 1

At a feed flow rate of 095 Lpm the initial trans-mem-brane osmotic pressures were about 14 and 21 psi in the

364 HOEK ET AL

Table 1 Film-theory predicted mass transfer parameters for experimental CMF units

Item CMFa Qb uc g0d Ree kf df Cm Cb

fDpm

g

no unit [Lpm] [cms] [s21] [2] [mms] [mm] [2] [psi]

1 68 095 96 334 372 13 126 30 212 68 189 192 668 745 16 100 24 173 68 379 384 1336 1489 20 79 20 144 34 095 192 1336 372 20 79 20 145 34 189 384 2671 745 26 63 17 126 34 379 769 5342 1489 32 50 15 11

Operation conditions used in the calculations are J0 5 142 3 1025 ms (30 gfd) Cb 5 001 M NaCl and Ro 5 98 aChannelheight (Hc) 5 0864 mm (34) and 173 mm (68) channel length (Lc) 5 146 mm channel width (Wc) 5 95 mm bQ 5 volumetricfeed flow rate in liters per minute (Lpm) cu 5 QAx Ax 5 channel cross-sectional area dg0 5 6uHc and is the channel wall shearrate eRe 5 udhn and is the channel crossflow Reynolds number dh 5 2Hc n 5 kinematic viscosity fconcentration polarization(CP) modulus calculated from Equation (4) geffective trans-membrane osmotic pressure calculated from Equation 5

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

tration separations (Davis 1992) The transient flux isdescribed by

J(t) 5 Rm 1

DpRc(t)

(8a)

where the solvent flux J is a function of the net (or ef-fective) applied pressure Dp(5DP 2 Dpm) the mem-brane hydraulic resistance Rm (51A) and the cake layerresistance Rc (Faibish et al 1998) Flux at constant pres-sure is solely governed by the product of a constant spe-cific cake resistance (a) and transient deposit layer massper unit membrane area (Md) as

Rc(t) 5 aMd (t) 5 3 4 Md (t) (8b)

where m0 is the solvent viscosity laquo is the cake layerporosity ap is the particle radius and rp is the particledensity The specific cake resistance (the term in brack-ets) cannot be determined a priori without knowing thecake layer porosity However the following discussionleads to an analytical expression for directly estimatingcake layer porosity and cake-enhanced osmotic pressurefrom known constants and experimentally measurable pa-rameters

Cake-enhanced osmotic pressure model

In the standard cake filtration model the transientflux decline (or decline in trans-membrane pressure) isassumed to arise solely from the added hydraulic re-sistance of the cake layer However it was previouslydemonstrated that this is an unreasonable assumptionfor salt rejecting membranes because the primarymechanism of the flux decline is a transient cake-en-hanced osmotic pressure (Hoek 2002) The cake-en-hanced osmotic pressure model begins by rearrangingthe cake filtration equation into a series of pressuredrops

Dpm(t) 5 DP 2 Dpm(t) 2 Dpc(t) (9a)

where the cake-enhanced osmotic pressure is describedby

Dpm(t) 5 DP 2 J(t)Rm

2 J(t) 3 4Md (t) (9b)

The transient driving force for permeation the trans-membrane pressure (Dpm) is a function of the constantapplied pressure (DP) the transient cake-enhanced os-motic pressure (Dpm) and the transient trans-cake hy-draulic pressure (Dpc)

It is hypothesized that for thin cake layers (comparedto the film layer thickness) the cake-enhanced osmotic

45m(1 2 laquo)

rpa2plaquo3

45 m0(1 2 laquo)

rpa2plaquo

3

pressure results solely from the hindered back-diffusionof salt ions trapped within the colloid-cake layer (Hoek2002) Figure 1 illustrates this effect With no particlesdeposited (top) the solute concentration polarizationlayer quickly reaches steady state whereby solute trans-port by convection towards the membrane (minus thatwhich permeates) is balanced by solute back-transport bydiffusion As particles accumulate and form a thin cakelayer over the surface of the membrane (bottom) the dif-fusion of salt ions back into the bulk is hindered becauseof the tortuous path the ions must follow to circumnavi-gate the deposited colloids Hindered back-diffusion ofsalt ions trapped in the cake layer leads to an enhancedmembrane surface salt concentration (Cm) and thus en-hanced osmotic pressure drop across the membrane(Dpm)

The mathematical model that follows is based on threeimportant assumptions First the cake layer is thin com-pared to the salt film-layer thickness Past investigationshave shown that the tangential flow field is relatively un-affected when the cake layer is thin with respect to thechannel height (Faibish et al 1998) because the cakelayer does not occupy a significant fraction of the chan-

360 HOEK ET AL

Figure 1 Conceptual illustration of ldquocake-enhanced osmoticpressurerdquo effect In the absence of a colloid deposit layer (topfigure) the elevated concentration at the membrane surface(Cm) decays to the bulk concentration (Cb) over the salt con-centration polarization (film) layer thickness (df) The salt con-centration drops across the membrane thickness (dm) due to saltrejection For a thin deposit layer (bottom figure) the film layerthickness remains constant and the difference between df andcake thickness (dc) is ds In the presence of a colloid depositlayer the membrane surface salt concentration is enhanced(Cm) due to hindered back-diffusion of salt ions and a decreasein salt rejection results The elevated Cm will also result in el-evated permeate salt concentration Cp

nel cross section (Davis 1992) Crossflow shear rate isrelatively unaffected by the presence of the cake layerand thus the CP layer thickness remains at the film thick-ness determined prior to particle deposition Second thecolloid deposit layer does not reject salt ions so the pro-file of salt concentration above the colloid deposit layeris unchanged from that prior to cake formation Thirdthe effective diffusion coefficient for salt ions trappedwithin the colloid deposit layer can be estimated withknowledge of the cake layer porosity

A simple analytical expression for estimating the de-pendence of the hindered diffusion coefficient (D) onporosity is given by

D 5 (laquot) D (10)

where D is the solute diffusivity in the bulk laquo is theporosity and t(lt1 2 lnlaquo2) is the diffusive tortuosity(Boudreau 1996) Recent investigations have shown thatcake layer porosities for silica colloids filtered under sim-ilar physical and chemical conditions were typically inthe range of 03 to 07 (Faibish et al 1998 Yiantsiosand Karabelas 1998 Endo and Alonso 2001) The ratioof the effective diffusion coefficient to the bulk diffusioncoefficient is plotted against cake layer porosity in Fig2 Over the range of typical porosity values the effectivediffusion coefficient may be reduced to between 10 and40 of the bulk diffusion coefficient which results insignificantly enhanced salt concentration at the mem-brane surface

Next the effective mass transfer coefficient is brokendown into two partsmdashone describing mass transferthrough the colloid deposit layer and one describing masstransfer from the interface of the colloid layer back into

the bulk The resulting ldquohinderedrdquo mass transfer coeffi-cient (k) is estimated from

5 1 (11)

where dc is the colloid deposit layer thickness and ds isthe difference between the film (df) and cake layer thick-nesses Equation (11) comes directly from integratingEquation (2) separately across the cake and CP layersEven if the cake layer is very thin (dc ds) the cake-enhanced osmotic pressure may be significant becausethe hindered diffusion coefficient can be an order of mag-nitude smaller than the bulk diffusion coefficient

Because the film layer thickness was assumed con-stant the salt layer thickness over the cake is the dif-ference between the original film thickness and thecake thickness (ie ds 5 df 2 dc) Note that the cakelayer thickness can be written in terms of cake massper unit membrane area as dc 5 Md rp(1 2 laquo) (Faibishet al 1998) Rewriting Equation (11) the hinderedmass transfer coefficient expression in terms of df anddc and substituting into Equation (5) results in the fol-lowing expression for the cake-enhanced osmotic pres-sure

Dpm 5 2CbRTRo

exp3 1 1 2 24 (12)

All parameters in this equation are constant or exper-imentally measurable except cake porosity (laquo) and cake-enhanced osmotic pressure (Dpm) Setting Equation (12)equal to Equation (9b) allows direct calculation of thecake layer porosity and thus cake-enhanced osmoticpressure

MATERIALS AND METHODS

Membranes

Four commercial RONF polyamide thin-film com-posite membranes were used in this study The RO mem-branes were Hydranautics LFC1 (Oceanside CA) andTrisep X20 (Goleta CA) The NF membranes were Dow-FilmTec NF70 (Minneapolis MN) and Osmonics HL(Minnetonka MN) All membranes were stored in deion-ized water at 5degC with water replaced regularly Themembranes were characterized for relevant performanceproperties such as pure water permeability (A) and ob-served salt rejection (Ro) Salt rejection experiments wereconducted at 001 M NaCl and unadjusted pH of 68 602 which are the same feed conditions used in all foul-ing experiments All four membranes are thought to be

1D`

1 2 ln(laquo2)

D`laquo

JMd rp(1 2 laquo)

Jkf

dsD

dcD

1k

CROSSFLOW MEMBRANE FILTER GEOMETRY 361

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 2 Ratio of the cake-hindered salt diffusion coefficientto the bulk diffusion coefficient predicted by Equation (10) fora range of cake layer porosities

moderately negatively charged (215 to 225 mV) at typ-ical solution chemistries based on streaming potentialanalyses reported elsewhere (Vrijenhoek et al 2001)

Reagents and model colloids

Salt stock solutions were prepared using ACS gradeNaCl (Fisher Scientific Pittsburgh PA) dissolved indeionized water (Nanopure Infinity Ultrapure BarnsteadDubuque IA) Nissan Chemical America Corporation(Houston TX) provided the colloidal particles used inthe fouling experiments The particles were certified as010 mm (6003 mm) silica particles in an aqueous sus-pension Chemical analysis by the manufacturer indicatesthe suspension to be 407 (ww) amorphous silica witha specific gravity of 13 Based on the specific gravityand weight percent of the suspension the particle densitywas calculated to be 236 gcm3 Gravimetric analysis ofthe particle suspension revealed the particle density to be211 gcm3 which compares well with the above calcu-lation and other reported values (Faibish et al 1998)Particles were negatively charged (225 mV) at pH 68 602 and 001 M NaCl as determined from electrophoreticmobility measurements reported elsewhere (Vrijenhoeket al 2001)

Laboratory-scale crossflow membrane filters

The test apparatus was a modified version of twocommercially available stainless steel crossflow mem-brane filtration (CMF) units (Sepa CF Osmonics IncMinnetonka MN) The crossflow membrane filtrationunits are rated for operating pressures up to 6895 kPa(1000 psi) Both crossflow units have dimensions of146 and 95 cm for channel length (Lc) and width (Wc)respectively while the channel heights (Hc) are 34 mil(086 mm) and 68 mil (173 mm) respectively The twocrossflow membrane filtration units will hereafter be de-scribed simply as the ldquo34rdquo and ldquo68rdquo units thus indi-cating their respective channel heights These channeldimensions provide an effective membrane area (Am) of139 3 1022 m2 per unit and cross-sectional flow areas(Ax) of 082 3 1024 m2 for the 34 unit and 164 3 1024

m2 for the 68 unit The applied pressure (DP) was con-stant and monitored by a pressure gage (Cole-ParmerChicago IL) and flux was monitored in real time by adigital flow meter (Optiflow 1000 Humonics RanchoCordova CA) Specific modifications to the manufac-turerrsquos setup were reported elsewhere (Vrijenhoek et al2001) a schematic diagram of the experimental systemis presented in Fig 3

362 HOEK ET AL

Figure 3 Crossflow membrane filtration (CMF) apparatus used in experiments designed to simultaneously test the influenceof crossflow hydrodynamics and membrane filter geometry on colloidal fouling The two crossflow membrane filters may be fedin parallel from a common feed tank or individually

Measuring membrane hydraulic resistance

Different membrane coupons were used for each fil-tration experiment so the membrane hydraulic resis-tance was determined prior to each fouling experimentFirst deionized (DI) water was circulated at 250 psi(1724 kPa) for up to 24 h to dissociate flux decline dueto membrane compaction (and other unknown causesinherent of lab-scale recirculation systems) Flux wasmonitored continuously for the duration of the experi-ment and recorded in real time on a laboratory com-puter After DI equilibration the pressure was changedin increments of 50 psi (345 kPa) from a high of 250psi to a low of 50 psi and flux recorded at a feed flowrate of 095 liters per minute (Lpm) At each pressureflux was monitored for at least 30 min to ensure stableperformance The crossflow was then increased to 190Lpm and flux was recorded at 50 psi increments from50 to 250 psi Finally feed flow rate was set at 379Lpm and the flux was recorded at 50 psi incrementsfrom 250 psi down to 50 psi At each crossflow andpressure the average of all of the stable flux measure-ments was plotted against applied pressure The slopeof a line fitted to pure water flux vs pressure data bya least-squares linear regression provided the mem-brane hydraulic resistance As expected there was nomeasured influence of feed flow rate on pure water fluxfor any experiments but the procedure provided extradata points for the regression analysis The pH of feedwas monitored throughout the pure water flux experi-ments to ensure constant feed solution chemistry

Measuring CP modulus and initial osmoticpressure drop

After the membrane pure water hydraulic resistance(Rm) was determined concentration polarization effectscould be quantified using film-theory and the velocityvariation technique described herein An appropriatevolume of 1 M stock NaCl solution was added to thefeed tank to provide the desired experimental ionicstrength The same feed solution ionic strength (001M) was used for all filtration experiments in this studyThe sequence of varying applied pressure and feed flowrate was repeated The effective osmotic pressure dropacross the membrane (Dpm) for each velocity variationwas determined from Equation (1) with A 5 1Rm Eachcombination of pressure and flow yielded different per-meate and crossflow velocities respectively and hencethe description as the ldquovelocity variationrdquo techniqueThe experimental film-theory mass transfer coefficientwas calculated from the measured Dpm and Equation(5) and then the experimental CP modulus was calcu-lated from Equation (4) for each velocity variation The

feed solution pH was monitored throughout the salt wa-ter experiments to ensure stable feed conditions Ob-served salt rejection (Ro) was determined by measur-ing feed and permeate conductivity Conductivity wasdetermined to be linearly proportional to NaCl con-centration by performing a least-squares linear regres-sion of conductivity measurements for solutions withknown NaCl concentrations

Measuring decline in flux and salt rejection dueto colloidal fouling

After the salt water experiments were finished pres-sure and crossflow were adjusted to produce the de-sired initial flux and wall shear for the fouling exper-iment After stable performance (flux and saltrejection) was achieved for a minimum of 60 min adose of silica particles was added to the feed tank toprovide the appropriate particle feed concentrationThe concentration of 100 nm silica particles was0008 (vv) which yielded an average turbidity of532 NTU The same concentration of particles wasused in all colloidal fouling experiments performed forthis study Conductivity pH and turbidity measure-ments were made at the start end and at several pointsduring the fouling experiment to determine salt rejec-tion to ensure complete rejection of particles and toensure feed conditions were constant throughout thetest The transient flux at constant pressure was down-loaded in real time from the digital permeate flow me-ter to a laboratory computer

Measuring colloid deposit layer mass

In some experiments the mass of colloid deposit lay-ers was measured using a previously published technique(Faibish et al 1998) The feed tank volume was reducedsuch that the mass of particles dosed into the feed tankwould be measurably reduced by the mass of particlesaccumulated in the cake layer over the membrane Asmaller feed volume was used for these experiments suchthat a small but measurable decrease in feed turbidityoccurred within in the time scale of the experiment Inthese experiments only one crossflow filter was used sothat the decline in feed suspension turbidity was relatedto a single crossflow membrane filter No significant dif-ference in mass transfer parameters flux decline data orsalt rejection data was found when compared to data fromexperiments using constant feed particle concentrationfed in parallel to both crossflow membrane filters Themeasured colloid deposit layer mass was then combinedwith other relevant measured and constant parametersinto Equations (9) and (12) to determine the cake poros-ity and cake-enhanced osmotic pressure

CROSSFLOW MEMBRANE FILTER GEOMETRY 363

ENVIRON ENG SCI VOL 19 NO 6 2002

RESULTS AND DISCUSSION

Predicted and measured concentrationpolarization effects

The film-theory predicted mass transfer parameters forthe lab-scale CMF units are provided in Table 1 Thelisted volumetric feed flow rates (Q) are those used infouling experiments and the data are arranged in order of decreasing CP modulus Velocity shear rate andReynolds number all increase with increasing feed flowHowever at a given volumetric flow rate velocity is dou-bled as dh is halved so the Reynolds number is the samein either channel The wall shear rate captures both thedifference in channel geometry and crossflow and so itcan be made identical in the two units at certain cross-flow rates The mass transfer coefficients CP moduliand osmotic pressure drops predicted from the film-the-ory equations all increase in proportion to the change inshear rate again highlighting the usefulness of this pa-rameter The theoretical film layer thickness was calcu-lated from kf 5 Ddf using 1611 3 1029 m2s as the dif-fusion coefficient for NaCl and ranged from about 50 to125 mm The most important data from Table 1 are items3 and 4 The shear rate is identical so the film-theorypredicted mass transfer parameters (kf df Cm Cb andDpm) are identical

The theoretical and experimental concentration polar-ization moduli for the crossflow membrane filters areplotted against crossflow Reynolds number in Fig 4 Ex-perimentally determined salt rejection is labeled next toeach experimental data point The labels 1 to 6 corre-spond to the same item numbers in Table 1 The exper-imental osmotic pressure drop was determined at a sta-ble flux of 142 3 1025 ms (30 gfd) and combined withobserved salt rejection data in Equation (5) to calculatethe experimental mass transfer coefficient The experi-

mental CP modulus was then calculated from Equation(4) The theoretical concentration polarization modulusdata plotted in Fig 4 was calculated from Equation (4)using the experimental salt rejection values at the corre-sponding Reynolds flows and linearly interpolating (orextrapolating) salt rejection values for flow rates in be-tween (or beyond) The theoretical CP modulus was rel-atively insensitive to Ro over the range of experimentallyobserved rejection values in Fig 4 so this simple linearinterpolation should not introduce significant error

Both the predicted and experimental concentration po-larization effects are shown to be more severe in the 68unit than in the 34 unit over the entire range of flow ratesThe experimental data are in fairly good agreement withpredicted CP modulus data although the experimentaldata appear relatively flat over the range of Reynoldsnumbers This may be due in part to the fact that wall-suction (permeation) is ignored in the film-theory pre-dicted mass transfer coefficient In items 3 and 4 of Table1 the hydrodynamic conditions are predicted to yield thesame CP modulus in the two filters but experimental CPmoduli differed by about 17 This film-theory ldquoerrorrdquomay be due to entrance and side-wall effects not ac-counted for in film theory predictions as well as otherpotential unknown experimental errors

Figure 5 presents the predicted trans-cake hydraulicpressures cake-enhanced osmotic pressures and perme-ate fluxes in the 34 and 68 units for varied cake layerthickness and porosity Hydrodynamic conditions werethose described in items 1 and 4 of Table 1 Howeverbecause the mass transfer parameters are identical initems 3 and 4 the 34 unit curves displayed in Fig 5 the-oretically represent the cake-enhanced osmotic pressuresfor the 68 unit under the conditions of item 3 in Table 1

At a feed flow rate of 095 Lpm the initial trans-mem-brane osmotic pressures were about 14 and 21 psi in the

364 HOEK ET AL

Table 1 Film-theory predicted mass transfer parameters for experimental CMF units

Item CMFa Qb uc g0d Ree kf df Cm Cb

fDpm

g

no unit [Lpm] [cms] [s21] [2] [mms] [mm] [2] [psi]

1 68 095 96 334 372 13 126 30 212 68 189 192 668 745 16 100 24 173 68 379 384 1336 1489 20 79 20 144 34 095 192 1336 372 20 79 20 145 34 189 384 2671 745 26 63 17 126 34 379 769 5342 1489 32 50 15 11

Operation conditions used in the calculations are J0 5 142 3 1025 ms (30 gfd) Cb 5 001 M NaCl and Ro 5 98 aChannelheight (Hc) 5 0864 mm (34) and 173 mm (68) channel length (Lc) 5 146 mm channel width (Wc) 5 95 mm bQ 5 volumetricfeed flow rate in liters per minute (Lpm) cu 5 QAx Ax 5 channel cross-sectional area dg0 5 6uHc and is the channel wall shearrate eRe 5 udhn and is the channel crossflow Reynolds number dh 5 2Hc n 5 kinematic viscosity fconcentration polarization(CP) modulus calculated from Equation (4) geffective trans-membrane osmotic pressure calculated from Equation 5

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

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BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

nel cross section (Davis 1992) Crossflow shear rate isrelatively unaffected by the presence of the cake layerand thus the CP layer thickness remains at the film thick-ness determined prior to particle deposition Second thecolloid deposit layer does not reject salt ions so the pro-file of salt concentration above the colloid deposit layeris unchanged from that prior to cake formation Thirdthe effective diffusion coefficient for salt ions trappedwithin the colloid deposit layer can be estimated withknowledge of the cake layer porosity

A simple analytical expression for estimating the de-pendence of the hindered diffusion coefficient (D) onporosity is given by

D 5 (laquot) D (10)

where D is the solute diffusivity in the bulk laquo is theporosity and t(lt1 2 lnlaquo2) is the diffusive tortuosity(Boudreau 1996) Recent investigations have shown thatcake layer porosities for silica colloids filtered under sim-ilar physical and chemical conditions were typically inthe range of 03 to 07 (Faibish et al 1998 Yiantsiosand Karabelas 1998 Endo and Alonso 2001) The ratioof the effective diffusion coefficient to the bulk diffusioncoefficient is plotted against cake layer porosity in Fig2 Over the range of typical porosity values the effectivediffusion coefficient may be reduced to between 10 and40 of the bulk diffusion coefficient which results insignificantly enhanced salt concentration at the mem-brane surface

Next the effective mass transfer coefficient is brokendown into two partsmdashone describing mass transferthrough the colloid deposit layer and one describing masstransfer from the interface of the colloid layer back into

the bulk The resulting ldquohinderedrdquo mass transfer coeffi-cient (k) is estimated from

5 1 (11)

where dc is the colloid deposit layer thickness and ds isthe difference between the film (df) and cake layer thick-nesses Equation (11) comes directly from integratingEquation (2) separately across the cake and CP layersEven if the cake layer is very thin (dc ds) the cake-enhanced osmotic pressure may be significant becausethe hindered diffusion coefficient can be an order of mag-nitude smaller than the bulk diffusion coefficient

Because the film layer thickness was assumed con-stant the salt layer thickness over the cake is the dif-ference between the original film thickness and thecake thickness (ie ds 5 df 2 dc) Note that the cakelayer thickness can be written in terms of cake massper unit membrane area as dc 5 Md rp(1 2 laquo) (Faibishet al 1998) Rewriting Equation (11) the hinderedmass transfer coefficient expression in terms of df anddc and substituting into Equation (5) results in the fol-lowing expression for the cake-enhanced osmotic pres-sure

Dpm 5 2CbRTRo

exp3 1 1 2 24 (12)

All parameters in this equation are constant or exper-imentally measurable except cake porosity (laquo) and cake-enhanced osmotic pressure (Dpm) Setting Equation (12)equal to Equation (9b) allows direct calculation of thecake layer porosity and thus cake-enhanced osmoticpressure

MATERIALS AND METHODS

Membranes

Four commercial RONF polyamide thin-film com-posite membranes were used in this study The RO mem-branes were Hydranautics LFC1 (Oceanside CA) andTrisep X20 (Goleta CA) The NF membranes were Dow-FilmTec NF70 (Minneapolis MN) and Osmonics HL(Minnetonka MN) All membranes were stored in deion-ized water at 5degC with water replaced regularly Themembranes were characterized for relevant performanceproperties such as pure water permeability (A) and ob-served salt rejection (Ro) Salt rejection experiments wereconducted at 001 M NaCl and unadjusted pH of 68 602 which are the same feed conditions used in all foul-ing experiments All four membranes are thought to be

1D`

1 2 ln(laquo2)

D`laquo

JMd rp(1 2 laquo)

Jkf

dsD

dcD

1k

CROSSFLOW MEMBRANE FILTER GEOMETRY 361

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 2 Ratio of the cake-hindered salt diffusion coefficientto the bulk diffusion coefficient predicted by Equation (10) fora range of cake layer porosities

moderately negatively charged (215 to 225 mV) at typ-ical solution chemistries based on streaming potentialanalyses reported elsewhere (Vrijenhoek et al 2001)

Reagents and model colloids

Salt stock solutions were prepared using ACS gradeNaCl (Fisher Scientific Pittsburgh PA) dissolved indeionized water (Nanopure Infinity Ultrapure BarnsteadDubuque IA) Nissan Chemical America Corporation(Houston TX) provided the colloidal particles used inthe fouling experiments The particles were certified as010 mm (6003 mm) silica particles in an aqueous sus-pension Chemical analysis by the manufacturer indicatesthe suspension to be 407 (ww) amorphous silica witha specific gravity of 13 Based on the specific gravityand weight percent of the suspension the particle densitywas calculated to be 236 gcm3 Gravimetric analysis ofthe particle suspension revealed the particle density to be211 gcm3 which compares well with the above calcu-lation and other reported values (Faibish et al 1998)Particles were negatively charged (225 mV) at pH 68 602 and 001 M NaCl as determined from electrophoreticmobility measurements reported elsewhere (Vrijenhoeket al 2001)

Laboratory-scale crossflow membrane filters

The test apparatus was a modified version of twocommercially available stainless steel crossflow mem-brane filtration (CMF) units (Sepa CF Osmonics IncMinnetonka MN) The crossflow membrane filtrationunits are rated for operating pressures up to 6895 kPa(1000 psi) Both crossflow units have dimensions of146 and 95 cm for channel length (Lc) and width (Wc)respectively while the channel heights (Hc) are 34 mil(086 mm) and 68 mil (173 mm) respectively The twocrossflow membrane filtration units will hereafter be de-scribed simply as the ldquo34rdquo and ldquo68rdquo units thus indi-cating their respective channel heights These channeldimensions provide an effective membrane area (Am) of139 3 1022 m2 per unit and cross-sectional flow areas(Ax) of 082 3 1024 m2 for the 34 unit and 164 3 1024

m2 for the 68 unit The applied pressure (DP) was con-stant and monitored by a pressure gage (Cole-ParmerChicago IL) and flux was monitored in real time by adigital flow meter (Optiflow 1000 Humonics RanchoCordova CA) Specific modifications to the manufac-turerrsquos setup were reported elsewhere (Vrijenhoek et al2001) a schematic diagram of the experimental systemis presented in Fig 3

362 HOEK ET AL

Figure 3 Crossflow membrane filtration (CMF) apparatus used in experiments designed to simultaneously test the influenceof crossflow hydrodynamics and membrane filter geometry on colloidal fouling The two crossflow membrane filters may be fedin parallel from a common feed tank or individually

Measuring membrane hydraulic resistance

Different membrane coupons were used for each fil-tration experiment so the membrane hydraulic resis-tance was determined prior to each fouling experimentFirst deionized (DI) water was circulated at 250 psi(1724 kPa) for up to 24 h to dissociate flux decline dueto membrane compaction (and other unknown causesinherent of lab-scale recirculation systems) Flux wasmonitored continuously for the duration of the experi-ment and recorded in real time on a laboratory com-puter After DI equilibration the pressure was changedin increments of 50 psi (345 kPa) from a high of 250psi to a low of 50 psi and flux recorded at a feed flowrate of 095 liters per minute (Lpm) At each pressureflux was monitored for at least 30 min to ensure stableperformance The crossflow was then increased to 190Lpm and flux was recorded at 50 psi increments from50 to 250 psi Finally feed flow rate was set at 379Lpm and the flux was recorded at 50 psi incrementsfrom 250 psi down to 50 psi At each crossflow andpressure the average of all of the stable flux measure-ments was plotted against applied pressure The slopeof a line fitted to pure water flux vs pressure data bya least-squares linear regression provided the mem-brane hydraulic resistance As expected there was nomeasured influence of feed flow rate on pure water fluxfor any experiments but the procedure provided extradata points for the regression analysis The pH of feedwas monitored throughout the pure water flux experi-ments to ensure constant feed solution chemistry

Measuring CP modulus and initial osmoticpressure drop

After the membrane pure water hydraulic resistance(Rm) was determined concentration polarization effectscould be quantified using film-theory and the velocityvariation technique described herein An appropriatevolume of 1 M stock NaCl solution was added to thefeed tank to provide the desired experimental ionicstrength The same feed solution ionic strength (001M) was used for all filtration experiments in this studyThe sequence of varying applied pressure and feed flowrate was repeated The effective osmotic pressure dropacross the membrane (Dpm) for each velocity variationwas determined from Equation (1) with A 5 1Rm Eachcombination of pressure and flow yielded different per-meate and crossflow velocities respectively and hencethe description as the ldquovelocity variationrdquo techniqueThe experimental film-theory mass transfer coefficientwas calculated from the measured Dpm and Equation(5) and then the experimental CP modulus was calcu-lated from Equation (4) for each velocity variation The

feed solution pH was monitored throughout the salt wa-ter experiments to ensure stable feed conditions Ob-served salt rejection (Ro) was determined by measur-ing feed and permeate conductivity Conductivity wasdetermined to be linearly proportional to NaCl con-centration by performing a least-squares linear regres-sion of conductivity measurements for solutions withknown NaCl concentrations

Measuring decline in flux and salt rejection dueto colloidal fouling

After the salt water experiments were finished pres-sure and crossflow were adjusted to produce the de-sired initial flux and wall shear for the fouling exper-iment After stable performance (flux and saltrejection) was achieved for a minimum of 60 min adose of silica particles was added to the feed tank toprovide the appropriate particle feed concentrationThe concentration of 100 nm silica particles was0008 (vv) which yielded an average turbidity of532 NTU The same concentration of particles wasused in all colloidal fouling experiments performed forthis study Conductivity pH and turbidity measure-ments were made at the start end and at several pointsduring the fouling experiment to determine salt rejec-tion to ensure complete rejection of particles and toensure feed conditions were constant throughout thetest The transient flux at constant pressure was down-loaded in real time from the digital permeate flow me-ter to a laboratory computer

Measuring colloid deposit layer mass

In some experiments the mass of colloid deposit lay-ers was measured using a previously published technique(Faibish et al 1998) The feed tank volume was reducedsuch that the mass of particles dosed into the feed tankwould be measurably reduced by the mass of particlesaccumulated in the cake layer over the membrane Asmaller feed volume was used for these experiments suchthat a small but measurable decrease in feed turbidityoccurred within in the time scale of the experiment Inthese experiments only one crossflow filter was used sothat the decline in feed suspension turbidity was relatedto a single crossflow membrane filter No significant dif-ference in mass transfer parameters flux decline data orsalt rejection data was found when compared to data fromexperiments using constant feed particle concentrationfed in parallel to both crossflow membrane filters Themeasured colloid deposit layer mass was then combinedwith other relevant measured and constant parametersinto Equations (9) and (12) to determine the cake poros-ity and cake-enhanced osmotic pressure

CROSSFLOW MEMBRANE FILTER GEOMETRY 363

ENVIRON ENG SCI VOL 19 NO 6 2002

RESULTS AND DISCUSSION

Predicted and measured concentrationpolarization effects

The film-theory predicted mass transfer parameters forthe lab-scale CMF units are provided in Table 1 Thelisted volumetric feed flow rates (Q) are those used infouling experiments and the data are arranged in order of decreasing CP modulus Velocity shear rate andReynolds number all increase with increasing feed flowHowever at a given volumetric flow rate velocity is dou-bled as dh is halved so the Reynolds number is the samein either channel The wall shear rate captures both thedifference in channel geometry and crossflow and so itcan be made identical in the two units at certain cross-flow rates The mass transfer coefficients CP moduliand osmotic pressure drops predicted from the film-the-ory equations all increase in proportion to the change inshear rate again highlighting the usefulness of this pa-rameter The theoretical film layer thickness was calcu-lated from kf 5 Ddf using 1611 3 1029 m2s as the dif-fusion coefficient for NaCl and ranged from about 50 to125 mm The most important data from Table 1 are items3 and 4 The shear rate is identical so the film-theorypredicted mass transfer parameters (kf df Cm Cb andDpm) are identical

The theoretical and experimental concentration polar-ization moduli for the crossflow membrane filters areplotted against crossflow Reynolds number in Fig 4 Ex-perimentally determined salt rejection is labeled next toeach experimental data point The labels 1 to 6 corre-spond to the same item numbers in Table 1 The exper-imental osmotic pressure drop was determined at a sta-ble flux of 142 3 1025 ms (30 gfd) and combined withobserved salt rejection data in Equation (5) to calculatethe experimental mass transfer coefficient The experi-

mental CP modulus was then calculated from Equation(4) The theoretical concentration polarization modulusdata plotted in Fig 4 was calculated from Equation (4)using the experimental salt rejection values at the corre-sponding Reynolds flows and linearly interpolating (orextrapolating) salt rejection values for flow rates in be-tween (or beyond) The theoretical CP modulus was rel-atively insensitive to Ro over the range of experimentallyobserved rejection values in Fig 4 so this simple linearinterpolation should not introduce significant error

Both the predicted and experimental concentration po-larization effects are shown to be more severe in the 68unit than in the 34 unit over the entire range of flow ratesThe experimental data are in fairly good agreement withpredicted CP modulus data although the experimentaldata appear relatively flat over the range of Reynoldsnumbers This may be due in part to the fact that wall-suction (permeation) is ignored in the film-theory pre-dicted mass transfer coefficient In items 3 and 4 of Table1 the hydrodynamic conditions are predicted to yield thesame CP modulus in the two filters but experimental CPmoduli differed by about 17 This film-theory ldquoerrorrdquomay be due to entrance and side-wall effects not ac-counted for in film theory predictions as well as otherpotential unknown experimental errors

Figure 5 presents the predicted trans-cake hydraulicpressures cake-enhanced osmotic pressures and perme-ate fluxes in the 34 and 68 units for varied cake layerthickness and porosity Hydrodynamic conditions werethose described in items 1 and 4 of Table 1 Howeverbecause the mass transfer parameters are identical initems 3 and 4 the 34 unit curves displayed in Fig 5 the-oretically represent the cake-enhanced osmotic pressuresfor the 68 unit under the conditions of item 3 in Table 1

At a feed flow rate of 095 Lpm the initial trans-mem-brane osmotic pressures were about 14 and 21 psi in the

364 HOEK ET AL

Table 1 Film-theory predicted mass transfer parameters for experimental CMF units

Item CMFa Qb uc g0d Ree kf df Cm Cb

fDpm

g

no unit [Lpm] [cms] [s21] [2] [mms] [mm] [2] [psi]

1 68 095 96 334 372 13 126 30 212 68 189 192 668 745 16 100 24 173 68 379 384 1336 1489 20 79 20 144 34 095 192 1336 372 20 79 20 145 34 189 384 2671 745 26 63 17 126 34 379 769 5342 1489 32 50 15 11

Operation conditions used in the calculations are J0 5 142 3 1025 ms (30 gfd) Cb 5 001 M NaCl and Ro 5 98 aChannelheight (Hc) 5 0864 mm (34) and 173 mm (68) channel length (Lc) 5 146 mm channel width (Wc) 5 95 mm bQ 5 volumetricfeed flow rate in liters per minute (Lpm) cu 5 QAx Ax 5 channel cross-sectional area dg0 5 6uHc and is the channel wall shearrate eRe 5 udhn and is the channel crossflow Reynolds number dh 5 2Hc n 5 kinematic viscosity fconcentration polarization(CP) modulus calculated from Equation (4) geffective trans-membrane osmotic pressure calculated from Equation 5

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

moderately negatively charged (215 to 225 mV) at typ-ical solution chemistries based on streaming potentialanalyses reported elsewhere (Vrijenhoek et al 2001)

Reagents and model colloids

Salt stock solutions were prepared using ACS gradeNaCl (Fisher Scientific Pittsburgh PA) dissolved indeionized water (Nanopure Infinity Ultrapure BarnsteadDubuque IA) Nissan Chemical America Corporation(Houston TX) provided the colloidal particles used inthe fouling experiments The particles were certified as010 mm (6003 mm) silica particles in an aqueous sus-pension Chemical analysis by the manufacturer indicatesthe suspension to be 407 (ww) amorphous silica witha specific gravity of 13 Based on the specific gravityand weight percent of the suspension the particle densitywas calculated to be 236 gcm3 Gravimetric analysis ofthe particle suspension revealed the particle density to be211 gcm3 which compares well with the above calcu-lation and other reported values (Faibish et al 1998)Particles were negatively charged (225 mV) at pH 68 602 and 001 M NaCl as determined from electrophoreticmobility measurements reported elsewhere (Vrijenhoeket al 2001)

Laboratory-scale crossflow membrane filters

The test apparatus was a modified version of twocommercially available stainless steel crossflow mem-brane filtration (CMF) units (Sepa CF Osmonics IncMinnetonka MN) The crossflow membrane filtrationunits are rated for operating pressures up to 6895 kPa(1000 psi) Both crossflow units have dimensions of146 and 95 cm for channel length (Lc) and width (Wc)respectively while the channel heights (Hc) are 34 mil(086 mm) and 68 mil (173 mm) respectively The twocrossflow membrane filtration units will hereafter be de-scribed simply as the ldquo34rdquo and ldquo68rdquo units thus indi-cating their respective channel heights These channeldimensions provide an effective membrane area (Am) of139 3 1022 m2 per unit and cross-sectional flow areas(Ax) of 082 3 1024 m2 for the 34 unit and 164 3 1024

m2 for the 68 unit The applied pressure (DP) was con-stant and monitored by a pressure gage (Cole-ParmerChicago IL) and flux was monitored in real time by adigital flow meter (Optiflow 1000 Humonics RanchoCordova CA) Specific modifications to the manufac-turerrsquos setup were reported elsewhere (Vrijenhoek et al2001) a schematic diagram of the experimental systemis presented in Fig 3

362 HOEK ET AL

Figure 3 Crossflow membrane filtration (CMF) apparatus used in experiments designed to simultaneously test the influenceof crossflow hydrodynamics and membrane filter geometry on colloidal fouling The two crossflow membrane filters may be fedin parallel from a common feed tank or individually

Measuring membrane hydraulic resistance

Different membrane coupons were used for each fil-tration experiment so the membrane hydraulic resis-tance was determined prior to each fouling experimentFirst deionized (DI) water was circulated at 250 psi(1724 kPa) for up to 24 h to dissociate flux decline dueto membrane compaction (and other unknown causesinherent of lab-scale recirculation systems) Flux wasmonitored continuously for the duration of the experi-ment and recorded in real time on a laboratory com-puter After DI equilibration the pressure was changedin increments of 50 psi (345 kPa) from a high of 250psi to a low of 50 psi and flux recorded at a feed flowrate of 095 liters per minute (Lpm) At each pressureflux was monitored for at least 30 min to ensure stableperformance The crossflow was then increased to 190Lpm and flux was recorded at 50 psi increments from50 to 250 psi Finally feed flow rate was set at 379Lpm and the flux was recorded at 50 psi incrementsfrom 250 psi down to 50 psi At each crossflow andpressure the average of all of the stable flux measure-ments was plotted against applied pressure The slopeof a line fitted to pure water flux vs pressure data bya least-squares linear regression provided the mem-brane hydraulic resistance As expected there was nomeasured influence of feed flow rate on pure water fluxfor any experiments but the procedure provided extradata points for the regression analysis The pH of feedwas monitored throughout the pure water flux experi-ments to ensure constant feed solution chemistry

Measuring CP modulus and initial osmoticpressure drop

After the membrane pure water hydraulic resistance(Rm) was determined concentration polarization effectscould be quantified using film-theory and the velocityvariation technique described herein An appropriatevolume of 1 M stock NaCl solution was added to thefeed tank to provide the desired experimental ionicstrength The same feed solution ionic strength (001M) was used for all filtration experiments in this studyThe sequence of varying applied pressure and feed flowrate was repeated The effective osmotic pressure dropacross the membrane (Dpm) for each velocity variationwas determined from Equation (1) with A 5 1Rm Eachcombination of pressure and flow yielded different per-meate and crossflow velocities respectively and hencethe description as the ldquovelocity variationrdquo techniqueThe experimental film-theory mass transfer coefficientwas calculated from the measured Dpm and Equation(5) and then the experimental CP modulus was calcu-lated from Equation (4) for each velocity variation The

feed solution pH was monitored throughout the salt wa-ter experiments to ensure stable feed conditions Ob-served salt rejection (Ro) was determined by measur-ing feed and permeate conductivity Conductivity wasdetermined to be linearly proportional to NaCl con-centration by performing a least-squares linear regres-sion of conductivity measurements for solutions withknown NaCl concentrations

Measuring decline in flux and salt rejection dueto colloidal fouling

After the salt water experiments were finished pres-sure and crossflow were adjusted to produce the de-sired initial flux and wall shear for the fouling exper-iment After stable performance (flux and saltrejection) was achieved for a minimum of 60 min adose of silica particles was added to the feed tank toprovide the appropriate particle feed concentrationThe concentration of 100 nm silica particles was0008 (vv) which yielded an average turbidity of532 NTU The same concentration of particles wasused in all colloidal fouling experiments performed forthis study Conductivity pH and turbidity measure-ments were made at the start end and at several pointsduring the fouling experiment to determine salt rejec-tion to ensure complete rejection of particles and toensure feed conditions were constant throughout thetest The transient flux at constant pressure was down-loaded in real time from the digital permeate flow me-ter to a laboratory computer

Measuring colloid deposit layer mass

In some experiments the mass of colloid deposit lay-ers was measured using a previously published technique(Faibish et al 1998) The feed tank volume was reducedsuch that the mass of particles dosed into the feed tankwould be measurably reduced by the mass of particlesaccumulated in the cake layer over the membrane Asmaller feed volume was used for these experiments suchthat a small but measurable decrease in feed turbidityoccurred within in the time scale of the experiment Inthese experiments only one crossflow filter was used sothat the decline in feed suspension turbidity was relatedto a single crossflow membrane filter No significant dif-ference in mass transfer parameters flux decline data orsalt rejection data was found when compared to data fromexperiments using constant feed particle concentrationfed in parallel to both crossflow membrane filters Themeasured colloid deposit layer mass was then combinedwith other relevant measured and constant parametersinto Equations (9) and (12) to determine the cake poros-ity and cake-enhanced osmotic pressure

CROSSFLOW MEMBRANE FILTER GEOMETRY 363

ENVIRON ENG SCI VOL 19 NO 6 2002

RESULTS AND DISCUSSION

Predicted and measured concentrationpolarization effects

The film-theory predicted mass transfer parameters forthe lab-scale CMF units are provided in Table 1 Thelisted volumetric feed flow rates (Q) are those used infouling experiments and the data are arranged in order of decreasing CP modulus Velocity shear rate andReynolds number all increase with increasing feed flowHowever at a given volumetric flow rate velocity is dou-bled as dh is halved so the Reynolds number is the samein either channel The wall shear rate captures both thedifference in channel geometry and crossflow and so itcan be made identical in the two units at certain cross-flow rates The mass transfer coefficients CP moduliand osmotic pressure drops predicted from the film-the-ory equations all increase in proportion to the change inshear rate again highlighting the usefulness of this pa-rameter The theoretical film layer thickness was calcu-lated from kf 5 Ddf using 1611 3 1029 m2s as the dif-fusion coefficient for NaCl and ranged from about 50 to125 mm The most important data from Table 1 are items3 and 4 The shear rate is identical so the film-theorypredicted mass transfer parameters (kf df Cm Cb andDpm) are identical

The theoretical and experimental concentration polar-ization moduli for the crossflow membrane filters areplotted against crossflow Reynolds number in Fig 4 Ex-perimentally determined salt rejection is labeled next toeach experimental data point The labels 1 to 6 corre-spond to the same item numbers in Table 1 The exper-imental osmotic pressure drop was determined at a sta-ble flux of 142 3 1025 ms (30 gfd) and combined withobserved salt rejection data in Equation (5) to calculatethe experimental mass transfer coefficient The experi-

mental CP modulus was then calculated from Equation(4) The theoretical concentration polarization modulusdata plotted in Fig 4 was calculated from Equation (4)using the experimental salt rejection values at the corre-sponding Reynolds flows and linearly interpolating (orextrapolating) salt rejection values for flow rates in be-tween (or beyond) The theoretical CP modulus was rel-atively insensitive to Ro over the range of experimentallyobserved rejection values in Fig 4 so this simple linearinterpolation should not introduce significant error

Both the predicted and experimental concentration po-larization effects are shown to be more severe in the 68unit than in the 34 unit over the entire range of flow ratesThe experimental data are in fairly good agreement withpredicted CP modulus data although the experimentaldata appear relatively flat over the range of Reynoldsnumbers This may be due in part to the fact that wall-suction (permeation) is ignored in the film-theory pre-dicted mass transfer coefficient In items 3 and 4 of Table1 the hydrodynamic conditions are predicted to yield thesame CP modulus in the two filters but experimental CPmoduli differed by about 17 This film-theory ldquoerrorrdquomay be due to entrance and side-wall effects not ac-counted for in film theory predictions as well as otherpotential unknown experimental errors

Figure 5 presents the predicted trans-cake hydraulicpressures cake-enhanced osmotic pressures and perme-ate fluxes in the 34 and 68 units for varied cake layerthickness and porosity Hydrodynamic conditions werethose described in items 1 and 4 of Table 1 Howeverbecause the mass transfer parameters are identical initems 3 and 4 the 34 unit curves displayed in Fig 5 the-oretically represent the cake-enhanced osmotic pressuresfor the 68 unit under the conditions of item 3 in Table 1

At a feed flow rate of 095 Lpm the initial trans-mem-brane osmotic pressures were about 14 and 21 psi in the

364 HOEK ET AL

Table 1 Film-theory predicted mass transfer parameters for experimental CMF units

Item CMFa Qb uc g0d Ree kf df Cm Cb

fDpm

g

no unit [Lpm] [cms] [s21] [2] [mms] [mm] [2] [psi]

1 68 095 96 334 372 13 126 30 212 68 189 192 668 745 16 100 24 173 68 379 384 1336 1489 20 79 20 144 34 095 192 1336 372 20 79 20 145 34 189 384 2671 745 26 63 17 126 34 379 769 5342 1489 32 50 15 11

Operation conditions used in the calculations are J0 5 142 3 1025 ms (30 gfd) Cb 5 001 M NaCl and Ro 5 98 aChannelheight (Hc) 5 0864 mm (34) and 173 mm (68) channel length (Lc) 5 146 mm channel width (Wc) 5 95 mm bQ 5 volumetricfeed flow rate in liters per minute (Lpm) cu 5 QAx Ax 5 channel cross-sectional area dg0 5 6uHc and is the channel wall shearrate eRe 5 udhn and is the channel crossflow Reynolds number dh 5 2Hc n 5 kinematic viscosity fconcentration polarization(CP) modulus calculated from Equation (4) geffective trans-membrane osmotic pressure calculated from Equation 5

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

Measuring membrane hydraulic resistance

Different membrane coupons were used for each fil-tration experiment so the membrane hydraulic resis-tance was determined prior to each fouling experimentFirst deionized (DI) water was circulated at 250 psi(1724 kPa) for up to 24 h to dissociate flux decline dueto membrane compaction (and other unknown causesinherent of lab-scale recirculation systems) Flux wasmonitored continuously for the duration of the experi-ment and recorded in real time on a laboratory com-puter After DI equilibration the pressure was changedin increments of 50 psi (345 kPa) from a high of 250psi to a low of 50 psi and flux recorded at a feed flowrate of 095 liters per minute (Lpm) At each pressureflux was monitored for at least 30 min to ensure stableperformance The crossflow was then increased to 190Lpm and flux was recorded at 50 psi increments from50 to 250 psi Finally feed flow rate was set at 379Lpm and the flux was recorded at 50 psi incrementsfrom 250 psi down to 50 psi At each crossflow andpressure the average of all of the stable flux measure-ments was plotted against applied pressure The slopeof a line fitted to pure water flux vs pressure data bya least-squares linear regression provided the mem-brane hydraulic resistance As expected there was nomeasured influence of feed flow rate on pure water fluxfor any experiments but the procedure provided extradata points for the regression analysis The pH of feedwas monitored throughout the pure water flux experi-ments to ensure constant feed solution chemistry

Measuring CP modulus and initial osmoticpressure drop

After the membrane pure water hydraulic resistance(Rm) was determined concentration polarization effectscould be quantified using film-theory and the velocityvariation technique described herein An appropriatevolume of 1 M stock NaCl solution was added to thefeed tank to provide the desired experimental ionicstrength The same feed solution ionic strength (001M) was used for all filtration experiments in this studyThe sequence of varying applied pressure and feed flowrate was repeated The effective osmotic pressure dropacross the membrane (Dpm) for each velocity variationwas determined from Equation (1) with A 5 1Rm Eachcombination of pressure and flow yielded different per-meate and crossflow velocities respectively and hencethe description as the ldquovelocity variationrdquo techniqueThe experimental film-theory mass transfer coefficientwas calculated from the measured Dpm and Equation(5) and then the experimental CP modulus was calcu-lated from Equation (4) for each velocity variation The

feed solution pH was monitored throughout the salt wa-ter experiments to ensure stable feed conditions Ob-served salt rejection (Ro) was determined by measur-ing feed and permeate conductivity Conductivity wasdetermined to be linearly proportional to NaCl con-centration by performing a least-squares linear regres-sion of conductivity measurements for solutions withknown NaCl concentrations

Measuring decline in flux and salt rejection dueto colloidal fouling

After the salt water experiments were finished pres-sure and crossflow were adjusted to produce the de-sired initial flux and wall shear for the fouling exper-iment After stable performance (flux and saltrejection) was achieved for a minimum of 60 min adose of silica particles was added to the feed tank toprovide the appropriate particle feed concentrationThe concentration of 100 nm silica particles was0008 (vv) which yielded an average turbidity of532 NTU The same concentration of particles wasused in all colloidal fouling experiments performed forthis study Conductivity pH and turbidity measure-ments were made at the start end and at several pointsduring the fouling experiment to determine salt rejec-tion to ensure complete rejection of particles and toensure feed conditions were constant throughout thetest The transient flux at constant pressure was down-loaded in real time from the digital permeate flow me-ter to a laboratory computer

Measuring colloid deposit layer mass

In some experiments the mass of colloid deposit lay-ers was measured using a previously published technique(Faibish et al 1998) The feed tank volume was reducedsuch that the mass of particles dosed into the feed tankwould be measurably reduced by the mass of particlesaccumulated in the cake layer over the membrane Asmaller feed volume was used for these experiments suchthat a small but measurable decrease in feed turbidityoccurred within in the time scale of the experiment Inthese experiments only one crossflow filter was used sothat the decline in feed suspension turbidity was relatedto a single crossflow membrane filter No significant dif-ference in mass transfer parameters flux decline data orsalt rejection data was found when compared to data fromexperiments using constant feed particle concentrationfed in parallel to both crossflow membrane filters Themeasured colloid deposit layer mass was then combinedwith other relevant measured and constant parametersinto Equations (9) and (12) to determine the cake poros-ity and cake-enhanced osmotic pressure

CROSSFLOW MEMBRANE FILTER GEOMETRY 363

ENVIRON ENG SCI VOL 19 NO 6 2002

RESULTS AND DISCUSSION

Predicted and measured concentrationpolarization effects

The film-theory predicted mass transfer parameters forthe lab-scale CMF units are provided in Table 1 Thelisted volumetric feed flow rates (Q) are those used infouling experiments and the data are arranged in order of decreasing CP modulus Velocity shear rate andReynolds number all increase with increasing feed flowHowever at a given volumetric flow rate velocity is dou-bled as dh is halved so the Reynolds number is the samein either channel The wall shear rate captures both thedifference in channel geometry and crossflow and so itcan be made identical in the two units at certain cross-flow rates The mass transfer coefficients CP moduliand osmotic pressure drops predicted from the film-the-ory equations all increase in proportion to the change inshear rate again highlighting the usefulness of this pa-rameter The theoretical film layer thickness was calcu-lated from kf 5 Ddf using 1611 3 1029 m2s as the dif-fusion coefficient for NaCl and ranged from about 50 to125 mm The most important data from Table 1 are items3 and 4 The shear rate is identical so the film-theorypredicted mass transfer parameters (kf df Cm Cb andDpm) are identical

The theoretical and experimental concentration polar-ization moduli for the crossflow membrane filters areplotted against crossflow Reynolds number in Fig 4 Ex-perimentally determined salt rejection is labeled next toeach experimental data point The labels 1 to 6 corre-spond to the same item numbers in Table 1 The exper-imental osmotic pressure drop was determined at a sta-ble flux of 142 3 1025 ms (30 gfd) and combined withobserved salt rejection data in Equation (5) to calculatethe experimental mass transfer coefficient The experi-

mental CP modulus was then calculated from Equation(4) The theoretical concentration polarization modulusdata plotted in Fig 4 was calculated from Equation (4)using the experimental salt rejection values at the corre-sponding Reynolds flows and linearly interpolating (orextrapolating) salt rejection values for flow rates in be-tween (or beyond) The theoretical CP modulus was rel-atively insensitive to Ro over the range of experimentallyobserved rejection values in Fig 4 so this simple linearinterpolation should not introduce significant error

Both the predicted and experimental concentration po-larization effects are shown to be more severe in the 68unit than in the 34 unit over the entire range of flow ratesThe experimental data are in fairly good agreement withpredicted CP modulus data although the experimentaldata appear relatively flat over the range of Reynoldsnumbers This may be due in part to the fact that wall-suction (permeation) is ignored in the film-theory pre-dicted mass transfer coefficient In items 3 and 4 of Table1 the hydrodynamic conditions are predicted to yield thesame CP modulus in the two filters but experimental CPmoduli differed by about 17 This film-theory ldquoerrorrdquomay be due to entrance and side-wall effects not ac-counted for in film theory predictions as well as otherpotential unknown experimental errors

Figure 5 presents the predicted trans-cake hydraulicpressures cake-enhanced osmotic pressures and perme-ate fluxes in the 34 and 68 units for varied cake layerthickness and porosity Hydrodynamic conditions werethose described in items 1 and 4 of Table 1 Howeverbecause the mass transfer parameters are identical initems 3 and 4 the 34 unit curves displayed in Fig 5 the-oretically represent the cake-enhanced osmotic pressuresfor the 68 unit under the conditions of item 3 in Table 1

At a feed flow rate of 095 Lpm the initial trans-mem-brane osmotic pressures were about 14 and 21 psi in the

364 HOEK ET AL

Table 1 Film-theory predicted mass transfer parameters for experimental CMF units

Item CMFa Qb uc g0d Ree kf df Cm Cb

fDpm

g

no unit [Lpm] [cms] [s21] [2] [mms] [mm] [2] [psi]

1 68 095 96 334 372 13 126 30 212 68 189 192 668 745 16 100 24 173 68 379 384 1336 1489 20 79 20 144 34 095 192 1336 372 20 79 20 145 34 189 384 2671 745 26 63 17 126 34 379 769 5342 1489 32 50 15 11

Operation conditions used in the calculations are J0 5 142 3 1025 ms (30 gfd) Cb 5 001 M NaCl and Ro 5 98 aChannelheight (Hc) 5 0864 mm (34) and 173 mm (68) channel length (Lc) 5 146 mm channel width (Wc) 5 95 mm bQ 5 volumetricfeed flow rate in liters per minute (Lpm) cu 5 QAx Ax 5 channel cross-sectional area dg0 5 6uHc and is the channel wall shearrate eRe 5 udhn and is the channel crossflow Reynolds number dh 5 2Hc n 5 kinematic viscosity fconcentration polarization(CP) modulus calculated from Equation (4) geffective trans-membrane osmotic pressure calculated from Equation 5

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

RESULTS AND DISCUSSION

Predicted and measured concentrationpolarization effects

The film-theory predicted mass transfer parameters forthe lab-scale CMF units are provided in Table 1 Thelisted volumetric feed flow rates (Q) are those used infouling experiments and the data are arranged in order of decreasing CP modulus Velocity shear rate andReynolds number all increase with increasing feed flowHowever at a given volumetric flow rate velocity is dou-bled as dh is halved so the Reynolds number is the samein either channel The wall shear rate captures both thedifference in channel geometry and crossflow and so itcan be made identical in the two units at certain cross-flow rates The mass transfer coefficients CP moduliand osmotic pressure drops predicted from the film-the-ory equations all increase in proportion to the change inshear rate again highlighting the usefulness of this pa-rameter The theoretical film layer thickness was calcu-lated from kf 5 Ddf using 1611 3 1029 m2s as the dif-fusion coefficient for NaCl and ranged from about 50 to125 mm The most important data from Table 1 are items3 and 4 The shear rate is identical so the film-theorypredicted mass transfer parameters (kf df Cm Cb andDpm) are identical

The theoretical and experimental concentration polar-ization moduli for the crossflow membrane filters areplotted against crossflow Reynolds number in Fig 4 Ex-perimentally determined salt rejection is labeled next toeach experimental data point The labels 1 to 6 corre-spond to the same item numbers in Table 1 The exper-imental osmotic pressure drop was determined at a sta-ble flux of 142 3 1025 ms (30 gfd) and combined withobserved salt rejection data in Equation (5) to calculatethe experimental mass transfer coefficient The experi-

mental CP modulus was then calculated from Equation(4) The theoretical concentration polarization modulusdata plotted in Fig 4 was calculated from Equation (4)using the experimental salt rejection values at the corre-sponding Reynolds flows and linearly interpolating (orextrapolating) salt rejection values for flow rates in be-tween (or beyond) The theoretical CP modulus was rel-atively insensitive to Ro over the range of experimentallyobserved rejection values in Fig 4 so this simple linearinterpolation should not introduce significant error

Both the predicted and experimental concentration po-larization effects are shown to be more severe in the 68unit than in the 34 unit over the entire range of flow ratesThe experimental data are in fairly good agreement withpredicted CP modulus data although the experimentaldata appear relatively flat over the range of Reynoldsnumbers This may be due in part to the fact that wall-suction (permeation) is ignored in the film-theory pre-dicted mass transfer coefficient In items 3 and 4 of Table1 the hydrodynamic conditions are predicted to yield thesame CP modulus in the two filters but experimental CPmoduli differed by about 17 This film-theory ldquoerrorrdquomay be due to entrance and side-wall effects not ac-counted for in film theory predictions as well as otherpotential unknown experimental errors

Figure 5 presents the predicted trans-cake hydraulicpressures cake-enhanced osmotic pressures and perme-ate fluxes in the 34 and 68 units for varied cake layerthickness and porosity Hydrodynamic conditions werethose described in items 1 and 4 of Table 1 Howeverbecause the mass transfer parameters are identical initems 3 and 4 the 34 unit curves displayed in Fig 5 the-oretically represent the cake-enhanced osmotic pressuresfor the 68 unit under the conditions of item 3 in Table 1

At a feed flow rate of 095 Lpm the initial trans-mem-brane osmotic pressures were about 14 and 21 psi in the

364 HOEK ET AL

Table 1 Film-theory predicted mass transfer parameters for experimental CMF units

Item CMFa Qb uc g0d Ree kf df Cm Cb

fDpm

g

no unit [Lpm] [cms] [s21] [2] [mms] [mm] [2] [psi]

1 68 095 96 334 372 13 126 30 212 68 189 192 668 745 16 100 24 173 68 379 384 1336 1489 20 79 20 144 34 095 192 1336 372 20 79 20 145 34 189 384 2671 745 26 63 17 126 34 379 769 5342 1489 32 50 15 11

Operation conditions used in the calculations are J0 5 142 3 1025 ms (30 gfd) Cb 5 001 M NaCl and Ro 5 98 aChannelheight (Hc) 5 0864 mm (34) and 173 mm (68) channel length (Lc) 5 146 mm channel width (Wc) 5 95 mm bQ 5 volumetricfeed flow rate in liters per minute (Lpm) cu 5 QAx Ax 5 channel cross-sectional area dg0 5 6uHc and is the channel wall shearrate eRe 5 udhn and is the channel crossflow Reynolds number dh 5 2Hc n 5 kinematic viscosity fconcentration polarization(CP) modulus calculated from Equation (4) geffective trans-membrane osmotic pressure calculated from Equation 5

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

34 and 68 CMF units respectively Trans-cake hydraulicpressure (Dpc) was determined from JRc where the cakeresistance was obtained from the cake thickness insteadof cake mass [recall Equation (8b)] by the relation dc 5Md rp(1 2 laquo) (Faibish et al 1998) Note that there wasa very subtle difference in trans-cake hydraulic pressurebetween the 34 and 68 units because the flux was dif-ferent but difference was negligible with respect to allother pressures Cake-enhanced osmotic pressure (Dpm)was calculated from Equation (12) The salt rejection waslinearly varied from 97 to 96 and 96 to 95 as cakelayer increased from 0 to 25 mm in the 34 and 68 unitsrespectively

Flux was determined iteratively to account for the in-terrelated effects of cake layer hydraulic pressure droposmotic pressure drop and salt rejection at each theoret-ical cake thickness At the initial flux of 142 3 1025 ms(30 gfd) Dpc and Dpm were predicted from Equations(9) and (12) and a new flux was determined by solvingEquation (9a) using the predicted Dpc and Dpm Thisflux was then used to recalculate the predicted Dpc andDpm The calculations were performed iteratively untilthe flux value used in Equations (9) and (12) was returnedequally by Equation (9a) to six significant figures Thisallowed for accurate prediction of pressure drops and fluxby accounting for the declining flux at each cake thick-ness

In Fig 5 the hydraulic pressure drop across the cakelayer increased approximately linearly with cake layerthickness such that a cake thickness of 25 mm accountedfor a pressure drop between 1 and 5 psi The cake-en-hanced osmotic pressure increased from the initial os-motic pressure drop by as much as 40 psi in the 68 unitat the lowest porosity The cake-enhanced osmotic pres-sure in the 68 unit is 15 times greater than that in the 34unit across the entire range of cake thicknesses and forall three porosity values However this proportional dif-ference yields flux decline that is always more severe inthe 68 unit because the actual cake-enhanced osmotic

CROSSFLOW MEMBRANE FILTER GEOMETRY 365

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 4 Comparison of theoretical and experimental con-centration polarization (CP) modulus (Cm Cb) vs Reynoldsnumber for the lab-scale CMF units The numbers in parenthe-ses correspond to the item numbers in Table 1 According tothe ldquofilm-theoryrdquo predictions the CP modulus should be thesame for experiments 3 and 4 Both predicted and experimen-tal CP modulus values were determined at J0 5 142 3 1025

ms (30 gfd) Cb 5 001 M NaCl pH 5 68 6 02 and 25degC

Figure 5 Plot of calculated cake-enhanced osmotic pressure(Dpm) and trans-cake pressure (Dpc) as a function of cakelayer thickness for several porosities Mass transfer related ef-fects are simulated using the hydrodynamic conditions de-scribed in items (1) and (4) in Table 1 The following param-eters used in the calculations J0 5 142 3 1025 ms (30 gfd)Rm 5 10211 Pa-sm DP34 5 220 psi and DP68 5 227 psi Q 5095 Lpm g034 5 1336 s21 and g068 5 334 s21 Cb 5 001 MNaCl and 097 $ Ro34 $ 096 and 096 $ Ro68 $ 095

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

pressure increases more quickly due to the initial differ-ence in mass transfer Another factor to consider in ac-tual filtration experiments is that the rate of cake layergrowth and the deposit layer porosity may be affected bydifferent tangential shear rates So at a given crossflowrate the flux decline in the 68 unit may be even more se-vere if a thicker or more dense colloid deposit layer isformed

Relative influence of channel height and shear oncolloidal fouling

Preliminary fouling experiments were performed tomeasure the influence of crossflow membrane filtergeometry on colloidal fouling of four commercial RONFmembranes Normalized flux decline data (JJ0) are plot-ted in Fig 6 for the hydrodynamic and mass transfer con-ditions described by items 1 and 4 in Table 1 Open sym-bols represent data obtained from the 34 unit and closed

symbols represent data from the 68 unit All four mem-branes were tested at the same physical and chemical op-erating conditions and feed solution chemistry Thesefour membranes were chosen to validate the fact that anyinfluence of channel height and shear rate was signifi-cant for membranes with different physical and chemi-cal properties The most important differences in mem-brane properties were the membrane resistance which onaverage was three times greater for the RO membranesand the salt rejection which ranged from about 20 to over95 At the same feed flow rate initial osmotic pressureeffects in experiments depicted by Fig 6 were differentdue to the different channel heights and to the differentsalt rejections

The difference in flux decline within the first hour wasindistinguishable for all four membranes After the firsthour flux decline in the 34 unit slowed and in the 68unit it continued to decline rapidly for all four mem-branes In the 34 unit all four membranes fouled moder-

366 HOEK ET AL

Figure 6 Normalized flux decline data for colloidal fouling experiments conducted with four commercial RONF membranesHL (a) X20 (b) NF70 (c) and LFC1 (d) All experiments were conducted at constant physico-chemical conditions of 14 31025 ms (30 gfd) initial flux 001 M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degC and pH 68 6 02 A constantfeed flow rate of 095 Lpm provided shear rates of 1336 s21 and 334 s21 in the 34 unit (Hc 5 0864 mm) and the 68 unit (Hc 5173 mm) respectively

a

c

b

d

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

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ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

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ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

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ENVIRON ENG SCI VOL 19 NO 6 2002

ately while in the 68 unit all four membranes fouled se-verely Few mechanistic conclusions can be drawn fromthe limited data presented in Fig 6 but it is clear that thecoupled influence of channel height and shear rate on col-loidal fouling was significant regardless of any differ-ences in membrane properties

Six additional filtration experiments were conductedin the 34 and 68 units at each of the feed flow rates listedin Table 1 Normalized flux decline data from these ex-periments are plotted in Fig 7 (above the break in the Y-axis) with corresponding crossflow channel heights andshear rates summarized in the figure key The reverse os-mosis membrane LFC1 was used and all other experi-mental conditions were the same as in Fig 6 Open sym-bols indicate fouling data obtained from the 34 unit andsolid symbols indicate data obtained from the 68 unitThe numbers in the figure key correspond to the sameitem numbers in Table 1

The flux data from the 34 and 68 units was similar forabout 1 h into the experiment regardless of channelheight or shear rate After this initial period the flux de-cline in the 34 unit was distinctly less than that in the 68unit Within each filter the flux at each shear rate wasthe same for about 8 h At various times beyond 8 h mea-sured flux values decrease in order of decreasing shearrate For example data from the 68 unit at shear rates of

334 and 1336 s21 resulted in 22 and 28 flux declinerespectively at 25 h

Perhaps the most interesting data points in Fig 7 arethose obtained at the same shear rate (1336 s21) in the34 and 68 units The flux decline data are the open tri-angles and the closed squares respectively The dramaticdifference in flux decline suggests the possibility that asignificantly thicker andor more compact cake layerformed in the 68 unit It is also interesting to investigatefurther the data from the 68 unit at the lowest shear rate(334 s21) to decipher the sole influence of shear rate onfouling An iterative solution of Equations (9) and (12)was performed similarly to the calculations described forthe theoretical data of Fig 5 However in these calcula-tions a porosity of 48 was assumed and cake layerthickness was used to fit the cake layer and cake-en-hanced osmotic pressure drops to the measured flux dataAll other parameters used in the calculations were iden-tical to those used in determining the theoretical data inFig 5

The resulting cake layer masses (in grams) are plottedbelow the break on the Y-axis of Fig 7 It is typically as-sumed that the shear rate limits cake growth in crossflowmembrane filtration (Davis 1992) Indeed the data ofFig 7 suggest that more colloids deposited in the 68 unitat the lower shear rate but only after about 10 h So there

CROSSFLOW MEMBRANE FILTER GEOMETRY 367

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 7 Normalized flux decline and fitted cake mass data for reverse osmosis membrane LFC1 in CMF units with differentchannel height over a range of feed flow rates crossflow velocities and shear rates All runs in the thin-channeled 34 unit (Hc 50864 mm) exhibit less flux decline than those in the 68 unit (Hc 5 173 mm) Other experimental conditions are as in Fig 6

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

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ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

is a period of time for which crossflow did not signifi-cantly change the mass of particles deposited These re-sults were expected and are consistent with previouslypublished experimental colloidal fouling data (Hong etal 1997) However fewer colloids deposited in the 34unit than in the 68 unit at the same shear rate of 1336s21 which was not expected and even more interestingBecause porosity and cake mass were both used as fit-ting parameters it may be argued that the fitted cake mass

values may be arbitrary hence the need for in situ cakemass measurements

Verification of the influence of channel geometryand shear rate on colloidal fouling

The three key colloidal fouling experiments from Fig7 were repeated but the particle suspension was fed toonly one crossflow membrane filter so that colloid de-posit layer mass could be measured as described in theexperimental section These experiments are labeled (1)(3) and (4) in Fig 7 indicating that the mass transferproperties employed coincide with those labeled by thesame item number in Table 1 The results are presentedin Figs 8ndash10 The starting time in the figures is 260 min

368 HOEK ET AL

Figure 8 Data for LFC1 from experiments 1 and 4 (Fig 7) inthe 68 and 34 units respectively conducted at constant physico-chemical conditions of 14 3 1025 ms (30 gfd) initial flux 001M NaCl 200 mgL (008 vv) 100 nm silica colloids 25degCand pH 68 6 02 The feed-flow rate was 095 Lpm in both fil-ters resulting in wall shear rates of 334 and 1336 s21 in the 68and 34 units respectively In (a) measured values of normalizedflux decline (JJ0) observed salt rejection (Ro) and deposit layermass (Mc in grams) are plotted against time of filtration Cakelayer mass Mc comes from multiplying the deposit layer massper unit membrane area Md by the membrane area (001387m2) In (b) applied pressure (DP) trans-membrane pressure(Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cakepressure (Dpc) are plotted against time of filtration

Figure 9 Data for LFC1 from experiments 1 and 3 (Fig 7)in the 68 unit conducted at constant physico-chemical condi-tions of 14 3 1025 ms (30 gfd) initial flux 001 M NaCl 200mgL (008 vv) 100 nm silica colloids 25degC and pH 68 602 The feed flow rates were 095 and 38 Lpm resulting inwall shear rates of 334 and 1336 s21 respectively In (a) mea-sured values of normalized flux decline (JJ0) observed salt re-jection (Ro) and cake layer mass (Mc) are plotted against timeof filtration In (b) applied pressure (DP) trans-membrane pres-sure (Dpm) cake-enhanced osmotic pressure (Dpm) and trans-cake pressure (Dpc) are plotted against time of filtration

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

indicating that flux and salt rejection were stable for atleast 60 min before addition of silica particles at timeequal to zero The equilibration and mass transfer analy-ses occurred prior to the 60 min preparticle stabilizationperiod In part (a) of each figure the normalized fluxsalt rejection and cake layer mass Mc (in grams) are plot-ted against time Cake layer mass Mc comes from mul-tiplying the deposit layer mass per unit membrane areaMd by the membrane area (001387 m2) In part (b) ofthe figures the corresponding pressure drops (appliedmembrane cake and osmotic) are plotted against thesame time scale The data allows direct comparison of

fouling data resulting from different shear rates in dif-ferent channels (Fig 8) different shear rates in the samechannel (Fig 9) and the same shear rate in different chan-nels (Fig 10)

Data from experiments at mass transfer conditions 1and 4 are plotted in Fig 8 In these two experimentschannel heights were 0864 and 173 mm and shear rateswere 334 and 1336 s21 respectively Cake layer masswas noticeably different 1 h into the experiment but fluxdecline was only marginally different After 5 h the fluxdeclines to 97 and 90 in the 34 and 68 units respec-tively Flux decline in Fig 8 is comparable to the corre-sponding flux decline curves in Fig 7 (note that data inFig 8 are shown for only 5 h) The initial salt rejectionis higher in the 34 unit (969) than the 68 unit (953)which was consistent with data observed in previous ex-periments and assumed in theoretical calculations Fol-lowing addition of particles there was an initial increasein salt rejection followed by a gradual (slight) declineover the duration of the experiment The initial increasemay be due to disruption of the concentration polariza-tion layer by the first few layers of colloids depositedAfter 5 h the cake layer mass was nearly a factor of fourgreater in the 68 unit than the 34 unit The higher shearrate resulting from the lower channel height in the 34 unitappears to limit particle accumulation and cake layergrowth

In Fig 8(b) the slight difference in applied and trans-membrane pressure at the start of the experiment is dueto differences in both salt rejection and membrane per-meability The difference in the initial osmotic pressureis assumed due to the different shear rate which isthought to govern concentration polarization Cake lay-ers in both filters provide negligible hydraulic pressuredrop (Dpc) regardless of differences in cake layer massThe substantial difference in cake-enhanced osmoticpressure is primarily due to the greater cake layer massin the 68 unit and to a lesser extent the lower mass trans-fer coefficient The cake porosity was estimated by min-imizing the difference between the osmotic pressures cal-culated from Equations (9) and (12) The estimated cakelayer porosity averaged over 5 h was 534 (629) in the68 unit and 659 (679) percent in the 34 unit which isa significant difference

In summary the data of Fig 8 indicate that the com-bination of lower channel height and higher shear reducedthe initial osmotic pressure and cake layer growth whichled to higher cake porosity lower cake-enhanced osmoticpressure higher flux and higher salt rejection

Data from experiments at mass transfer conditions 1and 3 are plotted in Fig 9 In these two experiments theshear rate was set at 334 s21 (1) and 1336 s21 (3) butthe channel height was fixed at 173 mm The flux was

CROSSFLOW MEMBRANE FILTER GEOMETRY 369

ENVIRON ENG SCI VOL 19 NO 6 2002

Figure 10 Data for LFC1 from experiments 3 and 4 (Fig 7)in the 68 and 34 units respectively conducted at constantphysico-chemical conditions of 14 3 1025 ms (30 gfd) initialflux 001 M NaCl 200 mgL (008 vv) 100 nm silica col-loids 25degC and pH 68 6 02 The feed flow rates were 095and 38 Lpm in the 34 and 68 units respectively resulting ina fixed shear rate of 1336 s21 In (a) measured values of nor-malized flux decline (JJ0) observed salt rejection (Ro) andcake layer mass (Mc) are plotted against time of filtration In(b) applied pressure (DP) trans-membrane pressure (Dpm)cake-enhanced osmotic pressure (Dpm) and trans-cake pres-sure (Dpc) are plotted against time of filtration

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

only marginally different after 5 h declining to 90 and92 at shear rates of 334 and 1336 s21 respectivelyThis is nearly identical to the corresponding data of Fig7 The observed salt rejection is slightly higher through-out the entire experiment at the higher shear rate Againthis may be related as much to variability in membraneproperties for different samples of LFC1 as to crossflowhydrodynamics

Cake layer growth appears unaffected by any differ-ence in shear rate up to about the first hour of particlefiltration This is consistent with the data of Fig 7 aswell as other investigations where the initial stage of col-loidal fouling was shown to be independent of crossflowhydrodynamics (Hong et al 1997) At later times as ex-pected slightly less cake mass was deposited at the highershear rate The average estimated porosity for these ex-periments over 5 h were 534 (629) and 502 (654)percent for wall shear rates of 334 and 1336 s21 re-spectively which is not a significant difference

In Fig 9(b) the applied pressure is shown to be con-stant throughout the experiment and is significantly dif-ferent due to slight differences in membrane permeabil-ity salt rejection and crossflow hydrodynamics Theactual trans-cake pressure is less than 1 psi after 5 h ineither experiment which is practically negligible Thetransient cake-enhanced osmotic pressure drop is lowerat the higher flow rate as predicted by the film-theory(mass transfer was enhanced by the higher shear rate)

In summary the data of Fig 9 suggests that increas-ing shear rate within a given filter reduces the initial os-motic pressure enhances salt rejection and marginallyreduces cake layer growth which leads to slightly higherflux

Data from experiments at mass transfer conditions 3and 4 are plotted in Fig 10 In these experiments theshear rate was fixed at 1336 s21 for channel heights of0864 (34 unit) and 173 mm (68 unit) At the same shearrate nearly identical initial salt rejection and osmotic pres-sure resulted This is consistent with film-theory predic-tions However significantly more cake mass depositedon the membrane in the 68 unit The average porosity

over 5 h was estimated to be 502 (654) and 659 (679)percent in the 68 and 34 units respectively which is asignificant difference A more compact cake with nearlydouble the mass formed in the crossflow membrane fil-ter with greater channel height

The applied pressures were roughly the same in thiscase (212 psi in the 68 unit 216 psi in the 34 unit) Thedifference was almost entirely due to the pure water per-meability of the two membrane coupons The differencein initial trans-membrane osmotic pressure was 1 psiwhich is explained by the slight difference (02) in ini-tial salt rejection and the difference in experimental CPmodulus previously discussed The trans-cake pressureis below 1 psi in both units proving to be essentially neg-ligible compared to cake-enhanced osmotic pressure

In summary the lower channel height significantly re-duced both osmotic pressure effects and cake layergrowth which resulted in higher salt rejection and lessflux decline A potential explanation for these results liesin analysis of the corresponding cake layer thicknesseswith respect to the channel heights The predicted andexperimental film layer thickness and cake layer thick-ness for Experiments 1 3 and 4 are compared in Table2 First film-theory under predicted the concentration po-larization layer thickness Second the cake thickness isbetween 8 and 18 of the experimental film layer thick-ness which supports the hindered diffusion model as-sumption of a relatively thin cake layer for the durationof the experiments in this study

The key information to be derived from the data ofTable 2 is the ratio of cake layer thickness to channelheight (at 5 h) Cake layer thickness is calculated fromdc 5 Md rc (1 2 laquo) (Faibish et al 1998) The percent ofthe channel (height) occupied by the cake layer was thesame when the shear rate was the same even thoughchannel height varied by a factor of 2 The percent of thechannel (height) occupied by the cake layer was differ-ent when the shear rate was different The shear-limitedcake growth is consistent with past investigations of col-loidal fouling in microfiltration (Davis 1992) The sig-nificance is confirmation that the tangential flow field

370 HOEK ET AL

Table 2 Film layer and colloid cake layer thicknesses for filtration experiments of Figs 8ndash10

Item CMF Hc u g0 dftha dfex

b dcexc laquoc

d dfth Hc dfex Hc dcex Hc

no unit [mm] [cms] [s21] [mm] [mm] [mm] [] [2] [2] [2]

1 68 1727 96 334 12600 139 25 53 73 80 143 68 1727 384 1336 792 117 19 50 46 68 114 34 864 192 1336 792 109 92 66 92 13 11

aTheoretical film layer thickness according to Equation (10) bexperimental film layer thickness according to Equation (8) cex-perimental cake layer thickness (at 5h) derived from Equations (12) and (15) dexperimental cake layer porosity (at 5h) derived fromEquations (12) and (15)

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

was sensitive to thin deposit layers (lt1 of channelheight)

CONCLUSION

Laboratory-scale crossflow membrane filters withdifferent channel heights were used to test the influenceof channel height and shear rate on colloidal fouling ofsalt rejecting membranes The cake-enhanced osmoticpressure model was used to predict the effect of colloiddeposit layers on both flux decline and salt rejectionWhen combined with cake layer mass measurementsthe model provided a more complete picture of the roleof crossflow channel height and shear rate in colloidalfouling

Within a crossflow membrane filter of fixed channelheight increasing shear rate decreased the initial osmoticpressure drop colloid deposition and resultant flux de-cline while salt rejection was enhanced At constant vol-umetric feed flow rate higher shear in the filter with re-duced channel height dramatically reduced the initialosmotic pressure drop colloid deposition and flux de-cline At a fixed shear rate the initial salt rejection andosmotic pressure drops were nearly identical in filterswith different channel heights However the primarymechanism of flux decline cake-enhanced osmotic pres-sure was substantially higher in the filter with greaterchannel height Even though the same shear rate was ap-plied the deposit layer growth and extent of fouling waslimited by the channel height Finally by reducing chan-nel height all mechanisms of flux decline were reducedmdashinitial osmotic pressure trans-cake hydraulic pressureand cake-enhanced osmotic pressure while salt rejectionwas enhanced

ACKNOWLEDGMENTS

The authors would like to acknowledge the financialsupport of the American Water Works Association Re-search Foundation the National Science Foundation(Grant BES-0114527) and the Yale Institute of Bio-spheric Studies The authors would also like to thank Hy-dranautics Dow-FilmTec Trisep and Osmonics for sup-plying membranes and Nissan Chemical America Corpfor providing the colloidal silica particles

REFERENCES

BHATTACHARJEE S CHEN JC and ELIMELECH M(2001) Coupled model of concentration polarization andpore transport in crossflow nanofiltration AIChE J 47 2733

BHATTACHARJEE S KIM AS and ELIMELECH M(1999) Concentration polarization of interacting solute par-ticles in cross-flow membrane filtration J Colloid InterfaceSci 212 81

BLATT WF DRAVID A MICHAELS AS and NEL-SON L (1970) In JE Flinn Ed Membrane Science andTechnology Industrial Biological and Waste TreatmentProcesses Columbus OH Plenum Press p 47

BOUDREAU BP (1996) The diffusive tortuosity of fine-grained ulithified sediments Geochim Cosmochim Acc 603139

BRAGHETTA A DIGIANO FA and BALL WP (1998)Nom accumulation at nf membrane surface Impact of chem-istry and shear J Environ Eng-ASCE 124 1087

CHELLAM S and TAYLOR JS (2001) Simplified analy-sis of contaminant rejection during ground- and surface wa-ter nanofiltration under the information collection rule Wa-ter Res 35 2460

DAVIS RH (1992) Modeling of fouling of crossflow micro-filtration membranes Sep Purif Method 21 75

ELIMELECH M and BHATTACHARJEE S (1998) Anovel approach for modeling concentration polarization incrossflow membrane filtration based on the equivalence ofosmotic pressure model and filtration theory J Membr Sci145 223

ENDO Y and ALONSO M (2001) Physical meaning of spe-cific cake resistance and effects of cake properties in com-pressible cake filtration Filtr Sep 38 43

EVANGELISTA F (1985) A short cut method for the designof reverse-osmosis desalination plants Ind Eng Chem ProcD D 24 211

FAIBISH RS ELIMELECH M and COHEN Y (1998)Effect of interparticle electrostatic double layer interactionson permeate flux decline in crossflow membrane filtration ofcolloidal suspensions An experimental investigation J Col-loid Interface Sci 204 77

HOEK EMV (2002) PhD Thesis Department of ChemEng Yale University New Haven CT

HONG S FAIBISH RS and ELIMELECH M (1997) Ki-netics of permeate flux decline in crossflow membrane fil-tration of colloidal suspensions J Colloid Interface Sci 196267

HONG SK and ELIMELECH M (1997) Chemical andphysical aspects of natural organic matter (nom) fouling ofnanofiltration membranes J Membr Sci 132 159

KATAOKA T TSURU T NAKAO S and KIMURA S(1991) Permeation equations developed for prediction ofmembrane performance in pervaporation vapor permeationand reverse-osmosis based on the solution-diffusion modelJ Chem Eng Jpn 24 326

MALLEVIALLE J ODENDAAL PE and WIESNER MR

CROSSFLOW MEMBRANE FILTER GEOMETRY 371

ENVIRON ENG SCI VOL 19 NO 6 2002

(1996) Water treatment membrane processes In AmericanWater Works Association Research Foundation LDE andWater Research Commission of South Africa New York McGraw-Hill

MASKAN F WILEY DE JOHNSTON LP andCLEMENTS DJ (2000) Optimal design of reverse osmo-sis module networks AIChE J 46 946

MURTHY ZVP and GUPTA SK (1997) Estimation ofmass transfer coefficient using a combined nonlinear mem-brane transport and film theory model Desalination 109 39

PORTER MC (1972) Concentration polarization with mem-brane ultrafiltration Ind Eng Chem Prod Res Dev 11 234

SIRKAR KK DANG PT and RAO GH (1982) Approxi-mate design equations for reverse-osmosis desalination by spi-ral-wound modules Ind Eng Chem Prod Res Dev 21 517

SIRKAR KK and RAO GH (1981) Approximate designequations and alternate design methodologies for tubular re-verse-osmosis desalination Ind Eng Chem Prod Res Dev20 116

SONG L and ELIMELECH M (1995) Theory of concen-tration polarization in crossflow filtration J Chem SocFaraday Trans 91 3389

VAN DER MEER WGJ and VAN DIJK JC (1997) The-oretical optimization of spiral-wound and capillary nanofil-tration modules Desalination 113 129

VOROS NG MAROULIS ZB and MARINOSKOURISD (1997) Short-cut structural design of reverse osmosis de-salination plants J Membr Sci 127 47

VRIJENHOEK EM ELIMELECH M and HONG S(2001) Influence of membrane surface properties on initialrate of colloidal fouling of reverse osmosis and nanofiltra-tion membranes J Membr Sci 188 115

WIJMANS JG and BAKER RW (1995) The solution-dif-fusion modelmdashA review J Membr Sci 107 1

WILEY DE FELL CJD and FANE AG (1985) Optimization of membrane module design for brackish water desalination Desalination 52YIANTSIOS SGand KARABELAS AJ (1998) The effect of colloid stability on membrane fouling Desalination 118143

ZHU X and ELIMELECH M (1997) Colloidal fouling ofreverse osmosis membranes Measurements and foulingmechanisms Environ Sci Technol 31 3654

ZHU MJ ELHALWAGI MM and ALAHMAD M (1997)Optimal design and scheduling of flexible reverse osmosisnetworks J Membr Sci 129 161

ZYDNEY AL (1997) Stagnant film model for concentrationpolarization in membrane systems J Membr Sci 130275

372 HOEK ET AL