Filtration of Unipolarly Charged Aerosol Nanoparticles

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Journal of Colloid and Interface Science216,71–76 (1999)Article ID jcis.1999.6277, available online at http://www.idealibrary.com on

with an Initially Discharged Dielectric Screen

Manuel Alonso and Francisco Jose´ Alguacil

National Center of Metallurgical Research (CSIC), Avenida Gregorio del Amo 8, E-28040 Madrid, Spain

Received November 30, 1998; accepted April 14, 1999

PENETRATION MODEL

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This paper presents experimental results of penetration of nano-eter-sized aerosol particles through an initially discharged di-

lectric screen. Experiments have been carried out with two typesf monodisperse unipolarly charged particles having different di-lectric constants (Ag and NaCl) and mobility-equivalent particleiameters between 2 and 10 nm (Peclet number between 4 and 80).t the very beginning of the process, the screen is uncharged andltration is controlled by particle diffusion. As the number ofharges on the screen increases due to the diffusional deposition ofharged particles, an electric field of increasing strength is devel-ped between the dielectric screen and the conductive metallicalls of the cylinder where the screen is placed. As a result,articles are also driven and lost to the walls and penetrationecreases. This transient process can be well described by twoimensionless parameters, namely the Peclet number and a non-imensional number expressing the ratio of the particle driftelocity due to the field to the particle convective velocity due tohe flowing medium (air). © 1999 Academic Press

Key Words: aerosol penetration; aerosol filtration; dielectriccreen; Coulombic capture.

INTRODUCTION

Aerosol filtration efficiency is greatly enhanced by the pnce of electric charges on the filtering medium, regardlesharging state of the particles. Electrect filters, i.e., filaving a permanent electric charge (1), are widely usedleaning applications requiring high filtration efficiency.hese filters, both charged and neutral particles are capturlectrical forces in addition to other conventional mechanuch as interception, inertial impaction, and diffusion. In snstances, filtration efficiency may deteriorate with time aslter is loaded with particles (2).So far, investigation of electrostatic effects on filtrationainly dealt with relatively large submicrometric particles

lters having a permanent and roughly constant charge (3ontrast, we examine here the transient filtration procesighly diffusive very small (,10 nm) unipolarly charged pa

icles through an initially neutral dielectric filter which gradlly becomes charged as particles diffuse and deposit on

71

-hesir

bysee

s

Inof

it.

In the case of aerosol particles with diameters of the ordfew nanometers, the penetrationP (fraction of particles

assing uncaptured through the filter) through a singlecreen is uniquely controlled by Brownian diffusion ofarticles (4),

P 5 exp~2ShD!, [1]

here

S54ah

p~1 2 a!df[2]

s the screen parameter (a, screen solid volume fraction;h,creen thickness;df, fiber diameter), and

hD 5 2.7Pe22/3 [3]

s the single fiber efficiency for diffusional capture. Here,

Pe5udf

D[4]

s the Peclet number, relating the particle convectiveiffusive velocities (u, air flow velocity through the screen;D,article diffusion coefficient).The diffusional penetration model summarized above

een shown to be correct for particle size down to 0.6 nmor aerosol particles in any state of charge (positive, negatieutral) (5, 6).When the screen is made of a dielectric material the situ

s different. In the experimental work discussed below, aular dielectric screen is placed inside a grounded meylinder, in such a manner that the border of the screenontact with the metal wall. A certain fraction (given by 12 P)f the unipolarly charged particles flowing within the cylin

mpinge and stick on the screen fibers. The deposited chaissipated toward the grounded metal wall at a very slow

0021-9797/99 $30.00Copyright © 1999 by Academic Press

All rights of reproduction in any form reserved.

much slower than the rate at which new incoming particles arec utrb lopb f thp y te n ot net l)i ths rtal

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Ie ilityi nZ leea

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w ntcle

t etw

T perm

Estimation of the Electric Field

wp asf thecp thes agni-t onb end

w thes ed

T ens

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72 ALONSO AND ALGUACIL

aptured by the screen. As a result, the screen, initially neecomes gradually charged and an electric field is deveetween the screen and the cylinder wall. The motion oarticles toward the screen is then increasingly hindered bxistence of the electric field, and an increasing fractio

hem will be driven and lost to the cylinder wall. In this manhe efficiency of the filter (screen1 grounded metal walncreases with time. Particles are able to diffuse towardcreen as long as the electric field strength is below a ceimiting value (this will be estimated below).

According to these qualitative considerations, and assuhat mechanical (diffusion) and electric effects are additiveenetration model for a dielectric screen in contact wirounded metal wall can be written as

P 5 exp@2S~hD 1 hE!#, [5]

here hE is the single fiber efficiency for the electrostaapture mode. The electrostatic efficiency is usually givenunction of several dimensionless numbers which relatearticle drift velocity due to the field to the particle convecelocity u. Brown (3) has developed separate dimensionumbers to account for fiber-particle Coulomb and polariza

orces. Polarization forces are relevant when the particleeutral, which is not our present case. We have to connly the Coulomb field developed between the fiber andall, for which the corresponding dimensionless numbere expressed as

NC 5ZEf

u. [6]

n this equation,Z is the particle electric mobility, andEf is thelectric field at the fiber surface. In turn, the particle mob

s related to its diffusion coefficientD by Einstein’s equatio5 peD/kT, wherep is the number of charges on the particthe elementary charge,k the Boltzmann’s constant, andT thebsolute temperature.The electrostatic capture efficiency can also be affecte

he particle diffusive motion, so that in general we can w

hE 5 k1Pek2NCk3, [7]

here thek’s are constants to be determined from experimeSummarizing, the penetration of nanometer parti

hrough a dielectric screen in contact with a grounded mall can be finally expressed as

P 5 exp@2S~2.7Pe22/3 1 k1Pek2NCk3!#. [8]

his is the equation that will be used to correlate the exental results.

al,edehef

r

ein

ngea

ae

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,

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i-

The electric field at the fiber surface is given by (3)

Ef 5l

pe0df, [9]

herel is the charge per unit fiber length, ande0 the vacuumermittivity. The line charge densityl can be estimated

ollows. As long as the electric field strength is belowritical limit, a fraction [1 2 exp(2ShD)] of the unipolararticles flowing within the cylinder are deposited oncreen. Each of these particles contributes a charge of mude pe. Denoting byN0 the particle number concentratiefore the screen, the total chargeQ deposited onto the screuring a time intervalDt can be calculated as

Q 5 N0@1 2 exp~2ShD!# peqDt, [10]

here q is the aerosol flow rate through the screen. Ifcreen containsnf fibers of average lengthL f, the line chargensity can be written as

l 5Q

nfL f. [11]

he total fiber lengthnfL f can be calculated from the screolid volume fraction as

nfL f 5ahds

2

d f2 , [12]

hereds is the diameter of the circular screen, and all the oariables have been introduced before. Besides, the solid volume fraction can also be estimated from (6)

a 5ms

p

4d s

2rsh

, [13]

herems is the screen mass, andrs its density. Therefore, ahe variables in the right-hand side of [12] are known, andan insert this value into Eqs. [9]–[11] to evaluate the fielhe fiber surface.

It is important to remark that the validity of Eq. [10]imited by the value of the fiber electric field. Indeed, ifeld strength is too high, the diffusion of particles towardcreen is greatly hindered and the number of particles dted on the screen duringDt is smaller than N0[1 2xp(2ShD)]qDt, so that [10] no longer applies. The criticalue of the field above which [10] ceases to be valid ca

e them

T

w st aris s od cac xpm

wt cti t oc m,w8 owwt ep rticd get th

c ns ofE

no-p con-d bev eatedt ssest to aw ationt ationm f thed per-a ereg 6.1)a

r d ina heu ina sedt e-d derw tra-t unter(w reeno thed toa ticlel NC;f 10).

73AEROSOL FILTRATION WITH DIELECTRIC SCREEN

stimated as follows. The particle drift velocity towardetal wall due to the field is

vE 5 ZE 5ZQ

pe0dfnfL f. [14]

he particle mean thermal velocity is given by (7)

vD 5 Î8kT

pmp, [15]

heremp is the particle mass. The ratiovE/vD thus measurehe relative importance of the field-driven motion in compon with the diffusive motion. Assuming spherical particleensity 2 g cm23, and inserting the values of the physionstants and those of the screen used in the present eents, we find

vE

vD5 8.4 3 107

QZdp3/2

p, [16]

hereQ is in Coulombs,Z in cm2 V21 s21, anddp in nm. Inhe experiments, aerosol particles were charged in a radioaonizer. In this case, nanometer particles acquire at mosharge, so thatp 5 1. For a typical particle size of, say, 5 ne haveZdp

3/2 ' 1 (using the above units) and thus (vE/vD) '.4 3 107 Q. All the experimental results reported belere obtained for total screen chargeQ # 2 3 10210 C, so

hat the ratiovE/vD was below ;0.015. That is, we haverformed the experiments under the condition that the paiffusive velocity is at least two orders of magnitude lar

han the field-driven velocity and, therefore, estimation of

FIG. 1. Exp

-fleri-

ivene

lere

harge acquired by the screen at any given time by meaq. [10] is reasonably accurate.

EXPERIMENTAL METHOD

The experimental set-up is shown in Fig. 1. Aerosol naarticles where generated by a conventional evaporation–ensation method (8). A solid sample of the material toaporized is placed on a boat in an electric furnace and ho a prescribed temperature. A clean dry air stream pahrough the furnace and conveys the vaporized materialater bath at room temperature, where vapor condens

akes place and particles are formed. With this generethod one can, to a certain extent, produce particles oesired size by selecting appropriate values of heating temture and air flow rate. Particles of two different materials wenerated in this way: sodium chloride (dielectric constantnd silver.Aerosol particles were then bipolarly charged using a85Kr

adioactive ionizer (TSI 3077) and electrostatically classifiedifferential mobility analyzer (DMA, TSI short column). Tnipolarly (positive) charged particles with electric mobilitynarrow range leaving the DMA were alternately pas

hrough either a metal cylinder containing the filtrating mium (screen) or through a geometrically identical cylinith no screen in it (dummy unit). Particle number concen

ions were measured with a condensation nucleus coCNC, TSI 3025). Penetration was calculated asP 5 N/N0,here N is the particle number concentration at the scutlet, andN0 the number concentration at the outlet ofummy unit. The values ofN andN0 were both correctedccount for the CNC counting efficiency (9) and the par

osses in the tubing between the cylinder outlet and the Cor the latter, the Gormley–Kennedy equation was used (

mental setup.

eri

The filter unit consisted of a grounded cylinder made ofa rede mw reew tleT thg ds sea thfi acem s tt ths

esw en9fe thl ractt m-e

obi(v sizc tic( g tt t ip var esew (fun pet thes thl s io zine siw ap f ths

gd reo n iB lacb ugi n in tivec reem g1 clet thc ert do

for the selected particle size. Next, a different DMA voltagew n andd nor-m sixd sized cal-c n twos ens rought meds er-v tions( endo f( ffu-s ver-a se thes nt ofd r them btainp ounto

R

Eqs.[ sized Thep heckt hisc andd linesi mingt cha-n theo-r thodw mt .

C

ged att t isg atedw arep wellw uentr dica-t tatice ticle,t here etal

74 ALONSO AND ALGUACIL

luminum, 118 mm in length and 32 mm i.d., with tapends. Inside the cylinder, a series of aluminum rings 5 midth, 32 mm o.d., and 28 mm i.d. were placed. A mesh scas fixed between the two rings closest to the cylinder ouhe screen was thus in contact with the metal rings androunded cylinder wall, so that deposited charges can beipated away from the screen (at a very low rate in the cadielectric screen). The dummy unit was exactly equal to

lter unit, except that it contained no screen inside it. Plent of the screen at the rear end of the cylinder assure

he laminar flow is fully developed before approachingcreen.Preliminary experiments (see below the objective of there done with a wire screen made of stainless steel, op8 mm, fiber diameter 71mm, thickness 151mm, solid volume

raction 0.28, giving a screen parameterS 5 1.06. Themainxperiments were done with a PET (polyethylene tereph

ate, dielectric constant 3.0) screen with the following chaeristics: nominal opening, 100mm, fiber diameter, 70mm;hickness, 161mm; solid volume fraction, 0.24; screen parater,S 5 0.92.Particle size was inferred from the measured electric m

ty by means of the Stokes–Einstein equationZ 5 peC/3pmdp

p 5 1), whereC is the slip correction factor, andm the airiscosity. The use of a single DMA to measure the particlean give rise to considerable errors in the case of nanopar11, 12). The sizing error is large for particles correspondinhe tails of the original aerosol particle size distribution, buractically negligible for particles with sizes close to the aage particle size. We have made use of this fact in the prork. For a given set of generator operating conditionsace temperature and air flow rate), we have measured

rations only for particles with size in the neighborhood ofize distribution peak. Experiments were carried out wiarge number of different generator operating conditionrder to expand the range of particle size avoiding DMA sirrors. Preliminary penetration experiments were done uire screens, for which electrostatic effects are absentenetration theory quite accurate, to check the reliability oingle DMA size measurements.The main experiments of this work, i.e., those usin

ielectric screen, were carried out as follows. The PET scriginally, as received, had a certain level of charge oefore the experiments, the screen was left overnight petween the metal rings inside the cylinder (no air flow thro

t), in order to let it dissipate the charge. With the screeeutral state, experiments were done by passing posiharged particles of known size during 15 s through the sceasuring the concentrationN (average CNC output durin5 s), and immediately after diverting the stream of parti

oward the dummy unit for another 15 s and measuringorresponding number concentrationN0 (also averaged ovhe 15 s interval). Three more such measurements were

innt.e

is-ofe-

hate

e)ing

a--

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r-ne-

angngnde

aent.edhnlyn,

se

ne

as selected, and the four double measurements (screeummy) repeated for another particle size. A whole runally consisted of penetration measurements for five toifferent particle sizes (in the neighborhood of the aerosolistribution peak). Penetration for each particle size wasulated as the average of the four measurements. Betweeuchmeasuring runs,positively charged particles of a givize were passed continuously through the screen (only thhe screen) during a longer time interval; this can be tercreen charging run.Charging runs were done for time intals of a few minutes up to several hours, and concentraN andN0) were measured only at the beginning and at thef the screen charging period. The initial and final values oN0

corrected to account for CNC counting efficiency and diion losses in the tubing between filter and CNC) were aged. Knowledge ofN0 and dp (i.e., Peclet number) allowstimation of the total charge deposited by diffusion oncreen during the charging run, using Eq. [10]. The amoueposited charge was also calculated in the same way foeasuring runs themselves. In this manner, we could oenetration values as a function of particle size and the amf charge on the screen.

RESULTS AND DISCUSSION

eliability of Single DMA Particle Size Measurement

The Cheng–Yeh penetration theory, summarized by1]–[4] above, gives quite accurate predictions for particleown to 0.6 nm in the case of wire screens (5, 6).reliminary experiments with a wire screen were done to c

he validity of our single DMA sizing measurements. Thecking is shown in Figs. 2 and 3 for NaCl particlesifferent aerosol flow rates through the wire screen. The

n these two plots were calculated using Eq. [1], i.e., assuhat diffusional deposition is the only particle capture meism. As seen, the agreement between experimental andetical values is excellent. This proves that our sizing meith a single DMA, i.e., using only particles with size far fro

he tails of the aerosol particle size distribution, is reliable

harging and Discharging of the Dielectric Screen

We have stated above that the PET screen was discharhe beginning of the first run. The proof of this statemeniven by the results plotted in Fig. 4. The line was calculith Eq. [1], that is, assuming that no electrostatic effectsresent. The experimental data for the first run agree quiteith the diffusional penetration model. However, subseq

uns resulted in decreasing penetration values, a clear inion of filtration efficiency enhancement due to electrosffects. Furthermore, Fig. 4 shows that the smaller the par

he larger the filtration improvement—smaller particles (higlectric mobility) are more easily driven toward the m

c be-t

n wl airfl out q.( itiv

c beens then n wasa

D

n asa . As

el ford

beE

eteE

, andi

75AEROSOL FILTRATION WITH DIELECTRIC SCREEN

ylinder wall by the gradually developing electric fieldween the screen and the wall.

After run 4, the experiments were stopped and the screeeft overnight inside the cylinder (in contact with it) with noowing through it. The first penetration measuring run carriedhe next day gave again results in excellent agreement with Eline drawn in Fig. 4). The explanation is simple: the net pos

FIG. 2. Penetration through wire screen as a function of Peclet numxperiments done to check the accuracy of the particle sizing method.

FIG. 3. Penetration through wire screen as a function of particle diamxperiments done to check the accuracy of the particle sizing method.

as

t[1]e

harge deposited on the screen during the previous day hadlowly dissipated toward the grounded cylinder wall duringight, so that at the beginning of the second day the screegain electrically neutral.

etermination of the Constants in Eq. [8]

Figure 5 shows typical experimental values of penetratiofunction of particle size and the screen charge level

FIG. 5. Typical results of penetration against the screen charge levifferent particle sizes.

r.

r.

FIG. 4. Demonstration of the initial charging state of the PET screents evolution with time. Aerosol flow rate through the screen5 2 l min21.

e esw ond allep

set Eq[

T iner isfi zet set Naa df (ima

mc inr sea trefi Int ion(d ese

work has shown thathE is proportional to Pe20.49. The reasonf rentfi filterc s thec ddi-t n thec r. Asa o thes nceo herr d anyo

no-p n car-r res-s s ar thes en isp bers,p thea tione ncyd3

D

and

.

ngi-

.,

111 l

ptun

76 ALONSO AND ALGUACIL

xplained in a previous section, measurements were doncreen chargeQ below about 23 10210 C; it is in this rangehereQ can be estimated with a reasonable degree of cence using Eq. [10]. This figure shows again that for smarticles the decrease of penetration withQ is faster.The whole set of experimental data obtained in the cour

his work is plotted in Fig. 6. A regression analysis using8] gave the following result:

P 5 exp@2S~2.7Pe22/3 1 3.73Pe20.49NC0.69!#. [17]

his equation is plotted in Fig. 6 as a full line. The dashed lepresent the610% error interval. The data points in thgure have been obtained for several values of particle sihe range 2–10 nm (Peclet number between 4 and 80). Ashere is no systematic difference between penetration ofnd Ag particles, despite that these materials have quite

erent dielectric constants. This means that polarizationge) forces are not relevant in our case.It is interesting to note that the exponent of the Coulo

apture number, 0.69, is quite analogous to that obtaecently by Romayet al. (1) using electrect filters. Theuthors did experiments with three different types of eleclters and found exponents ofNC between 0.69 and 0.90.heir work, as well as in many other previous investigatsee (3) for a review), the electric capture efficiencyhE did notepend directly on the Peclet number. In contrast, our pr

FIG. 6. Correlation between penetration and Peclet and Coulomb caumbers.

for

fi-r

of.

s

inen,Clif--

bed

ct

s

nt

or this discrepancy must be found in the conceptually diffelter design we have used in this work. In our case, thean be regarded as consisting of the screen itself pluylinder wall, because the electric field promoting the aional particle capture mechanism is developed betweeharged screen and the grounded metal wall of the cylinderesult, in our experiments particles are deposited ont

creen (by diffusion) and onto the wall (mainly by the presef the electric field). In the previous investigations of otesearchers, particles were captured (by electric forces anther mechanism(s)) by the filtering medium alone.

SUMMARY

An experimental study of unipolarly charged aerosol naarticles penetration through a dielectric screen has beeied out. The screen, initially discharged, becomes progively charged as particles deposit by diffusion onto it. Aesult, an electric field is gradually developed betweencreen and the wall of the metal cylinder where the screlaced. Besides diffusional deposition onto the screen fiarticles are also driven and lost to the cylinder wall byction of the electric field, thereby enhancing the filtrafficiency of the system. The additional single fiber efficieue to Coulombic capture can be described ashE 5.73Pe20.49NC

0.69.

ACKNOWLEDGMENT

This work was supported by the Spanish Ministerio de Educacio´n y Cultura,GES, Grant PB96-0920.

REFERENCES

1. Romay, F. J., Liu, B. Y. H., and Chae, S. J.,Aerosol Sci. Technol.28,224(1998).

2. Walsh, D. C., and Stenhouse, J. I. T.,J. Aerosol Sci.28, 307 (1997).3. Brown, R. C., “Air Filtration: An Integrated Approach to the Theory

Applications of Fibrous Filters.” Pergamon, Oxford, 1993.4. Cheng, Y. S., and Yeh, H. C.,J. Aerosol Sci.11, 313 (1980).5. Alonso, M., Kousaka, Y., Hashimoto, T., and Hashimoto, N.,Aerosol Sci

Technol.27, 471 (1997).6. Ramamurthi, M., Strydom, R., and Hopke, P. K.,J. Aerosol Sci.21, 203

(1990).7. Flagan, R. C., and Seinfeld, J. H., “Fundamentals of Air Pollution E

neering.” Prentice-Hall, Englewood Cliffs, NJ, 1988.8. Scheibel, H. G., and Porstendo¨rfer, J.,J. Aerosol Sci.14, 113 (1983).9. Fissan, H., Po¨cher, A., Neumann, S., Boulaud, D., and Pourprix, MJ.

Aerosol Sci.29, 289 (1998).0. Gormley, P. G., and Kennedy, M.,Proc. R. Ir. Acad.52, 163 (1949).1. Alonso, M., and Kousaka, Y.,J. Aerosol Sci.27, 1201 (1996).2. Alonso, M., Kousaka, Y., Hashimoto, T., and Hashimoto, N.,J. Aeroso

Sci.29, 985 (1998).

re