review article a reconciliation of packed column

Review ArticleA Reconciliation of Packed Column Permeability DataColumn Permeability as a Function of Particle Porosity

Hubert M Quinn

TheWrangler Group LLC 40 Nottinghill Road Brighton MA 02135 USA

Correspondence should be addressed to Hubert M Quinn hubertwranglergroupcom

Received 14 November 2013 Accepted 2 January 2014 Published 1 April 2014

Academic Editor Carmen Alvarez-Lorenzo

Copyright copy 2014 Hubert M Quinn This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In his textbook teaching of packed bed permeability Georges Guiochon uses mobile phase velocity as the fluid velocity term inhis elaboration of the Darcy permeability equation Although this velocity frame makes a lot of sense from a thermodynamicpoint of view it is valid only with respect to permeability at a single theoretical boundary condition In his more recent writingshowever Guiochon has departed from his long-standing mode of discussing permeability in terms of the Darcy equation andhas embraced the well-known Kozeny-Blake equation In this paper his teaching pertaining to the constant in the Kozeny-Blakeequation is examined and as a result a new correlation coefficient is identified and defined herein based on the velocity frameused in his teaching This coefficient correlates pressure drop and fluid velocity as a function of particle porosity We show thatin their experimental protocols Guiochon et al have not adhered to a strict material balance of permeability which creates amismatch of particle porosity and leads to erroneous conclusions regarding the value of the permeability coefficient in the Kozeny-Blake equation By correcting the experimental data to properly reflect particle porosity we reconcile the experimental results ofGuiochon and Giddings resulting in a permeability reference chart which is presented here for the first time This reference chartdemonstrates that Guiochonrsquos experimental data when properly normalized for particle porosity and other related discrepanciescorroborates the value of 267 for the constant in the Kozeny-Blake equation which was derived by Giddings in 1965

1 Introduction

The value of the constant of proportionality between pressuregradient and fluid flow velocity in a column packed withgranular material and how it relates to column porosity havebeen controversial topics for some time [1] This is especiallytrue in the field of chromatography because columns packedwith porous particles have at least for the last 50 years beenthe main vehicle by which chromatographic separations havebeen carried out and thus this feature has added a newdimension to the controversy The complication arises inpart because of the difficulty of differentiating between thefree space between the particles and the free space withinthe particles in columns packed with porous particles aproblem that does not exist in the case of columns filled withnonporous particles

More recently because current chromatographic ana-lytical and purification applications are being driven by

the need for faster and faster separations the relationshipbetween pressure gradient and high rates of fluid velocityhas taken on a special significance [2] For example it isnow common to see the use of very small particles (circa2 micrometers) in combination with very large operatingcolumn pressures (circa 15000 psi) [3] Because of the obvi-ous impact of high operating pressure on the friability ofchromatographic support particles this development hascreated a new focus on the design criteria for packed columnsespecially with regard to the fractional porosities within thecolumns It will be appreciated that as the internal porosityof chromatographic support particles increases the particlesrsquoability to withstand high pressures decreases This physicalreality would seem to dictate that chromatographic supportparticles suitable for this newly defined operational regimeof high column pressures ought to have a lower particleporosity than those in common use for conventional columnpressures Paradoxically however one finds examples in the

Hindawi Publishing CorporationJournal of MaterialsVolume 2014 Article ID 636507 22 pageshttpdxdoiorg1011552014636507

2 Journal of Materials

recent literature pertaining to fully porous particles wherelow values for the constant of proportionality in the Kozeny-Blake equation are being justified on the basis of particleporosities which purportedly run counter to this principle[4] Clearly something is wrong

The value of the permeability coefficient dictated bythe necessity to balance the pressure gradientfluid flowequation after all independent variables are accounted for(and which presumably has its origin in the fundamentalmechanisms which underlie the generation of pressure in thefirst place) is by no means self-evident From the standpointof first principles it would appear that its value ought to beconstant regardless of the physical parameters comprising thefluid flow apparatus However no fully developed theoreticalexplanation for any constant of permeability has yet beenpublished On the other hand the literature is replete withdiscussions of the value for this parameter which purportedlyare justified on the basis of empirical data The problem isthat the authors of this literature do not agree with eachother and sometimes the same author disagrees with himselfIn the last few years Georges Guiochon in particular haspublished conflicting values for this parameter all of whichare supposedly based uponmeasured values yet he has madeno serious effort to reconcile the conflicts or to provide anyplausible underlying rationale for their differences

As we discuss below there are several inherent flawsin Guiochonrsquos teaching of permeability which are at theroot of his conflicting values for the coefficient We suggestthat these flaws originate in the fact that his teaching doesnot distinguish between the respective impacts on columnpermeability of (a) mass transfer by convection versus masstransfer by diffusion and (b) spherical particles versus par-ticles having an irregular morphology Accordingly withoutsubstantial refinement and adjustment Guiochonrsquos teachingof column permeability at best does little to overcome theshortcomings of Darcyrsquos law and at worst adds fuel to thefire of the aforementioned controversy

2 Guiochonrsquos Textbook Teaching

In his influential textbook Fundamentals of Preparativeand Nonlinear Chromatography [5] Guiochon (togetherwith his coauthors) bases his teaching of the pressureflowrelationship in streamline flow on the Darcy equation whichhe displays therein as his equation (526b) a rearrangementof which we repeat here

Δ119875

119871=

120583119905120578

11989601198892119901119898

(1)

where Δ119875 = pressure drop along column 119871 = length ofcolumn 120583

119905= mobile phase velocity 120578 = absolute viscosity of

fluid 119889119901119898

= average particle diameter and 1198960= Guiochonrsquos

residual permeability coefficientAll terms are self-consistent from a unit-of-measure

perspectiveNote that Guiochon does not discriminate in his expres-

sion of the Darcy equation between spherical and irregularparticles In other words in his statement of the equation

a spherical particle with a measured diameter of 119909 cm isequivalent to an irregularly shaped particle of the samemeasured diameter Peculiarly however he goes on to say thatldquotraditionally a value of 119896

0= 1 times 10minus3 is used for irregular

particles and 12 times 10minus3 for spherical onesrdquo [5 p 153]Similarly without including any porosity dependence

term in the pressurefluid flow relationship or specifyingany particular relationship between columnpressure gradientand column porosity for columns packed with either porousor nonporous particles he states that 119896

0varies ldquobetween 5 times

10minus4 and 2 times 10minus3 depending upon the compactness of thepacked bed that is on the external porosityrdquo [5 p 153]

In essence then Guiochon bundles the variables ofparticle morphology and column porosity into his residualpermeability coefficient 119896

0 Indeed this is why we call it his

residual permeability coefficientIn order to explore these implicit terms which are embed-

ded inGuiochonrsquos teaching for his 1198960 we turn for comparison

purposes to the well-known Kozeny-Blake equation

Δ119875

119871=1198750(1 minus 120576

0)2

120583119904120578

120576301198892119901

(2)

where 1198750= the KozenyBlake permeability coefficient 120576

0=

external porosity of column 120583119904= fluid superficial velocity

and 119889119901= spherical particle diameter equivalent

As we noted above Guiochon acknowledges in his teach-ing that particle irregularity does influence pressure drop Ina modification of the Kozeny-Blake equation proposed byCarman this factor was expressly accounted for by adding aparameter to represent particle sphericity which we denotewith the symbol Ω

119901(Carman gave it the symbol 120601 in his

original publication [6]) It will be appreciated that the valueof Ω

119901is equal to 1 for spherical particles and is less than 1

for particles having an irregular morphology Accordinglythe Kozeny-Blake equation (as modified by Carman)1 isexpressed as

Δ119875

119871=1198750(1 minus 120576

0)2

120583119904120578

12057630(119889

119901119898Ω

119901)2 (3)

where Ω119901= Carmanrsquos particle adjustment factor for devia-

tions from perfect sphericity and 119889119901119898Ω

119901= 119889

119901

As for column porosity note that the Kozeny-Blakeequation includes a combination of porosity terms whichtaken together can be viewed as its porosity dependenceparameter which we notate with the symbol Ψ

119900

Ψ0=(1 minus 120576

0)2

12057630

(4)

where 1205760= the volume of free space between the particles in

the columnthe volume of the empty columnComparing (1) and (3) the reader will observe that

there still is another difference the fluid velocity frames aredifferent Accordingly in order to establish the relationshipbetween the values of Kozeny-Blakersquos 119875

0and the value

of Guiochonrsquos 1198960 one needs to delineate the impact of

Journal of Materials 3

Guiochonrsquos velocity frame upon his permeability coefficientBefore attempting to do this a review of the various velocityframes typically used to characterize flow in porous mediamay be helpful

3 Fluid Velocity Frames

31 Superficial Velocity The fluid velocity term in both theDarcy equation and the Kozeny-Blake equation is the volu-metric flow rate of the fluid divided by the cross-sectional areaof the empty column This velocity is known as the ldquoaveragefluid superficial linear velocityrdquo or simply the ldquosuperficialvelocityrdquo and is defined as follows

120583119904=119876

A (5)

where 119876 = volumetric flow rate 119860 = cross-sectional area ofthe column and 120583

119904= superficial velocity

Thus superficial velocity is not influenced in any way bythe existence or structure of the packed bed Furthermore itdoes not change depending upon whether the particles in thebed are porous or nonporous

32 Interstitial Velocity Theconvective fluid velocity betweenthe particles of a packed bed is called the ldquoaverage fluidinterstitial linear velocityrdquo or simply the ldquointerstitial velocityrdquoInterstitial velocity is the superficial velocity adjusted for thecross-section of the actual fluid flow in a packed columnIt is related to the superficial velocity through the externalporosityof the column 120576

0 as follows

120583119894=120583119904

1205760

(6)

where 120583119894= average fluid interstitial linear velocity

If interstitial velocity is to be substituted for superficialvelocity in the Kozeny-Blake equation one must also includethe external porosity term This term is the compensationfactor that maintains the integrity of the value of the per-meability coefficient 119875

0between pressure gradient and fluid

superficial velocity The equation then becomes

Δ119875

119871=1198750(1 minus 120576

0)2

120583119894120578

120576201198892119901

(7)

33 Mobile Phase Velocity Guiochon does not use either thesuperficial velocity or the interstitial velocity in the equationsin his textbook Instead he uses the ldquomobile phase velocityrdquoMobile phase velocity is uniquely a chromatographic term Itis the velocity calculated as a result of injecting an unretainedfully permeating solute into the column and measuring thetime ofits elution It is defined as follows

120583119905=119871

1199050

(8)

where 1199050= the time it takes an unretained fully permeating

solute to traverse the column and 120583119905=mobile phase velocity

The velocity experienced by the flowing fluid in a columnunder steady state conditions is not altered by the existence ofldquoblindrdquo pores in the particles of that column Blind pores arepores within the particles which have only one fluid openingthat is they are not through-pores Accordingly under steadystate conditions the pores are already filled with identicalstagnant fluid and there exists no driving force to exchangethis stagnant fluid with the fluid flowing in the interstices ofthe particles It will be appreciated that column permeabilitydata is usually taken under steady state conditions in orderto take advantage of a constant value for fluid viscosityAlthough a solute which is dissolved in the flowing fluid willpenetrate the stagnant fluid in the pores (assuming it is notstrictly excluded by either physical dimension or chemicalinteraction) because of molecular diffusion the driving forcefor this solute migration is the concentration gradient of thesolute between the fluid outside the particles and the fluidinside the particles This intraparticle migration of the solutedoes not contribute to friction and thus must not be includedin velocity considerations related to pressure gradientMobilephase velocity therefore is not strictly a fluid velocity terminstead it is a misnomer and it would better be termed theldquounretained fully permeating solute velocityrdquo

Although Guiochon defines the relationship betweenfluid flow and pressure gradient in the context of a residualpermeability coefficient 119896

0 and acknowledges that column

porosity plays a role in that relationship his use of mobilephase velocity fails to recognize that molecular diffusion inblind pores of the particle fraction of a column packed withporous particles does not influence pressure gradient

Mobile phase velocity is related to fluid superficial veloc-ity however through the total porosity of the column ldquoTotalcolumn porosityrdquo 120576

119905 is a term peculiar to the chromato-

graphic literature which relates to the use of columns packedwith porous particles It is the fraction of the column volumetaken up by the free space between the particles plus thefraction of the column volume taken up by the free space inthe internal pores of the particles Thus it is the sum of theexternal and the internal column porosities

120576119905= 120576

0+ 120576

119894 (9)

where 120576119905= total column porosity and 120576

119894= internal column

porosityMobile phase velocity is related to fluid superficial veloc-

ity through the total porosity of the column as follows

120583119905120576119905= 120583

119904 (10)

Thus if mobile phase velocity is used in the Kozeny-Blakeequation one must insert the compensation factor 120576

119905into the

equation in order to maintain the integrity of the value of thepermeability coefficient 119875

0 between pressure gradient and

fluid superficial velocity and the equation then becomes

Δ119875

119871=1198750(1 minus 120576

0)2

120583119905120576119905120578

120576301198892119901

(11)


And now reconciling (1) and (3) we get

1198750(1 minus 120576

0)2

120583119904

120576301198892119901

=120583119905120576119905

1198960(119889

119901119898Ω

119901)2 (12)

4 The Flow Resistance Parameter

Before proceeding any further we digress to define anotherterm which will become important to our understanding ofGuiochonrsquos work The chromatographic literature containsa term called the ldquoflow resistance parameterrdquo [7] The fluidvelocity underlying this parameter is based upon Giddingsrsquodefinition of ldquomean fluid velocity through a cross-sectionrdquoand is found in his 1965 text book at page 207 [8]2 It is definedas follows

120601 =Δ119875119889

2

119901

120583119905120578119871

(13)

where 120601 = flow resistance parameterThe flow resistance parameter therefore is equivalent to

the reciprocal of Guiochonrsquos term 1198960

120601 =1

1198960

(14)

5 Refining the Terms For Column Porosity

In order to continue with our comparison of Guiochonrsquosteaching to that embodied in the Kozeny-Blake equation andin particular to accommodate columns packed with porousparticles we need to refine the porosity dependence term inthe Kozeny-Blake equation To accomplish this we adopt thedefinition of column porosity as taught by J Calvin Giddings[8] namely

Ψ =(1 minus 120576

119905Φ)

2

(120576119905Φ)

3 (15)

where Ψ = the porosity dependence term in Kozeny-Blake(porous particles) and

Φ =1205760

120576119905

(16)

where Φ = the ratio between the external and total columnporosities

Using thismethodology in themost general case involvingporous particles to express total column porosity (where totalcolumn porosity is not the same as external column porosity)as opposed to in the special case involving nonporous particles(where total column porosity and external column porosityare the same) the Kozeny-Blake equation (using mobilephase velocity as in (10)) may now be reexpressed as follows

Δ119875

119871=1198750(1 minus 120576

119905Φ)

2

120583119905120576119905120578

(120576119905Φ)

3

(119889119901)2

(17)

It will be appreciated that in the special case of columnspacked with nonporous particles (17) is identical to (3)because here 120576

119905= 120576

0and thus 120583

119905= 120583

119894= 120583

119904120576

0and Φ = 1

6 The Relationship between 1198960

and 1198750

We can now connect the teaching of Guiochon to thatembodied in the Kozeny-Blake equation as follows

1198750=

1

1198960Ψ

(18)

or

1198750=120601

Ψ (19)

As illustrated by (19) the term 1198750in the Kozeny-Blake

equation is the flow resistance parameter normalized for thecolumn porosity dependence term

Note that if1198750is a true constant the two parameters upon

which it depends 120601 and Ψ will vary in direct proportion toeach other This is illustrated by the data in Table 1 hereinwhich is a reference chart where particle porosity 120576

119901 is varied

from nonporous at one extreme to highly porous at the otherwhere 120576

119901= volume of the free space within the particles in

a packed columnthe total volume of all the particles in thecolumn

Figure 1(a) is a plot of the data contained in Table 1 as120601 versus Ψ Proceeding from the lower left hand corner tothe upper right hand corner of the plot particle porosityincreases It is obvious from the plot that all the data in Table 1falls on a single line with a slope of 267 which we say is theconstant value of 119875

0 As is illustrated by the plot in the range

of porosity covered by the data the values for 120601 vary fromabout 500 to about 1900 and correspondingly the values ofΨvary from approximately 2 to approximately 7 Note also thatthe upper boundary value of Ψ for packed columns is about55 with larger values related to capillaries

Finally we point out that once the value of 1198750is correctly

identified ameasured value for the flow resistance parametermay then be used to calculate the value of the externalporosity of the column 120576

0 when the latterrsquos value has not or

cannot be measured

7 Guiochonrsquos Modified PermeabilityCoefficient 119875

119905

As reflected in some of his recent publications which wewill explore in more depth later Guiochon inadvertentlyapparently confuses the term 119875

0with another parameter 119875

119905

which we identify here and define for the first time 119875119905is not

the same as 1198750because it is based upon Guiochonrsquos unique

(from a permeability perspective) teaching for fluid velocityIt is defined as follows

119875119905= 119875

0120576119905 (20)

where 119875119905= Guiochonrsquos modified permeability coefficient

It will be appreciated that Guiochonrsquos 119875119905 if used in the

Kozeny-Blake equation in place of 1198750 accommodates his use

of themobile phase velocity in away that is different from butequivalent to a direct conversion of mobile phase velocity tosuperficial velocity


Table1Colum

nperm

eabilityreferencetable

119870119865

Particlepo

rosity

rang

e120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905

(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm

cmgcmminus1 secminus1

cm3 m

inminus1

cmsecminus

1cm

secminus

1cm

secminus

1

Non

porous

particles

0380

1000

0380

000

0000

0160

711

1870

2662

701

141119864minus03

267

101

535119864minus10

15046

100

000100

000100

00100

038

0038

0100

0100

0390

1000

0390

000

0000

0147

653

1675

244

6627

153119864minus03

267

104

597119864minus10

15046

100

000100

000100

00100

039

0039

0100

0100

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

000100

000100

00100

040

004

00100

0100

0410

1000

0410

000

0000

0124

553

1349

2071

505

181119864minus03

267

109

742119864minus10

15046

100

000100

000100

00100

041

004

10100

0100

0420

1000

0420

000

0000

0115

509

1212

1907

454

196119864minus03

267

112

825119864minus10

15046

100

000100

000100

00100

042

004

20100

0100

Lowpo

rosity

particles

0507

0750

0380

0127

0204

213

948

1870

3549

701

106119864minus03

267

135

535119864minus10

15046

100

000100

000100

00100

051

0051

0133

0100

0520

0750

0390

0130

0213

196

871

1675

3261

627

115119864minus03

267

139

597119864minus10

15046

100

000100

000100

00100

052

0052

0133

0100

0533

0750

040

00133

0222

180

801

1502

2999

563

125119864minus03

267

142

666119864minus10

15046

100

000100

000100

00100

053

0053

0133

0100

0546

0750

0410

0136

0231

166

737

1349

2760

505

136119864minus03

267

146

742119864minus10

15046

100

000100

000100

00100

055

0055

0133

0100

0560

0750

0420

0140

0241

153

679

1212

2542

454

147119864minus03

267

149

825119864minus10

15046

100

000100

000100

00100

056

0056

0133

0100

Medium

porosity

particles

0613

0620

0380

0233

0376

258

1146

1870

4293

701

872119864minus04

267

164

535119864minus10

15046

100

000100

000100

00100

061

0061

0161

0100

0629

0620

0390

0239

0392

237

1053

1675

3946

627

949119864minus04

267

168

597119864minus10

15046

100

000100

000100

00100

063

0063

0161

0100

064

50620

040

00245

040

9218

969

1502

3629

563

103119864minus03

267

172

666119864minus10

15046

100

000100

000100

00100

064

0065

0161

0100

0661

0620

0410

0251

0426

201

892

1349

3340

505

112119864minus03

267

177

742119864minus10

15046

100

000100

000100

00100

066

006

60161

0100

0677

0620

0420

0257

044

4185

821

1212

3076

454

122119864minus03

267

181

825119864minus10

15046

100

000100

000100

00100

068

006

80161

0100

Highpo

rosity

particles

0760

0500

0380

0380

0613

320

1422

1870

5325

701

703119864minus04

267

203

535119864minus10

15046

100

000100

000100

00100

076

0076

0200

0100

0780

0500

0390

0390

0639

294

1306

1675

4891

627

766119864minus04

267

208

597119864minus10

15046

100

000100

000100

00100

078

0078

0200

0100

0800

0500

040

0040

0066

7270

1202

1502

4500

563

832119864minus04

267

214

666119864minus10

15046

100

000100

000100

00100

080

0080

0200

0100

0820

0500

0410

0410

0694

249

1105

1349

4140

505

905119864minus04

267

219

742119864minus10

15046

100

000100

000100

00100

082

0082

0200

0100

0840

0500

0420

0420

0724

229

1018

1212

3814

454

982119864minus04

267

224

825119864minus10

15046

100

000100

000100

00100

084

0084

0200

0100

Capillary

1000

0380

0380

0620

1000

421

1870

1870

7005

701

535119864minus04

267

267

535119864minus10

15046

100

000100

000100

00100

100

0100

0263

0100

1000

0390

0390

0610

1000

377

1675

1675

6273

627

597119864minus04

267

267

597119864minus10

15046

100

000100

000100

00100

100

0100

0256

0100

1000

040

0040

0060

010

00338

1502

1502

5625

563

666119864minus04

267

267

666119864minus10

15046

100

000100

000100

00100

100

0100

0250

0100

1000

0410

0410

0590

1000

303

1349

1349

5051

505

742119864minus04

267

267

742119864minus10

15046

100

000100

000100

00100

100

0100

0244

0100

1000

0420

0420

0580

1000

273

1212

1212

4541

454

825119864minus04

267

267

825119864minus10

15046

100

000100

000100

00100

100

0100

0238

0100


0200400600800

100012001400160018002000

20 30 40 50 60 70

NonporousLow porosityMedium porosity

CapillaryLinear (line)

Nonporous Low porosity particles

Medium porosity particles

High porosity particles

Capillary

Line slope (P0) = 267

y = 267x + 0

Ψ

120601

Line

High porosity

(a)

99111123135147159171183195207219231243255267

035 045 055 065 075 085 095

LineCapillaryLinear (line)

Capillary


y = 267x + 0

Pt

120576t

Φ = 10

Φ = 075

Φ = 062

Φ = 05

Φ = 075

Φ = 062

Φ = 05

Φ = 1

(b)

99111123135147159171183195207219231243255267

000 010 020 030 040 050 060 070 080 090 100

NonporousLow porosityMedium porosityHigh porosity

120576p

y = 160x + 107

Pt


(c)

Figure 1 (a) The balance between 120601 and Ψ (b) Column permeability reference chart (c) Particle permeability reference chart

In the 2006 edition of their textbook [9] Guiochon andhis coauthors provide the following worked example of hispressure dropfluid flow teaching3

In Table 2 a cross-reference is established between Guio-chonrsquos teaching for columns packed with both porous andnonporous particles the Kozeny-Blake equation (asmodifiedby Carman) and for validation purposes Giddingsrsquo teachingbased upon actual permeabilitymeasurements fromhis Table53-1 in his 1965 text [8]4

In his worked example Guiochonrsquos fluid velocity 119906is found in his text as his equation (256) [9] at page61 and equates to mobile phase not superficial velocityAccordingly when applied to columns packed with porousparticles his worked example combines the contributionto fluid velocity of mass transfer by molecular diffusionin the free space within the particles with mass transferby convection in the free space between the particles Asdiscussed above if one is attempting to compare Guiochonrsquos

teaching for the value of the permeability coefficient with thatof the Kozeny-Blake equation the conversion factor is thetotal porosity of the column

In addition because Guiochonrsquos particle sizeparameter has an embedded assumption due to particleshaperoughness his worked example also commingles thecontribution to spherical particle diameter equivalent ofparticle shaperoughness with other nonparticle variablesUnfortunately his worked example is not based uponcompletely spherical particles where this would not be anissue We know this because he states that 119896

0in his worked

example equals 1 times 10minus3 which he says is the value of thepermeability coefficient for columns packed with irregularparticles

In order to move forward one must simplify If this wereto be done experimentally it would best be accomplishedby experiments with nonporous particles in which case thevariable of molecular diffusion in the pores of the particles


Table2Cr

oss-referencefor

term

s119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm

cmgcmminus1 secminus1cm

3minminus1cm

secminus

1cm

secminus

1cm

secminus

1

Nonporousp

articles

Gidding

srsquotradition

alno

nporou

scolum

n040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

1000010

00010

0010

0399

004

00100

0100

Guiocho

nrsquostradition

alspheric

alparticle(app

arent)

0362

1000

0362

000

0000

0187

830

2293

3106

858

120119864minus03

267

97436119864minus10

15046

1000010

00010

0010

0361

0036

0100

0100

Gidd

ingrsquos

table5

3-1

5060meshglassb

eads

0422

1000

0422

000

0000

0113

500

1184

1873

444

200119864minus03

267

113

844119864minus10

15046

1000010

00010

0010

0421

004

20100

0100

5060meshglassb

eads

040

910

00040

9000

0000

0126

560

1371

2097

513

179119864minus03

267

109

729119864minus10

15046

1000010

00010

0010

040

70041

0100

0100

Guiochonrsquosteaching

ExA

irregular

particle

(app

arent)

040

010

00040

0000

0000

0225

1000

2500

2250

563

100119864minus03

444

178

400119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExA

correctedforp

article

irregularity

040

010

00040

0000

0000

0225

601

1502

2250

563

166119864minus03

267

107

400119864minus10

15046

078

00010

000

080010

0399

004

00100

0100

ExB

spheric

alparticle

(app

arent)

040

010

00040

0000

0000

0187

830

2075

2250

563

120119864minus03

369

148

482119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExB

corrected

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

Porous

particles

Gidding

srsquotradition

alpo

rous

column

060

0066

7040

00200

0333

203

900

1500

3375

563

111119864minus03

267

160

667119864minus10

15046

100

00010

00010

0010

0599

006

00150

0100

Gidd

ingrsquos

table5

3-1

3040meshalum

ina

0803

0498

040

00403

0672

271

1204

1499

4510

562

830119864minus04

267

214

667119864minus10

15046

100

00010

00010

0010

0801

0080

0201

0100

5060meshalum

ina

0837

0499

0417

0420

0721

235

1043

1246

3906

467

959119864minus04

267

224

803119864minus10

15046

100

00010

00010

0010

0835

0084

0201

0100

6080meshchromosorbW

(5DNP)

0766

0498

0382

0384

0621

316

1404

1833

5259

687

712119864minus04

267

204

545119864minus10

15046

100

00010

00010

0010

0764

0077

0201

0100

6080meshchromosorbW

(20

DNP)

0785

0495

0389

0396

064

8300

1333

1698

4991

636

750119864minus04

267

210

589119864minus10

15046

100

00010

00010

0010

0783

0079

0202

0100


would be eliminated and by using only smooth sphericalparticles such as glass beads in which case the variableof particle shaperoughness would be eliminated If both ofthese things were done one would be able to directly andunambiguously determine the true value of 119875

05

Accordingly since his textbook contains a general teach-ing without any expressed restrictions with respect to particleporosity let us first assume that the column in Guiochonrsquosworked example is packed with nonporous particles Sec-ondly let us assume that the value for the external porosityof the column (which is the same as the total porosity ina column packed with nonporous particles) is the valuetraditionally assumed for a typical well-packed column thatis 04

As illustrated by example A in Table 2 this would leadto an apparent value for 119875

0of 444 which is obviously much

too high6 Using the adjusted particle size of 8 micrometers(rounded) which is calculated based on a value of 078 forΩ

119901

we derive values of 267 for 1198750and 107 for 119875

119905(the relationship

between these two values is of course equal to the totalporosity of the column 120576

119905 as is dictated by (20))

Similarly as illustrated by example B in Table 2 when thecolumn of Guiochonrsquos worked example is adapted to accom-modate spherical nonporous particles Guiochonrsquos teachingof the value for 119896

0of 12 times 10minus3 results in an apparent value

of 369 for 1198750

7 again too high [10 11] On the other hand ifwe correct the value of 119875

0 we get a column external porosity

of 03620which is too low for a typical well-packed column(120576

0= 04) [8] Moreover in the case of both corrections

Guiochonrsquos teaching overstates the pressure gradient (187 psicompared to the 135 psi which Giddingsrsquo experiments wouldgenerate) Accordingly it is only when we correct for thepressure drop that we achieve appropriate values of 04 for1205760 267 for 119875

0 and 107 for 119875

119905

As is evident from Table 2 when the porosity of columnspacked with nonporous particles varies the value of 119875

119905also

varies because it is based upon the measurement of mobilephase velocity which in turn changeswith the porosity of thecolumn Indeed for typical columns packed with nonporousparticles having external porosities close to 04 (038ndash042)[8] Table 2 reveals that the value of 119875

119905varies by as much as 6

points while the value of 1198750remains constant at 267

Having established a range of values for 119875119905based upon

columns packed with nonporous particles one can nowproceed to evaluate the range of values for 119875

119905based upon

columns packed with porous particles which is to say thatwe can now evaluate the impact of particle porosity onpermeability Among other things Table 2 shows that whenit comes to porous particles Guiochonrsquos 119875

119905is even more

variable (and thus even less useful) because the value ofthe coefficient can differ on a column-to-column basis byas much as 90 points depending on the combination of theinternal andexternal column porosities at play

Figures 1(a) and 1(b) are a plot of the data found in Table 1In this plot Guiochonrsquos modified permeability coefficient 119875

119905

is plotted against column total porosity 120576119905 Once again it will

be appreciated that (a) all data falls on a line with a slope of267 which represents the value of 119875

0and (b) the line has no

intercept which means that when 120576119905is zero 119875

119905is also zero As

shown in the plot values of the parameter Φ are highest atlow values of 119875

119905and lowest at high values of 119875

119905 Further as is

evidenced by the respective definitions for the terms119875119905and119875

0

contained herein the only time that the value of Guiochonrsquos119875119905does not differ from the value of 119875

0(267) is when the value

of 120576119905is 1 its value in a theoretical packed column devoid of

particles that is acapillaryFinally Figure 1(c) is another plot of the data in Table 1

but this time the values for 119875119905are plotted against particle

porosity 120576119901 The equation of this line does have an intercept

which represents the value of 119875119905when the particles are

nonporous It is also obvious from the equation of this linethat it is only when particle porosity is unity that is in acapillary that the value of 119875

119905is 267

It will be appreciated that since 120576119905is the sumof the internal

and external porosities of a packed column any given valuefor 119875

119905involving a column packed with porous particles can

represent many different combinations of these parametersVice versa any given value for 120576

119905can generate many different

values for 119875119905depending on the amount of particle porosity

which is present On the other hand as is pointed outearlier column internal porosity andor particle porosityplay no role in determining the permeability of a packedcolumn the only porosity parameter which is relevant forsuch purposes is column external porosity In other words asa permeability coefficient 119875

119905is not a particularly informative

concept because it still fails to provide any meaningful tie tothe underlying physical phenomena that govern the pressuredropfluid flow relationship

In the case of permeability measurements one quan-tifies only total pressure drop Pressure drop however isa commingling of the contributions of the several differ-ent parameters embodied in the pressureflow relationshipTherefore one must accurately represent the contributionof each factor before adding them together to equal thepressure drop Obviously if one mistakes the contribution ofany given element for instance particle size this will skewthe contribution of some other element when summed forinstance column porosity

Our frame of reference has been calibratedwith respect tothe interrelationships between the values of 119875

0 119875

119905 120576

119905 and 120576

119901

based on the data reported in Giddingsrsquo table 53-1 in his 1965textbook Since his data base was derived from experimentsusing nonporous particles the permeability results of whichwere extended to columns packed with fully porous particlesby using his Φ parameter the validity of which in turn wasestablished by independent means there is no uncertaintywith respect to the critical variable of external porosity 120576

0

inherent in our frame of reference It is for this reasontherefore that our frame of reference trumps any reporteddata which uses any other technique including the techniqueof inverse size exclusion chromatography by itself to establishvalues for 120576

0[12] In addition our frame of reference is

internally consistent due to the grounding of the parametersat the boundary condition of a theoretical capillary at whichpoint the values of 120576

119905and 120576

119901are unity and the values of 119875

0and

119875119905are equal In essence these interrelationships exemplify the

conservation laws of nature which are the ultimate standard


of measure when considering partial fractions of a singleentity

Consequently as Figures 1(b) and 1(c) illustrate if oneknows based upon other independent means the value of acolumnrsquos total porosity or its particlesrsquo porosity respectivelyone can at least verify whether results of permeability exper-iments expressed in terms of 119875

119905are reasonable Or to put

it another way if the 119875119905results reported do not conform to

what these plots tell us one should expect from columns andparticles based upon independently derived porosity valuesfor the particles under study we know that something iswrong Accordingly this is the way in which we use 119875

119905below

to analyze and evaluate Guiochonrsquos experimental work of thelast decade

8 The Origin of Guiochonrsquos Value forColumn Permeability

In 1966 Guiochon wrote a review paper entitled ldquoProblemsRaised by the Operation of Gas Chromatographic Columnsrdquo[13] In that paper he reviewed the development of the per-meability equation from Darcy to the then present Amongother things he reported that ldquoa mean 120576 of 038 is foundfor a number of packings obtained from powdered prod-ucts of various origins consisting of spherical or irregularparticles Almost all the measured values are between035 and 045rdquo (p 14) He then went on to discuss what hecalled the ldquosemiempirical Blake-Kozeny equationrdquo which hereported as 119896 = [119889

2

1199011205762][150(1 minus 120576)

2] [13 p 15 Equation

(11)] What sticks out of course is the fact that Guiochonstates here that 119875

0equals 150 the value for the permeability

coefficient championed by Ergun not the value posited byCarman To be fair we should point out that Guiochongave warning that he was uncomfortable with any particularvalue for the permeability coefficient For even though herecited the Kozeny-Blake equation with a value of 150 for itspermeability coefficient he stated that ldquothe values of 119896 givenby (this) equation are not very accurate and the deviationscan be as large as 50rdquo [13 p 15] Guiochon attributedmost ofthis uncertainty to the inability of practitioners of that era toeffectively measure the value of a columnrsquos external porositySince as he pointed out ldquo(the Kozeny-Blake) equation isvery sensitive to variations in 120576rdquo he concluded that theequation is ldquoof little userdquo and that it was better practice torely upon grosser measurements of permeability [13 p 15]Thus Guiochon at this timeframe made a conscious decisionto staywithin the relatively safe but admittedlymore obscureboundaries of Darcyrsquos teaching on column permeability

In 2006 however Guiochon emerged from under theshadow of Darcy permeability when he published a reviewpaper which purported to be a comprehensive summaryof the current state of the art in chromatography [14]In light of the fact that Guiochon and his coauthors hadvirtually contemporaneously published a new version of theirtextbook one would have expected that Guiochon wouldtake this opportunity to reaffirm his textbook teaching So itshould come as no surprise that he would open his discussionof the pressure dropfluid flow relationshipwith the following

assertion ldquothe permeability of packed beds used in liquidchromatography is in the order of 1 times 10minus3rdquo [14 p 9] Asone would expect the authority which Guiochon cites forthis seemingly familiar proposition is the 2006 edition of hisown textbook For the first time however he also providessome citations to third party sources In particular he cites a1997 chromatography handbook written by Uwe Neue ChiefScientist for Waters Corporation [15 p 9] As one can seeNeuersquos equationmdashlike Guiochonrsquosmdashdoes indeed postulate apermeability coefficient with a value of 1 times 10minus3

At this point however Guiochon abandons his tradi-tional caution about the value of the permeability coeffi-cient and marries his permeability equation to the Kozeny-Blake equation thereby endorsing not only the porositydependence term in that equation but also a specific valuefor 119875

0 Referring to his value of 1 times 10minus3 he states the

following ldquothe specific column permeability is related to thecolumn porosity through the Kozeny-Carman equation 119896

119891=

12057630180 (1 minus 120576

0)2rdquo [14 p 9] Not surprisingly Neue makes

the same connection ldquothe specific permeability depends onthe particle size 119889

119901and the interstitial porosity 120576

0of the

packed bedThe relationship is known as theKozeny-Carmanequation 119861

0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]

Neuersquos permeability equation and Guiochonrsquos textbookpermeability equation however differ in that Neue uses thesuperficial not the mobile phase velocity Accordingly sinceall other features of their equations are the same one wouldexpect them to get different values for their permeabilitycoefficients Neue himself recognizes this when he says inhis handbook ldquothis value [1000] is also in good agreementwith our experience but values as low as 500 have beenreported in the literature8 However there are several reasonswhy different values reported by different workers do notrepresent true differences in the resistance parameter Firstlower values are obtained for porous packings if the specificpermeability is measured on the basis of the breakthroughtime of an unretained peak instead of using the flow raterdquo see[15 p 32] (when he distinguishes the ldquobreakthrough time ofan unretained peakrdquo from the ldquoflow raterdquo Neue is of coursereferring to the mobile phase velocity and the superficialvelocity resp) Consequently if one takes Neuersquos point andturns it on its head one can see that if he and Guiochonwere to get the same value for their permeability coefficients[1000] but one (Guiochon) is using mobile phase velocityto derive it and the other (Neue) uses superficial velocity toderive it this would indeed represent a ldquotrue differencerdquo intheir equations

So how can Guiochon cite both Neue and himself for theproposition in his review paper that ldquothe permeability of thepacked beds used in liquid chromatography is in the order of1times 10minus3rdquoThe answer is that at least for purposes of his reviewpaper he adopts Kozeny-Blakersquos fluid velocity convention inplace of the velocity frame he uses in his textbook Here iswhat he says ldquothis approximation [1 times 10minus3] is valid only ifthe superficial velocity is usedrdquo [14 p 9] (emphasis supplied)

As a matter of pure mathematics Guiochonrsquos permeabil-ity coefficient of 1 times 10minus3 can only be equal to 1205763

0180(1 minus 120576

0)2

if the value of 1205760is 04 the typical value for the interstitial


fraction of a well-packed column Guiochon confirms in hisreview paper that this is indeed what he assumes in his state-ment of the Kozeny-Blake equation [14 p 9] Accordinglyhis adoption of the value of 180 for 119875

0solely depends on the

validity of his assertion that the value of the permeabilitycoefficient is 1 times 10minus3

We already know from our discussion of Guiochonrsquostextbook teaching that when this value is associated with apermeability equation based on mobile phase velocity it iswrong As reflected in our Table 2 when Guiochonrsquos workedexample involving this figure is corrected to account for theembedded factor due to the irregularity of the particles whichhis worked example assumes the value of the permeabilitycoefficient generated by his equation is not 1 times 10minus3 it is 166times 10minus3

So where did this value of 1 times 10minus3 come from AlthoughGuiochon in his review paper cites Neuersquos handbook for thisvalue Neue himself offers absolutely no authority for it Onthe other hand Guiochon does provide one other citation inhis review paper for this value The citation is to an article byHalasz et al published in 1975 [16]

If one then goes to that article one sees that Halaszet al do indeed proffer the same equation as Neue (albeitin a somewhat different format) and yes it does containthe value of 1 times 10minus3 See [16 Equation (1)] Neverthelessthe authors fail to identify from whence they obtained thisvalue On the other hand they do make reference to apaper that Endele et al wrote a year earlier in 1974 withKlaus Unger entitled ldquoInfluence of the Particle Size (5ndash35 120583)of Spherical Silica on Column Efficiencies in High-PressureLiquid Chromatographyrdquo [17] It appears that this is wherethe body is buried for it is in this article that Halasz reportshaving actually derived a value of 1 times 10minus3 for the permeabilitycoefficient

In summarizing the results of their experiments whichincidentally are based on measurements of superficial notmobile phase velocity (see their Equation (7)) Halasz et alcalculate an average value for the permeability coefficient(which they notate as119870

119865) of 1198892

1199011080 Accordingly they state

the following ldquo[I]t is proposed to define an average particlesize 119889

119901 for columns packed with spherical silica using the

balanced density packing method by the equation 1198892119901

=

1198701198651000 = 1198651205781198711031199032120587Δ119875rdquo [17 p 382 their Equation (7)]To recapitulate it thus appears that (1) Halasz was the

source of the value of 1 times 10minus3 for the permeability coefficientwhich Guiochon adopts in his review paper (2)Halaszrsquo valuewas based upon measurements which involved sphericalparticles and (3)Halaszrsquo value was properly derived from anequation which utilized the superficial velocity as the fluidvelocity

However we still have a problem if we are going to acceptthe value of 1 times 10minus3 as a basis for calculating the constantin Kozeny-Blake we still need to know the value of Halaszrsquocolumnsrsquo external porosity For example in the absenceof measured values for the external porosity Guiochonrsquosassertion in his review paper that the value of the constantis 180 is without foundation

Unfortunately however Halasz bases his methodologyon ldquoassumedrdquo versus ldquomeasuredrdquo values for external porosityNevertheless he does provide some clues that may helpus peel back this onion First he says that his value forthe permeability coefficient applies to ldquocolumns using thebalanced density packing methodrdquo Secondly after statinghis proposed value for the coefficient we find the followingtelltale sentence ldquothe permeability of columns packed by theconventional ldquodryrdquo method are worse by a factor of about 2than those packed by the balanced density methodrdquo [17 p382] For this proposition Halasz cites yet another of his ownarticles this time a paper written by himself and M Naefein 1972 entitled ldquoInfluence of Column Parameters on PeakBroadening in High-Pressure Liquid Chromatographyrdquo [18]

When one follows this thread by going to Halaszrsquos 1972paper one finds a possible solution to the puzzle For this iswhere Halasz describes his calculations of the permeabilitycoefficient from experiments with a number of conventionaldry-packed columns containing spherical silica particlesNot surprisingly the resulting value for the permeabilitycoefficient for such columns was not 1 times 10minus3 Instead Halaszsays that his experiments with such columns resulted inthe following value for the permeability coefficient ldquo119870 sim

11988921199012000rdquo [18 p 78] In other words consistent with what

Halasz says in his 1974 article the value for the coefficient forthese dry-packed columns was indeed ldquoworse by a factor ofabout 2rdquo compared to its value for columns prepared with thebalanced density method

The obvious implication of this is that when Halasz gota value of 1 times 10minus3 for the permeability coefficient in 1974he must have been evaluating columns that were packed toan interstitial fraction considerably higher than the externalporosity of the columns that were the subject of his 1972experiments Our problem however is still not resolvedbecause Halasz did not accurately determine the externalporosity of the columns under study in either the 1972 or 1974columns

We surmise that in their 1972 paper Halasz and hiscoauthors made use of the teaching of Giddings outlinedin his 1965 textbook which at the time of their 1972 paperwas seven years old Here is what they say ldquoexperiencehas shown that in a regular packed column with the sievefractions usual for chromatography 120576

0is independent of the

particle size if the particles are more or less spherical In anacceptable approximation 120576

0is equal to 04 In those columns

packed with nonporous supports 119906V and 119906 are identicalUsing porous supports (ie silica gel alumina chromosorbPorasil and so forth) 119906 = 4119865(1205871198892

119888120576119879) where 120576

119879is the

total porosity and indicates the pore volume of the supportrdquoIt will be appreciated that 119906V stands for interstitial velocity(our 120583

119894) and 119906 stands for mobile phase velocity (our 120583

119905) The

ldquoexperiencerdquo which Halasz and his coauthors are referringto concerning ldquocolumns packed with nonporous supportsalumina and chromosorbrdquo is that recorded by Giddings inTable 53-1 in his 1965 text Continuing to establish theinterrelationships inherent in the various entities involvedin chromatographic columns with respect to both interstitialandmobile phase velocity the authors conclude ldquoformally 119906V


can be calculated for a porous support assuming 1205760is equal

to 04rdquo (emphasis supplied) The authors then announce themethodology underlying their frame of reference with regardto column permeability as follows ldquowe determined in all ofour columns the 119906119906V ratio to be 056 with a differentialrefractometer Consequently the total porosity 120576

119905was equal

to 0714rdquo It will be appreciated that their ratio of 119906119906V is oneand the same as GiddingsrsquoΦ parameter as utilized by him inhis 1965 textbook and as we define hereinabove

We can now identify the origin of the discrepancybetween Halasz and Giddings and by extension betweenHalasz and Guiochon (and Neue) For even though Halaszmakes use of the results in Giddingsrsquo Table 53-1 he failsto appreciate the teaching inherent therein regarding theimportance of an accurate value for column external porositywhen using porous particles In establishing his values forΦGiddings was careful to ground his values for the externalporosity of columns packed with porous particles in acomparison of their measured pressure drops with measuredpressure drops in columns packed with nonporous particleswhere the values for (external) porositywere accurate becausethey are equal to the columnsrsquo total porosity

In their 1972 paper Halasz et al used a refractometer todetect the inert solute 119899-pentane in the mobile phase of 119899-heptaneThey injected the 119899-pentane into the flowing mobilephase the flow rate of which they presumably measured witha volumetric cylinder and stop watch Since the exit timeof the 119899-pentane peak was identified by the refractometertheir measurement of holdup volume was accurate andaccordingly so was their value of 0714 for 120576

119905(there is no

uncertainty related to column total porosity when using inertsolutes)This in turn led to an accurate value for their119906 termmobile phase velocity However since they did not measurethe interstitial velocity 119906V but rather used an estimate basedupon the measured flow rate and an ldquoassumedrdquo value of 04for external porosity their calculatedestimated value for 119906Vwas arbitrary This in turn means that the value of 056 fortheirΦ ratio was likewise arbitrary

In Table 3 herein we show the results for column number1 in the 1972 study which we designate as Column A

1 Note

that the authorsrsquo raw values correspond to a value of 500 for1198750 a valuewhich is obviously far too high As is plainly evident

in our Figures 2 and 3 this column data set does not conformin any reasonable fashion to the norms in our referencecharts Accordingly the data is badly flawed In our correcteddata for Column A

1in Table 3 herein we adjust the column

external porosity to the lowest value permitted in our frame ofreference (038) This correction results in a revised value forGiddingsrsquoΦparameter of 0532 In additionwe are compelledto adjust the particle downward (to 11 micrometers approx)as is also dictated by our frame of reference We justify ourlow corrected value for external porosity and our downwardadjustment for particle size on the aggressive ldquodry-packingrdquoprocess described by the authors ldquo[T] the best results wereachieved with the following method the column (id =2mm) 25 cm long was packed with 25 equal portions of theldquobrushrdquo After adding each portion the column was vibratedand afterward tapped on the floor and also vigorously tappedwith a rod from the siderdquo Based upon a column packing

experience of the principal author herein spanningmore than30 years we believe that these packing conditions generateda packed column with a low external porosity and also one inwhich the particles experienced significant breakage

The main differences between the columns in the 1972and 1974 papers concerned the particle sizes and themethodsused to pack the columns The particle diameters in the 1972study fell in a range of about 15ndash200 micrometers while thosein the 1974 study were much smaller being in the range of 5ndash40 micrometers approximately Moreover while the columnsin the 1972 study were dry-packed the columns in the 1974study were slurry-packed (what Halasz calls ldquothe balanceddensity packing methodrdquo) The authors of the 1974 paperrecite that their permeability results shown in their Table 4correspond to values for 120601

0of 1080 and values for 120601 of 910

In Table 3 herein we show the results for the 1974 study as anaverage value in our column designated as A

2 Note that the

raw data reported by the authors which again has the built-inassumption that the column external porosity was 04 placesthe value of 119875

0at 192 In our corrected values for Column A

2

we show that a value of 267 for 1198750places the column external

porosity at a value of 043 The ratio of the value for 120601 of 910when compared to the value for 120601 in the 1972 study of 2007is about 22 (2007910 = 22) which is in good agreementwith the authorsrsquo statement that the permeability of the 1972columns was worse by a factor of about 2 Again based onthe experience of the principal author herein in the packingof hundreds of thousands of commercially sold slurry packedcolumns we conclude that the balanced density techniquedescribed by the authors in the 1974 paper is fully capable ofproducing columns with this high and external porosity

In summary we conclude that for purposes of theKozeny-Blake equation (a) the external porosity of theHalasz 1972 columns was 038 (b) the external porosity of thecolumns which he tested in 1974 was 043 and (c) Halaszrsquos1972 and 1974 studies when properly analyzed corroborateGiddingsrsquo value for 119875

0of 267 not Carmanrsquos value of 180

Although the fault for all of the misdirection about the valueof the permeability coefficient being 1 times 10minus3 therefore restsprimarily on the shoulders of Halasz one has to question whyGuiochon (andNeue) so readily adopted itWhatevermay bethe reason Guiochonrsquos support for this proposition has beenand continues to be a cause for much of the conventionalacceptance of Carmanrsquos (erroneous) figure of 180 as thecharacteristic value of the coefficient in the Kozeny-Blakeequation

9 Guiochonrsquos Experimental Data

In addition to the data from Halasz 1972 and 1974 studiesTable 3 herein contains data from a representative sampleof Guiochonrsquos personal experimental permeability investi-gations over approximately the last decade as reported inthe numerous trade journals particularly the Journal ofChromatography A In each case the table has a single rowdedicated to Guiochonrsquos reported raw data and a single rowdedicated to corrected values for each column based on thereference chart in Table 1 herein

12 Journal of MaterialsTa

ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm

cmgcmminus1secminus1cm

3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

000

028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

2161

400

173119864minus03

267

144

729119864minus11

393119864minus11

1500

046

088

000

023

000

0205

000

41300

030

070

056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

0419

197

725

1142

4865

766

138119864minus03

149

95399119864minus11

253119864minus11

300

021

100

000

017

000

0170

00035

100

048

129

076

Colum

nF 2

rawdata

064

200581

03730

0269

0429

361

807

1258

4863

758

124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

000

017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

03800

0259

0418

1014

752

1177

4476

701

133119864minus03

168

107

384119864minus11

246119864minus11

1500

021

100

000

017

000

0170

00035

100

048

127

075

Colum

nF 1

corrected

06350

0630

040

000235

0392

197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

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150

98434119864minus11

285119864minus11

1500

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100

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017

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0170

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050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085

LineAll corrected data

Linear (all corrected data)Squares raw data Triangles corrected data

Pt

120576t

D seriesI seriesJ seriesF series

H seriesA seriesB seriesC seriesE series

J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2

y = 267xLine slope = 267

Figure 2 Summary of experimental results

0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ

LineAll corrected dataD seriesI seriesJ seriesF series



J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6

Squares raw data Triangles corrected data


Figures 2 and 3 herein are graphical representations ofTable 31015840s raw and corrected data for Guiochonrsquos columnsplotted in the same reference frames as in Figures 1(a) and1(b) respectively

As shown in the plots of the thirty-one total columnsevaluated in this data base only six columns had reportedraw data values for 119875

0close to the normThese were columns

B2 C E

1 H

4 J

1and J

2 Interestingly of the six conforming

columns 3 of the columns were packed with fully porousparticles and 3 columns with partially porous particles Itcan be seen however that when properly interpreted andadjusted all of Guiochonrsquos experimental data falls fairlywithin the norms outlined in the reference chart in Table 1In order to explore the reasons why the raw data does notconform more closely to the norms outlined in Table 1 eachof Guiochonrsquos studies included in Table 3 is evaluated in turn

Finally Table 4 herein is a list of symbols and parameterdefinitions used throughout this paper as well as their unitsof measure

91 Guiochonrsquos 1998 Study In a 1998 publication by Kohand Guiochon entitled ldquoEffect of the Column Length on theCharacteristics of the Packed Bed and the Column Efficiencyin a Dynamic Axial Compression Columnrdquo [19] Guiochonand his coauthor report the results of a study they hadcarried out on column packing using a rather novel techniquewhich was a combination of slurry packing and mechanicalcompression

The study involved the packing of a single cylinder ofdiameter 5 cm to various column lengths ranging between 1and 25 cm approximately The particles were all silica basedand coated with a reverse stationary phase C

18 However two

different categories of particles were involved One categorycontained highly irregular particles which were about 130micrometers in average diameter In addition these particleshad a high specific pore volume (11mLg) and exhibitedsignificant particle breakage under the packing conditionsinvestigated in the study Conversely the other particlecategory involved very small particles (6 micrometers) whichwere spherical in shape had a low specific pore volume(03mLg) and exhibited a greater ability to withstandparticle breakage under the studyrsquos packing conditions

The permeability data for the irregular particles isneglected herein because according to the authors theparticles exhibited significant breakage during packing andwithout an accurate value for the characteristic dimensionof the particle the data cannot be used in the Kozeny-Blake model to determine the value of 119875

0 The spherical

particles on the other hand behaved successfully under thepacking conditions chosen and yielded values calculated bythe authors for 119875

0of 619 268 226 and 229 for the four

different lengths of columns studied The data for thesecolumns is reported in our Table 3 in the rows for ColumnsB1through B

4 The higher value of 619 (the shortest column)

was rejected by the authors because they felt that either theparticles had been somewhat broken during packing or thecolumn frits had been blocked with fines Accordingly thepermeability data for this column is likewise neglected herein

The remaining three columns however were not con-sistent with respect to the authorsrsquo calculated values for 119875

0

Since the particles were identical the range of values for 1198750

of 226 to 268 must be due to experimental error The rawdata for column B

2 which produced a 119875

0value of 268 is

all self-consistent For example it generates a value for 119875119905

of 148 which is a reasonable value based upon the knownlow particle porosity for these Nova Pak particles and acorresponding value for 120576

0of 04073 which is a reasonable

value for a well-packed column However the other twocolumns columns B

3and B

4 had the much lower value of

126 for 119875119905 Accordingly in Table 3 herein corrected values

for column external porosity for columns B3and B

4are

displayed These corrected values are only slightly differentthan the reported values are within the experimental errorof the measurement and therefore in combination with the


Table 4 Glossary of terms

Symbol Unit dimensions (cgs) Definition119860 cm2 Column cross-sectional area119863 cm Column diameter119889119901

cm Particle spherical diameter equivalentΔ119875 gcmminus1secminus2 Pressure drop along column119889119901119898

cm Average particle diameter (measured)1198960

None Guiochonrsquos residual reciprocal permeability coefficient119875119905

None Guiochonrsquos modified permeability coefficient in Kozeny-Blake equation119871 cm Column length1198750

None Permeability coefficient in Kozeny-Blake equation119876 cm3minminus1 (exception) Volumetric fluid flow rate1199050

sec Time for elution of totally permeating unretained solute119896 cm2 General permeability coefficient in Darcy equation119870

119865cm2 Halaszrsquos permeability coefficient in Darcy equation (1974 paper)

119870 cm2 Halaszrsquos permeability coefficient in Darcy equation (1972 paper)119870

119888None Guiochonrsquos permeability coefficient in the Kozeny-Blake equation (as modified by Carmen)

Greek1205760

None External column porosity120576119894

None Internal column porosity120576119905

None Total column porosity120576119901

None Particle porosityΦ None Giddingsrsquo ratio of external and total column porosity120601 None Flow resistance parameter based on mobile phase velocity1206010

None Flow resistance parameter based on superficial velocityΩ

119901None Particle sphericity factor

120578 gcmminus1secminus1 Fluid absolute viscosity120583119894

cmsecminus1 Average fluid interstitial linear velocity120583119904

cmsecminus1 Average fluid superficial linear velocity120583119905

cmsecminus1 Average mobile phase velocityΨ None Porosity dependence term in the Kozeny-Blake equation based on mobile phase velocityΨ

0None Porosity dependence term in the Kozeny-Blake equation based on superficial velocity

raw data for column B2 are supportive of the value of 267 for

1198750

92 Guiochonrsquos 1999 Study In a 1999 publication by Farkaset al entitled ldquoValidity of Darcyrsquos Law at Low Flow Rates inLiquid Chromatographyrdquo [20] Guiochon and his coauthorsreport the results of some very exactingmeasurements whichthey made to validate Darcyrsquos law at extremely low fluidflow rates Using a column containing particles packed toa measured external column porosity of 0399 and havinga measured total column porosity of 0593 (Figure 2 in thepaper) Guiochon et al measured the column pressure dropand fluid flow rate at flow rates ranging between 0015 and05mLminwith ethylene glycol as the fluidThe authors statethat the particles in the column are spherical and they appearto have gone to extraordinary lengths to obtain an accuratemeasure of the particle diameter and of course as a result ofmodern techniques of particle size classification the particlesize distribution is very narrow

In Figure 1 of the paper the authors show a plot ofcolumn measured pressure drop in bar versus ldquofluid linearvelocityrdquo in cmsec This plot represents their measurementstaken in the empty column The only velocity that exists in

an empty column is the superficial velocity and thus theabscissa values in the plot in Figure 1 designated as ldquofluidlinear velocityrdquo represent superficial linear velocity

In Figure 2 in their paper however the authors showanother plot of measured pressure drop in bar also versusldquofluid linear velocityrdquo in cmsec The velocity on the abscissain this plot although also designated as ldquofluid linear velocityrdquodoes not equate (for permeability related purposes) to theldquofluid linear velocityrdquo in Figure 1 This is because in Figure 2the columnwas filled with porous particles and themeasuredvelocity was the mobile phase velocity Indeed the onlyvelocity used throughout the entire paper is the mobile phasevelocity (mobile phase velocity and superficial velocity areone and the same in an empty column)

In Table 1 of their paper the authors report that for thecolumn represented in Figure 2 the slope of a line achievedwhen the mobile phase velocityin units of cmsec is plottedversus pressure drop in units of bar is 1829 They also reportthat the flow resistance parameter 120601 for this column is 865In Table 3 herein it can be seen that the raw data for thiscolumn (Column C) generates an apparent value of 257 for1198750 This value is very close to Giddingsrsquo value of 267 Indeed

by referring to Figures 2 and 3 herein one can see that thereported raw data in this study without any modification


whatsoever essentially confirms our frame of reference in allrespects

Although unnecessary because the small discrepancy inthe values of 119875

0could result from experimental error in

almost any of the measurements we believe that even thatcan be explained Because of the extraordinarily sensitivenature of the porosity dependence term in the Kozeny-Blakeequation it is suggested herein that this small differencearises from on the one hand the authorsrsquo technique ofusing a mixture of methanol and water as the fluid fortheir determination of the value of 120576

119905and their use of

dichloromethane as the fluid in their determination of thevalue of 120576

0and on the other hand their use of ethylene

glycol as the fluid when measuring the column pressuregradient A small difference in the wetting characteristics ofthese three fluids could easily disrupt the balance betweenthe measured values for 120601 and Ψ and accordingly accountfor all the discrepancies Therefore in the next row of Table3 we make a correction for column pressure to account forthis discontinuity in the authorsrsquo experimental protocol Notethat the corrected value is an adjustment upward of about 4which is within the experimental error of the measurementFinally the corrected data for this column establishes a valuefor 119875

119905of 158 which is indicative of an internal porosity for

these particles that is known to be slightly higher than theNova Pak particles reported in Guiochonrsquos 1998 paper Thecare with which the authors made their measurements ofparticle size and flow rates coupled with the measured valueof approximately 04 for 120576

0 again a reasonable value for awell-

packed columnmakes this study of column permeability oneof the most credible and most important in the publishedliterature

93 Guiochonrsquos 2006 Study In a 2006 publication with Fab-rice Gritti entitled ldquoExperimental Evidence of the Influenceof the Surface Chemistry of the Packing Material on theColumn Pressure Drop in Reverse-phase Liquid Chromatog-raphyrdquo [21] Guiochon and his coauthor claim to makewhat one can only characterize as a startling revelationIn their application of what they call the ldquoKozeny-Carmanequationrdquo they assert that their data support a value of 975 forthe Kozeny-Carman ldquoconstantrdquo which they acknowledge isldquonearly one-half the value traditionally acceptedrdquo Moreoverthe authors go on to suggestmdashequally surprisinglymdashthat thenature of the chemical coating on the surface of the particlesadds another variable to the relationship between pressuregradient and fluid flow We show the data for these columnsas our series D in Table 3 herein One can immediately see inFigure 3 herein that the raw data reported for these columnsdoes not resemble that of packed columns in any shape orform In fact the data is so bizarre that it falls outside all theboundaries of our frame of reference

To begin with the authors used a novel procedure todetermine the external porosity of the columns which isbased upon the so-called Donnan Effect Unfortunatelythe authors did not include for comparison purposes adetermination of the external columnporosities by some con-ventional technique In view of this lack of cross-validation

one is automatically skeptical of the very low values whichthey derived for the external column porosities

The authors recite the following in their paper ldquothecolumns used in this work are the same as those the adsorp-tion properties of which were reported earlier (referenceincluded)rdquo The reference was to another paper publishedin the same year by the same authors [22] in which thetotal porosity 120576

119905 of these same columns was measured and

reported in Table 1 It ismystifying therefore that the authorsignored these measurements in their analysis of permeabilityreported in this paper In Table 3 herein the values fromthis earlier paper for total column porosity for each of thecolumns in the study are included As can be seen in the tablethe difference between the total column porosities reportedfor these columns in the earlier study and the externalcolumn porosities reported for them in the present studywould indicate internal column porosities which are far toolarge for these particles when compared to the low valuesof 119875

119905dictated by the measured pressure drops

Similarly

such internal column porosities would be at significant oddswith the specifications published by the manufacturer forthese particles The results of ISEC (inverse size exclusionchromatography) measurements on a standard 39 times 150mmSymmetry column were reported by the manufacturer as120576119894= 0265 whereas the measurements by the authors would

establish a range of values for the internal column porositiesfrom 024 to 043

The other thing to note about this study is that thecolumns that the authors used in the study were ldquoprototypecolumnsrdquo which had all been ldquopacked and generously offeredby themanufacturer (Waters MilfordMA USA)rdquo [21 p 193]and rather thanmeasuring the particle diameters themselvesthe authors merely accepted the nominal particle size givenby the manufacturer This is a significant deviation fromGuiochonrsquos standard operating procedure described in his1999 paper discussed above inwhichGuiochon and his coau-thors went to extraordinary lengths to measure accuratelythe particle size underscoring its importance as followsldquothe nominal particle sizes given by manufacturers of silicaadsorbents used in chromatography are often approximateaverages which cannot be used for accurate calculationsof column permeability For this reason we measured theparticle size distribution by laser-beam scattering usinga Mastersizer instrument (Malvern Instruments Southbor-ough MA USA)rdquo [20 p 41] (emphasis added) In defenseof their failure to do likewise in this 2006 paper Guiochonand Gritti state the following ldquosince we did not emptythe columns we had no access to the inner diameter Wemeasured the external diameter of the tube insteadrdquo [21 p196] Although the condition that they not open the columnswas presumably imposed by the manufacturer this does notobviate the need for the authors to have obtained someindependent verification of the particle size especially sinceit is such a sensitive parameter in the pressure dropfluid flowrelationship9

It can be seen from Table 3 that both the nominal particlesize reported by the manufacturer and the external porositiesmeasured by the authors were too low For example lookingat Figure 3 herein it is obvious that the raw data values for


Ψ are greater than the maximum in our reference charts forpacked columns Similarly Figure 2 herein illustrates thatthe values for 119875

119905are too low and do not reflect values for

columns packed with fully porous particles Both the particlesize and the external porosity are suspects Accordingly wededuce that the particle size and value for Φ need to beadjusted As for the particle size we adopt the value of 55micrometers a reasonable deviation from the nominal sizegiven by themanufacturerThen usingGiddingsrsquo value of 267for119875

0 we show the impact upon internal columnporosity due

to variations in the level of surface modified stationary phaseThe corrected data all makes sense The column internal

porosity is at its highest for Column D1which contained

underivatized silica particles This is corroborated by thevalue of 119875

119905 which is also at its highest for this column

On the other hand both these two parameters are at theirlowest values for Column D

6 which is consistent with the

highest coating of C18stationary phase and is themore typical

value for commercially available reverse phase C18columns

Additionally the corrected column porosities are consistentwith reported values for standard symmetry columns soldby Waters and are consistent with a professionally developedslurry column packing protocol Finally the range of cor-rected 120601 values is totally consistent with what one wouldexpect

Finally it should be noted that in the very next yearafter they published this paper these same authors publishedanother paper on column permeability which is examinedbelow in which they discontinue the use of the DonnanEffect to measure column external porosity and where theyrevert to using the ISEC technique10 In essence then evenGuiochon himself has effectively abandoned this procedurebut paradoxically he still clings to the erroneous conclusionsbased upon its use (see his comments in his 2010 paperreviewed below concerning the allegedly embedded uniden-tified variables in the value of119870

119888)

94 Guiochonrsquos 2007 Study In a 2007 publication withcoauthors Gritti et al entitled ldquoComparison Between theEfficiencies of Columns Packed with Fully and PartiallyPorous C

18-bonded SilicaMaterialsrdquo [23] (ColumnE series in

Table 3 herein) Guiochon discusses the pressure dropfluidflow relationship in terms of the ldquoKozeny-Carman equationrdquoIn this paper the authors compare the permeability oftwo different types of columns one set filled with fullyporous particles and the other set filled with pellicular orpartially porous particles the latter of which they claim arerepresentative of a new paradigm in columnparticle designaimed at themore challengingmodern-day chromatographicapplications where speed of analysis combined with highefficiency require the use of very high total column pressures

In Figure 4 of their paper the authors display two valuesfor 119870

119888 which they define as the ldquoKozeny-Carman constantrdquo

The value of 250 supposedly corresponds to the permeabilitydata set for the columns containing the partially porousparticles and the value of 165 supposedly corresponds to thepermeability data set for the columns containing the fullyporous particles Although the plot shows a total of 13 data

points the methodology used to derive the values for theconstant on the ordinate of the plot is blind to the readerIn other words the authors do not show any connectionbetween the measured column pressures and the ordinatevalues in their Figure 4 for the values of the ldquoconstantrdquoMoreover although the caption under their Figure 4 statesthat the fluid used was acetonitrilewaterTFA (604001vv) at 119879 = 295K [23 p 297] none of the pressure datadisplayed in their Figure 2 matches this combination of fluidtemperature and eluent compositions Accordingly itmust beconcluded that the measured column pressures upon whichthe calculated values for the constant in their Figure 4 arebased are omitted from the paper

The authors conclude that ldquothe Kozeny-Carman constantof the Halo column is approximately 250 while that of theother column is close to 170 typical of the result found forconventional beds of spherical porous silica particles (119870

119888asymp

180) The much larger value of 119870119888for the Halo material is

unexpectedrdquo [23 p 295]Using Figure 2(B) from the paper as a reference it is

apparent that the values of 165 and 250 for 119870119888as displayed

in their Figure 4 do not compute These values for theKozeny-Carman constant would produce values of 230 and254 bar respectively for the total column pressure at a fluidvolumetric flow rate of 3mLmin which corresponds to theauthorsrsquo value for 119906

119904(which they display in Figure 2(B) as

being 3mmsecminus1) Surprisingly these values are less thanthose plotted in Figure 2(B) Therefore the values of 165 and250 cannot be representative of the value of119875

0for this data set

of measured column pressures Moreover the mobile phasewhich underlies their values for 119870

119888was at a temperature of

22∘C (295K) which is even lower than that used in Figure2(B) that is 60∘C Accordingly the column pressures whichsupport the 119870

119888values in their Figure 4 must be significantly

greater than 300 bar at this flow rate (fluid viscosity increasesas temperature decreases)

Table 3 herein contains the raw data for both columnsreported in the paper and is displayed as columns E

1and

E2 Referring again to our Figures 2 and 3 it is clear that the

authors mistook 119875119905for 119875

0 Accordingly we show the authorsrsquo

values for 119870119888in Table 3 as being values for 119875

119905 not 119875

0 Thus

corrected the raw data for the fully porous particles generatea value of 165 for 119875

119905and an apparent value of 256 for 119875

0

However themeasured value for external porosity of 03830 isstill on the low end of what is typical for well-packed columnsusing slurry packing In addition this would dictate a value of0425 for particle porosity a value which does notmake sense(too high) given the high pressure underwhich these particlesmust be slurry packed in order to sustain their very highoperating pressures It was the same high particle porosityfor instance in Guiochonrsquos 1998 study reviewed above thatcaused the irregular particles in that study to crush underthe hydraulic pressure of the slurry packing process usedtherein Accordingly we show an adjusted value of 04 forexternal porosity and as dictated by the microscopy resultsdisplayed in the paper for these particles a slightly loweraverage particle size On the basis of these adjustments wederive a value for 119875

0of 267 and a value of 172 for 119875

119905 both of


which are just what our frame of reference would cause us toexpect

With respect to the partially porous Halo particles theauthors refer to them as being ldquorugoserdquo Indeed the electron-micrographs confirm that these particles have a morphologywhich in addition to being quasi-spherical is also roughand scabrous In other words they correspond to whatGuiochon describes in his textbook as irregular particlesAccordingly in order to apply the Kozeny-Blake equation(as modified by Carman) to this data set one must knowthe value for the spherical particle diameter equivalent ofthese particles As displayed in Table 3 the raw data forthe partially porous particles generates a value of 250 for119875119905and an apparent value of 463 for 119875

0 When this data is

corrected for particle sphericity according to the Kozeny-Blake equation (as modified by Carman) the result is a valueof 088 for Ω

119901and a corresponding value of 21 micrometers

for the spherical particle diameter equivalent The resultingcorrected value of 144 for119875

119905is consistent with the low particle

porosity which characterizes the Halo particles used in thisstudy

95 Guiochonrsquos 2008 Study In another paper with Grittipublished in 2008 and entitled ldquoUltra High Pressure LiquidChromatography Column Permeability and Changes of theEluent Propertiesrdquo [3] (Column F series in Table 3 herein)Guiochon reports a study carried out on four columns whichagain were ldquogenerously offered by themanufacturerrdquo [3 p 2]In this paper he and his coauthor draw the conclusion thatldquothe average Kozeny-Carman permeability constant for thecolumns was 144 plusmn 35rdquo [3 p 1]

In Table 1 of their paper Guiochon and Gritti provide alist of column variables some of which were ldquogiven by themanufacturerrdquo and some of which were ldquomeasuredrdquo in theauthorsrsquo labThe authors describe the particles in the columnsunder study as ldquofine particles average119889

119901asymp 17 120583m of bridged

ethylsiloxanesilica hybrid-C18 named BEH-C

18rdquo [3 p 1]

Among the variables which they identify as having been givenby the manufacturer is the 17 120583m value for the particle size

Figure 5 of their paper is a plot of measured pressuredrop in bar versus fluid flow rate in mLmin In our Table 3herein the raw data from the authorsrsquo Figure 5 for eachof the columns in the study is displayed in the rows forColumns F

1through F

4The computed values for119875

0are based

upon the value of the particle size given in Table 1 of thepaper and are the same as those reported by the authorsfor their columns D1 through D4 namely 149 166 161 and168 The corresponding values for 119875

119905in the raw data average

are approximately 100 a value representative of nonporousparticles However we know that the particles under studyare porous because the reported values for 120576

119905are greater

than those reported for 1205760 Moreover the corresponding

particle porosity for these columns would be greater than04 which is entirely unreasonable (again too large) forfully porous particles which have to be slurry packed andoperated at extremely high pressures (greater than 15000 psi)Accordingly as is plainly evident from Figures 2 and 3 hereinthere is something fundamentally wrong with this data set

Since the reported values for total columnporosity are notin question this means that the values for external porosityare again too low and since the average particle size was notmeasured by the authors we adjust for these two parametersAccordingly in Table 3 herein a correction is made tothenominal particle size given by the manufacturer and theexternal porosities are set to the reasonable value of 04 Usingthe resultant corrected value of about 19 micrometers forparticle size (slightly higher than the nominal value given bythe manufacturer) reasonable values for 120601 as well as 119875

119905are

achieved for all columns in the study

96 Guiochonrsquos 2010 Studies Next we consider three moreGuiochon studies of permeability which were all reported in2010 and all of which he again coauthored with Gritti et alThe first of these articles is entitled ldquoPerformance of ColumnsPacked With the New Shell Particles Kinetex-C

18rdquo [24] In

this study the authors report permeability results for partiallyporous particles produced by two different manufacturersThe raw data reported for the two columns are included inour Table 3 as ColumnsH

1andH

2 As reflected in our Table 3

for the raw data and as is plainly evident from Figure 2 and 2herein the resulting values for119875

119905of 96 and 98 are way too low

being more representative of nonporous particles somethingwhich the particles under study are not

The authors after having gone into great detail describingwhat measurements and precautions they used to derive alltheir experimental measurements again fail to measure theaverage particle size Instead they back-calculate the valuefor particle size based upon the Kozeny-Blake equation withan embedded value of 180 for 119875

011 Additionally the external

porosity values are once again on the low side Accordinglyin our Table 3 for comparison purposes we show correctedvalues for the particles which are slightly higher than thecalculated valuesWe point out that using a value of 267 for119875

0

and a set value of 04 for external porosity establishes valuesfor 119875

119905of 142 and 145 values which are very reasonable based

upon the authorsrsquo own statement of the low particle porosityof these partially porous particles

The second of Guiochonrsquos 2010 papers entitled ldquoMassTransfer Resistance in Narrow-bore Columns Packed with17 120583m Particles in Very High Pressure Liquid Chromatog-raphyrdquo [25] further exemplifies the authorsrsquo reliance uponmanufacturersrsquo data as opposed to measuring things In thispaper the authors report two columns having the narrowdiameter of 21mm One column contains fully porousparticles while the other contains partially porous particlesThe authorsrsquo data sets are presented in our Table 3 as ColumnsH

3andH

4 respectively As can be seen from the rawdata and

Figures 2 and 3 herein the results for Column H4(233 for 119875

0

and 121 for 119875119905) are already essentially in conformance with

our frame of reference Moreover when we apply a modestadjustment for particle size over that obtained by the authorrsquosback-calculation technique we get even closer to the norm265 for 119875

0and 137 for 119875

119905

The authors rightfully point out that their ISEC mea-surements result in higher external porosity values for thecolumn containing partially porous particles reporting the


typical value of 04090 for the columnHowever surprisinglythey stop short of the obvious conclusion that since thetechnique of ISEC suffers from the limitation of not being ableto precisely differentiate between the free space between theparticles and the free space within the particles it is logicalthat nonporous particles would result in even higher externalporosities for these slurry packed columns representingas they do (nonporous particles that is) the limit of thephenomenon Indeed the authors appear to be willing to goto great lengths to justify their selective conclusions avoidingthe obvious and more technically relevant explanation whichis that the technique which they are using to determine avalue for external porosity is flawed and results in too lowan external porosity for columns packed with fully porousparticles

Not surprisingly then when we turn to the authorsrsquo dataon the fully porous column in this study we note that theexternal porosity is again low On the other hand when weset the value for external porosity at themore reasonable levelof 04 and again make a modest adjustment for particle sizewe derive the value of 267 for119875

0and the right-in-the-ballpark

value of 167 for 119875119905

The third of Guiochonrsquos 2010 papers entitled ldquoPerfor-mance of New Prototype Packed Columns for Very HighPressure Liquid Chromatographyrdquo [26] once again involvesa failure by the authors to accurately assess the contributionof the size of the particles under study to overall pressuredrop The authors use a value of 17 micrometers for theparticles the value supplied by the manufacturer of theseporous particles

We have included the raw data reported in this paper inour Table 3 as Columns I

1ndashI

6 As was the case in Guiochonrsquos

other recent studies involving fully porous particles thecolumn external porosities appear to be understated Amongother things the reported combination of a high value forcolumn total porosity and a low value for column exter-nal porosity dictates high particle porosity However thesecolumns and particles are designed to be run at extremelyhigh pressures Accordingly the particle porosities need to below in order for the particles towithstand suchhigh pressuresOn the other hand Guiochon and company report values for1198750(which they again notate as 119870

119888) ranging from 139 to 153

This in turn generates values for 119875119905from 91 to 98 values

which again when viewed in Figures 2 and 3 herein areclearly too low because they are representative of nonporousparticles If nothing else then the various reported porositiesare self-contradictory

In our corrected values in Table 3 we have corrected forboth column external porosity and particle size It can be seenthat an average value of 175 is generated for 119875

119905 which fairly

reflects the porosity of these particles (as described by theauthors themselves in their Table 1)

97 Guiochonrsquos 2011 Study Finally we come to Guiochonrsquos2011 publication relevant to our topic yet another paperhe coauthored with Gritti This paper is entitled ldquoThe MassTransfer Kinetics in Columns Packed with Halo-ES ShellParticlesrdquo [27] This study involved two columns of different

particle porosities One column contained particles havinga particle porosity 120576

119901 of 016 while the other contained

particles of porosity 027 The authors measured the averageparticle size for each column using SEM which resulted inparticle sizes of 287 and 302 micrometers for the respectivecolumns The pressure drop for each column was measuredin two different mixtures of Acetonitrile Water therebygenerating two data points for each column Both columnsin this study generated typical values of 04 for externalporosity The results are presented in Figure 3 in their paperIn Table 3 herein the results of the raw measurements arepresented as our Columns J

1and J

2 The values of 119875

0(which

yet again Guiochon and Gritti notate in their paper as 119870119888)

corresponding to the lower particle porosity column (J1) are

234 and 232 while values for the higher particle porositycolumn (J

2) are 289 and 273 The average of these four

measured values is 257Recognizing finally that their data indicates that Car-

manrsquos value of 180 for 1198750may be too low the authors proceed

to challenge their own data Singling out the highest value of1198750 289 the authors comment that such a high value could

be explained by a clogging of the column end frit Howeverthey also report that they adjusted for extra-column effectsin their reported pressure drop values Since this procedurepresumably required measurements in the empty columnsone would think that this would have provided the necessaryadjustments to eliminate the possibility of a clogging issueMoreover even if the highest value for119875

0represents a clogged

frit it is unlikely that the other value for the same columntaken in the other fluidmdashwhich at 273 was almost as highmdashalso represented a clogged frit And then of course there arethe two data points for the other column 234 and 232

Lacking any other explanation for these unexpectedly(from their point of view) high values of 119875

0 they jettison

their own measured values for particle size and instead optfor the manufacturersrsquo lower values of 27 micrometers Thislower particle size of course results in the lower calculatedvalues for 119875

0 As reflected in Figure 3 of their paper they

are now able to report values for 1198750of 231 and 218 for the

higher particle porosity column and 207 and 206 for the lowerparticle porosity column

As can be seen from Table 3 herein when permeabilitymeasurements are used to determine particle size a singlevalue for 119875

0of 267 for all four data points defines a particle

size range of 290ndash308 micrometers which is almost exactlywhat the authors actually measured by SEM Before herejected his own SEMmeasurements Guiochon obtained anaverage value of 257 for 119875

0 Suffice it to say that his value is

significantly closer to the expected (by us) value of 267 thanit is to 180 Moreover if one makes a reasonable allowance forexperimental error one could say that Guiochonrsquos 2011 studyessentially confirms that the value of 119875

0is 267 and accord-

ingly he confirms our permeability frame of reference12

10 Conclusions

Giddingsrsquo teaching of column permeability in columnspacked with fully porous particles is based upon a calibration


derived from nonporous particles which has been titrated forporous particles based upon independently derived data forparticle porosity via his Φ parameter whereas Guiochonrsquosteaching is not This is the fundamental reason for thediscrepancy between their respective teachings on columnpermeability Guiochonrsquos textbook teaching is based upon aterm derived from the chromatographic literaturemdashthe flowresistance parameter 120601mdashwhich has its roots in thermody-namic theory rather than hydrodynamic theory In additionthe fact that Guiochon based his worked example on particleshaving an irregular morphology (119896

0= 10 times 10minus3) without

specifying the degree of irregularity of the particles embed-ded in his hypothetical value for column pressure ratherthan basing it upon smooth spherical particles where thecharacteristic dimension of the particle is well-defined andcontains no ambiguity with regard to particle morphologyalmost makes it appear as if he was deliberately leavinghimself some wiggle room in his teaching

But there can be no wiggle room in the value of 1198750

To begin with as modified by Carman to accommodateparticles with an irregular shape the Kozeny-Blake equationspecifically accounts for particle morphology within therealm of streamline flow Moreover since the relationshipin the equation between pressure gradient and fluid velocitydepends to a first approximation on the fourth powerof the column external porosity the value of 119875

0must be

both accurate and precise This degree of accuracy andprecision however can only be realized experimentally whenall variables are accurately measured in which case thevalues for column pressure embedded in the flow resistanceparameter 120601 on the one hand and the value for column totalporosity embedded in the porosity dependence term Ψ onthe other hand are self-calibrating13

Moreover Guiochonrsquos occasional (albeit apparentlyunwitting) publication of the value of the modifiedpermeability coefficient 119875

119905 as if it were the value of 119875

0

has only exacerbated the confusion surrounding the valueof 119875

0 As has been demonstrated herein experimentally

derived values of 180 and 150 for 119875119905are not infrequent for

columns packed with porous particles and accordinglymay unfortunately be confused with the values of Carman(119875

0= 180) and Ergun (119875

0= 150) [28]14

As detailed above a recurrent theme in Guiochonrsquosexperimental studies of packed bed permeability over thelast decade or so has been that Carman was right 119875

0is a

constant and its value is 180 Accordingly when the resultsof his experiments have not supported this theme Guiochonand his coauthors have seemingly gone out of their wayto attempt to produce results that are consistent with hispredetermined worldview The devices by which this hasbeen pursued include (a) ignoringmeasured particle size datain favor of the particle manufacturerrsquos stated size (b) notmeasuring particle size at all and back-calculating particlesize from permeability measurements where a value for 119875

0

of 180 has been plugged into the Kozeny-Blake equation as agiven and (c) hypothesizing unrealistic explanations for thediscrepancy such as the existence of a ldquoclogged end fritrdquo

On the other hand facts being the stubborn thingsthat they are Guiochonrsquos efforts to make the results of his

experiments fall into line have not infrequently failed to meetwith success

However instead of considering the obvious possibilitythat Kozeny-Blake is valid and that 119875

0is indeed a constant

but that its value is not 180 Guiochon has hedged his betsby reverting back to the ambiguity (and safety) of DarcyismFor example even after Guiochon does a complete flip-flopin his review paper from his textbook teaching andmdashwithoutany explanation or analysismdashsigns on to the conventionalwisdom that the value of119875

0is 180 as if taking one step forward

and two steps backward he proceeds to announce ldquothere issome uncertainty on the value of the numerical coefficientbut since few authors report column permeability data asystematic study has not been made yetrdquo [14 p 9]

Likewise in the second of their 2010 papers which wereviewed above Guiochon and his frequent coauthor Grittimake this illuminating statement ldquothe external porosity 120576

119890

of packed beds is an important characteristic of HPLCcolumns because it affects the column permeability whichis essentially controlled by the average particle size 119889

119901 The

shape of the packed particles their size distribution andthe chemical nature of their external surface play also asignificant role in the column permeability but their impactis more difficult to assess Their effect is empirically lumpedinto the Kozeny-Carman constant119870

119888rdquo [21 p 1487] (emphasis

supplied) Suffice it to say that this assertion that 1198750is

nothing but a hodge-podge of unidentified variables is totallyinconsistent with the notion that it is a constant with a fixedvalue of 180

Ironically Guiochon has essentially ignored his ownstudy published in the 1999 paper with Farkas and Zhongwhich represents one of the most credible studies of columnpermeability available in the literature and which contradictsboth extremes of his pronouncements on column perme-ability (a) there is a constant and its value is 180 and(b) there is only a residual permeability coefficient whichis a variable number that one must plug in to balancethe two sides of the pressureflow equation Indeed it isour conclusion that Guiochon has actually ignored all ofhis experimental investigations which when appropriatelyunderstood uniformly corroborateGiddingsrsquo conclusion thatthe value of 119875

0is 267 a conclusion which was implicit in the

first edition of his textbook published in 1965 and becameexplicit in the second edition published in 1991 [29 p 65]

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

Sincere gratitude is expressed to Tivadar Farkas for providingthe raw measurements underlying the study reported inGuiochonrsquos 1999 paper of which Farkas was a coauthor


Endnotes

1 Endnotes The terminology ldquoKozeny-Carman equationrdquois not favored by the current authors This is because itrepresents the Kozeny-Blake equation with a value for1198750of 180 which is attributed to Carman and which is

believed by us to be in error Accordingly the terminol-ogy ldquoKozeny-Blake equation (as modified by Carman)rdquois preferred and represents Carmanrsquos contribution to theequation to accommodate nonspherical particles whichis a legitimate modification

2 For an in-depth review of Giddingsrsquo development of thisparameter see [1] herein

3 If the column length is in cm the particle diameter in120583m the viscosity in cP and the pressure drop in psi ourequation becomes

Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)

As an example of calculation assume the followingvalues linear velocity 010 cms viscosity 10 cP columnlength 15 cm particle size 10 120583m and permeability con-stant 1 times 10minus3 The pressure drop is

Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)

Note that we have corrected two obvious typographicalerrors in the worked example (1) the value of oneparameter used in (587d) compared to the statement ofthat value in Guiochonrsquos text (15 instead of 25 cm for thelength of the column) and (2) the value of the calculatedpressure drop (225 instead of 325 psi)

4 The data in Tables 1 and 2 both of which are referencecharts are based upon a column of the length (15 cm)packed with particles of the size (10 micrometers)with fluid of the viscosity (10 cP) and running at themobile phase velocity (10 cmsec) specified in Guio-chonrsquos worked example

5 This was the technique used by Giddings to establish thevalue of 267 for 119875

0which is implicit in Table 53-1 in his

1965 text [1] and [8 p 209]6 It also leads to an apparent value for Guiochonrsquos coeffi-

cient 119875119905of 178 Note the coincidental and unfortunately

confusing agreement between this value and Carmanrsquosmuch touted value of 180 for 119875

0[6]

7 It also generates a value of 148 for 119875119905 Again note the

confusing coincidence between this value and the valueof 150 which is also frequently reported in the literatureas being the value of 119875

0[10 11]

8 Neue uses the terminology of 1000 and 1 times 10minus3 inter-changeably apparently in his handbook This practiceis sometimes used throughout the literature as theldquoconstantrdquo in the Kozeny-Blake equationmay be thoughtof as either a reciprocal coefficient or a coefficientof direct proportionality depending on the authorrsquos

accepted convention For instance this is whywe refer toGuiochonrsquos use of his term 119896

0as a ldquoreciprocalrdquo coefficient

9 Additionally since the authors did not have firsthandknowledge of the value of either the particle size or thetube inner diameter their conclusion that ldquothe residualexplanation is that the interstitial velocity distributionbetween the packed particles depends on the chemicalnature of the external surface of these particlesrdquo isunjustified

10 On the other hand it is widely accepted that at leastwhen practiced with the currently available less thanadequate solute standards the ISEC technique does notprovide an accurate differentiation between pores withinand without the particle fraction of a chromatographiccolumn containing fully porous particles Beginningaround 2007 Guiochon compounded this problem bychanging his method of interpreting ISEC curves Theconventional method had been to use the intersectionof both branches of the ISEC curve [12] and [10 p 143]Guiochon is now extrapolating a single branch to zeroelution volume In addition he is now using ldquoholduprdquovolumes measured on a gravimetric basis to establishvalues for total column porosity Both of these practicesmay be contributing to even lower external porosityvalues for fully porous particles from those that wouldbe obtained by using traditional ISEC protocols

11 Even more surprising the authors reference Giddingsrsquo1965 text as authority for their chosen value of 180 for1198750 This is a clearly erroneous citation of Giddingsrsquo 1965

teaching on permeability While Giddings stated in his1965 text that themost commonly referenced value for119875

0

in theKozeny-Blake equationwas indeed 180 he rejectedthis value in favor of a much higher value for 119875

0 He did

this by using his 120601rsquo parameter in his own permeabilityequation thereby establishing that his measured valueswere in complete disagreement with Carmanrsquos valueMoreover he also stated that Carmanrsquos discrepancy hadalso been identified by Giddings [8 p 208]

12 Our discussion of Guiochonrsquos publications ends withthis 2011 paper The present authors have decided notto critique each and every Guiochon paper ever since2011mdashof which there have been severalmdashin which Guio-chon and his collaborators state a value for 119875

0(or as

he calls it 119870119888) However that is due to the following

decisions by the present authors (a) enough is enough(b) many of the assertions in those papers of valuesfor what should be measured parameters are apparentlyassumed not measured and are in general opaque toand indeterminable by the reader and (c) these paperslike their recent predecessors claim in the introductorynarrative that the value of 119875

0is 180 but then go on to

record supposedly different experimental values for 1198750

without ever reconciling the two13 On the other hand even carefully constructed and

controlled experiments can take us only so far We haveused 267 in this paper as the value of the constant inthe Kozeny-Blake equation That is the number that we


calculated from the results which Giddings obtainedfromhis experiments conducted in 1965 over forty yearsago [1] Giddings himself in the 1991 edition of histextbook rounded his results off at the figure of 270[29 p 65] We have no doubt that the exact value ofthe constant is somewhere between 265 and 270 andtherefore we feel very comfortable in using 267 whichis the average of those two values in our analysis ofGuiochonrsquos teaching and his recent experimental workHowever a definitive determination of the constantrsquosvalue will have to await its theoretical development fromfirst principles something which has never been done

14 It is also possible that this type of mistaken identity mayhave infected the work of some of the other contributorsto the hydrodynamic literature

References

[1] H M Quinn ldquoReconciliation of packed column permeabilitydatamdashpart 1 the teaching of Giddings revisitedrdquo Special Topicsamp Reviews in Porous Media vol 1 no 1 pp 79ndash86 2010

[2] H M Quinn and J J Takarewski ldquoHigh performance liq-uid chromatography method and apparatusrdquo US Patent no5772874 1998

[3] F Gritti and G Guiochon ldquoUltra high pressure liquid chro-matography Column permeability and changes of the eluentpropertiesrdquo Journal of Chromatography A vol 1187 no 1-2 pp165ndash179 2008

[4] F Gritti and G Guiochon ldquoAdsorptionmechanism in reversed-phase liquid chromatography Effect of the surface coverage of amonomeric C18-silica stationary phaserdquo Journal of Chromatog-raphy A vol 1115 no 1-2 pp 142ndash163 2006

[5] G Guiochon S G Shirazi and A M Katti Fundamentals ofPreparative and Nonlinear Chromatography Academic PressBoston Mass USA 1994

[6] P C Carman ldquoFluid flow through granular bedsrdquo Transactionsof the Institution of Chemical Engineers vol 15 pp 155ndash166 1937

[7] L R Snyder and J J Kirkland Introduction to Modern LiquidChromaTography John Wiley amp Sons 2nd edition 1979

[8] J C Giddings Dynamics of Chromatography Part I Principlesand Theory Marcel Dekker New York NY USA 1965

[9] G Guiochon S G Shirazi and A M Katti Fundamentals ofPreparative and Nonlinear Chromatography Academic PressBoston Mass USA 2nd edition 2006

[10] S Ergun ldquoFluid flow through packed columnsrdquo ChemicalEngineering Progress vol 48 pp 89ndash94 1952

[11] R B Bird W E Stewart and E N Lightfoot TransportPhenomena John Wiley amp Sons 2002

[12] H Guan and G Guiochon ldquoStudy of physico-chemical prop-erties of some packing materials I Measurements of theexternal porosity of packed columns by inverse size-exclusionchromatographyrdquo Journal of Chromatography A vol 731 no 1-2 pp 27ndash40 1996

[13] G Guiochon ldquoFlow of gases in porous media Problems raisedby the operation of gas chromatography columnsrdquo Chromato-graphic Reviews vol 8 pp 1ndash47 1966

[14] G Guiochon ldquoThe limits of the separation power of unidimen-sional column liquid chromatographyrdquo Journal of Chromatog-raphy A vol 1126 no 1-2 pp 6ndash49 2006

[15] U Neue HPLC Columns-Theory Technology and PracticeWiley-VCH 1997

[16] I Halasz R Endele and J Asshauer ldquoUltimate limits in high-pressure liquid chromatographyrdquo Journal of Chromatography Avol 112 no C pp 37ndash60 1975

[17] R Endele I Halz and K Unger ldquoInfluence of the particle size(5ndash35 120583m) of spherical silica on column efficiencies in high-pressure liquid chromatographyrdquo Journal of Chromatography Avol 99 pp 377ndash393 1974

[18] I Halasz and M Naefe ldquoInfluence of column parameterson peak broadening in high pressure liquid chromatographyrdquoAnalytical Chemistry vol 44 no 1 pp 76ndash84 1972

[19] J-H Koh and G Guiochon ldquoEffect of the column lengthon the characteristics of the packed bed and the columnefficiency in a dynamic axial compression columnrdquo Journal ofChromatography A vol 796 no 1 pp 41ndash57 1998

[20] T Farkas G Zhong and G Guiochon ldquoValidity of Darcyrsquoslaw at low flow-rates in liquid chromatographyrdquo Journal ofChromatography A vol 849 no 1 pp 35ndash43 1999

[21] F Gritti and G Guiochon ldquoExperimental evidence of theinfluence of the surface chemistry of the packingmaterial on thecolumn pressure drop in reverse-phase liquid chromatographyrdquoJournal of Chromatography A vol 1136 no 2 pp 192ndash201 2006


[23] F Gritti A Cavazzini N Marchetti and G Guiochon ldquoCom-parison between the efficiencies of columns packed with fullyand partially porous C18-bonded silica materialsrdquo Journal ofChromatography A vol 1157 no 1-2 pp 289ndash303 2007

[24] F Gritti I Leonardis D Shock P Stevenson A Shalliker andG Guiochon ldquoPerformance of columns packed with the newshell particles Kinetex-C18rdquo Journal of Chromatography A vol1217 no 10 pp 1589ndash1603 2010

[25] F Gritti and G Guiochon ldquoMass transfer resistance in narrow-bore columns packedwith 17120583mparticles in very high pressureliquid chromatographyrdquo Journal of Chromatography A vol 1217no 31 pp 5069ndash5083 2010

[26] F Gritti and G Guiochon ldquoPerformance of new prototypepacked columns for very high pressure liquid chromatographyrdquoJournal of Chromatography A vol 1217 no 9 pp 1485ndash14952010

[27] F Gritti and G Guiochon ldquoThe mass transfer kinetics incolumns packed with Halo-ES shell particlesrdquo Journal of Chro-matography A vol 1218 no 7 pp 907ndash921 2011

[28] M Rhodes Introduction to Particle Technology John Wiley ampSons 1998

[29] J C Giddings Unified Separation Science John Wiley amp Sons1991

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of



CeramicsJournal of


CompositesJournal of

NanoparticlesJournal of



International Journal of

Biomaterials


NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research



MetallurgyJournal of


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MaterialsJournal of


Nano

materials


Journal ofNanomaterials


recent literature pertaining to fully porous particles wherelow values for the constant of proportionality in the Kozeny-Blake equation are being justified on the basis of particleporosities which purportedly run counter to this principle[4] Clearly something is wrong

The value of the permeability coefficient dictated bythe necessity to balance the pressure gradientfluid flowequation after all independent variables are accounted for(and which presumably has its origin in the fundamentalmechanisms which underlie the generation of pressure in thefirst place) is by no means self-evident From the standpointof first principles it would appear that its value ought to beconstant regardless of the physical parameters comprising thefluid flow apparatus However no fully developed theoreticalexplanation for any constant of permeability has yet beenpublished On the other hand the literature is replete withdiscussions of the value for this parameter which purportedlyare justified on the basis of empirical data The problem isthat the authors of this literature do not agree with eachother and sometimes the same author disagrees with himselfIn the last few years Georges Guiochon in particular haspublished conflicting values for this parameter all of whichare supposedly based uponmeasured values yet he has madeno serious effort to reconcile the conflicts or to provide anyplausible underlying rationale for their differences

As we discuss below there are several inherent flawsin Guiochonrsquos teaching of permeability which are at theroot of his conflicting values for the coefficient We suggestthat these flaws originate in the fact that his teaching doesnot distinguish between the respective impacts on columnpermeability of (a) mass transfer by convection versus masstransfer by diffusion and (b) spherical particles versus par-ticles having an irregular morphology Accordingly withoutsubstantial refinement and adjustment Guiochonrsquos teachingof column permeability at best does little to overcome theshortcomings of Darcyrsquos law and at worst adds fuel to thefire of the aforementioned controversy

2 Guiochonrsquos Textbook Teaching

In his influential textbook Fundamentals of Preparativeand Nonlinear Chromatography [5] Guiochon (togetherwith his coauthors) bases his teaching of the pressureflowrelationship in streamline flow on the Darcy equation whichhe displays therein as his equation (526b) a rearrangementof which we repeat here

Δ119875

119871=

120583119905120578

11989601198892119901119898

(1)

where Δ119875 = pressure drop along column 119871 = length ofcolumn 120583

119905= mobile phase velocity 120578 = absolute viscosity of

fluid 119889119901119898

= average particle diameter and 1198960= Guiochonrsquos

residual permeability coefficientAll terms are self-consistent from a unit-of-measure

perspectiveNote that Guiochon does not discriminate in his expres-

sion of the Darcy equation between spherical and irregularparticles In other words in his statement of the equation

a spherical particle with a measured diameter of 119909 cm isequivalent to an irregularly shaped particle of the samemeasured diameter Peculiarly however he goes on to say thatldquotraditionally a value of 119896

0= 1 times 10minus3 is used for irregular

particles and 12 times 10minus3 for spherical onesrdquo [5 p 153]Similarly without including any porosity dependence

term in the pressurefluid flow relationship or specifyingany particular relationship between columnpressure gradientand column porosity for columns packed with either porousor nonporous particles he states that 119896

0varies ldquobetween 5 times

10minus4 and 2 times 10minus3 depending upon the compactness of thepacked bed that is on the external porosityrdquo [5 p 153]

In essence then Guiochon bundles the variables ofparticle morphology and column porosity into his residualpermeability coefficient 119896

0 Indeed this is why we call it his

residual permeability coefficientIn order to explore these implicit terms which are embed-

ded inGuiochonrsquos teaching for his 1198960 we turn for comparison

purposes to the well-known Kozeny-Blake equation

Δ119875

119871=1198750(1 minus 120576

0)2

120583119904120578

120576301198892119901

(2)

where 1198750= the KozenyBlake permeability coefficient 120576

0=

external porosity of column 120583119904= fluid superficial velocity

and 119889119901= spherical particle diameter equivalent

As we noted above Guiochon acknowledges in his teach-ing that particle irregularity does influence pressure drop Ina modification of the Kozeny-Blake equation proposed byCarman this factor was expressly accounted for by adding aparameter to represent particle sphericity which we denotewith the symbol Ω

119901(Carman gave it the symbol 120601 in his

original publication [6]) It will be appreciated that the valueof Ω

119901is equal to 1 for spherical particles and is less than 1

for particles having an irregular morphology Accordinglythe Kozeny-Blake equation (as modified by Carman)1 isexpressed as

Δ119875

119871=1198750(1 minus 120576

0)2

120583119904120578

12057630(119889

119901119898Ω

119901)2 (3)

where Ω119901= Carmanrsquos particle adjustment factor for devia-

tions from perfect sphericity and 119889119901119898Ω

119901= 119889

119901

As for column porosity note that the Kozeny-Blakeequation includes a combination of porosity terms whichtaken together can be viewed as its porosity dependenceparameter which we notate with the symbol Ψ

119900

Ψ0=(1 minus 120576

0)2

12057630

(4)

where 1205760= the volume of free space between the particles in

the columnthe volume of the empty columnComparing (1) and (3) the reader will observe that

there still is another difference the fluid velocity frames aredifferent Accordingly in order to establish the relationshipbetween the values of Kozeny-Blakersquos 119875

0and the value

of Guiochonrsquos 1198960 one needs to delineate the impact of





120583119904=119876

A (5)





0 as follows

120583119894=120583119904

1205760

(6)





Δ119875

119871=1198750(1 minus 120576

0)2

120583119894120578

120576201198892119901

(7)


120583119905=119871

1199050

(8)










120576119905= 120576

0+ 120576

119894 (9)





120583119905120576119905= 120583

119904 (10)


119905into the




Δ119875

119871=1198750(1 minus 120576

0)2

120583119905120576119905120578

120576301198892119901

(11)



1198750(1 minus 120576

0)2

120583119904

120576301198892119901

=120583119905120576119905

1198960(119889

119901119898Ω

119901)2 (12)



120601 =Δ119875119889

2

119901

120583119905120578119871

(13)



120601 =1

1198960

(14)



Ψ =(1 minus 120576

119905Φ)

2

(120576119905Φ)

3 (15)


Φ =1205760

120576119905

(16)



Δ119875

119871=1198750(1 minus 120576

119905Φ)

2

120583119905120576119905120578

(120576119905Φ)

3

(119889119901)2

(17)


119905= 120576

0and thus 120583

119905= 120583

119894= 120583

119904120576

0and Φ = 1


and 1198750


1198750=

1

1198960Ψ

(18)

or

1198750=120601

Ψ (19)





119901 is varied










cannot be measured


119905



119905




119875119905= 119875

0120576119905 (20)






Table1Colum

nperm


119870119865

Particlepo

rosity

rang

e120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905

(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


cm3 m

inminus1

cmsecminus

1cm

secminus

1cm

secminus

1

Non

porous

particles

0380

1000

0380

000

0000

0160

711

1870

2662

701

141119864minus03

267

101

535119864minus10

15046

100

000100

000100

00100

038

0038

0100

0100

0390

1000

0390

000

0000

0147

653

1675

244

6627

153119864minus03

267

104

597119864minus10

15046

100

000100

000100

00100

039

0039

0100

0100

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

000100

000100

00100

040

004

00100

0100

0410

1000

0410

000

0000

0124

553

1349

2071

505

181119864minus03

267

109

742119864minus10

15046

100

000100

000100

00100

041

004

10100

0100

0420

1000

0420

000

0000

0115

509

1212

1907

454

196119864minus03

267

112

825119864minus10

15046

100

000100

000100

00100

042

004

20100

0100

Lowpo

rosity

particles

0507

0750

0380

0127

0204

213

948

1870

3549

701

106119864minus03

267

135

535119864minus10

15046

100

000100

000100

00100

051

0051

0133

0100

0520

0750

0390

0130

0213

196

871

1675

3261

627

115119864minus03

267

139

597119864minus10

15046

100

000100

000100

00100

052

0052

0133

0100

0533

0750

040

00133

0222

180

801

1502

2999

563

125119864minus03

267

142

666119864minus10

15046

100

000100

000100

00100

053

0053

0133

0100

0546

0750

0410

0136

0231

166

737

1349

2760

505

136119864minus03

267

146

742119864minus10

15046

100

000100

000100

00100

055

0055

0133

0100

0560

0750

0420

0140

0241

153

679

1212

2542

454

147119864minus03

267

149

825119864minus10

15046

100

000100

000100

00100

056

0056

0133

0100

Medium

porosity

particles

0613

0620

0380

0233

0376

258

1146

1870

4293

701

872119864minus04

267

164

535119864minus10

15046

100

000100

000100

00100

061

0061

0161

0100

0629

0620

0390

0239

0392

237

1053

1675

3946

627

949119864minus04

267

168

597119864minus10

15046

100

000100

000100

00100

063

0063

0161

0100

064

50620

040

00245

040

9218

969

1502

3629

563

103119864minus03

267

172

666119864minus10

15046

100

000100

000100

00100

064

0065

0161

0100

0661

0620

0410

0251

0426

201

892

1349

3340

505

112119864minus03

267

177

742119864minus10

15046

100

000100

000100

00100

066

006

60161

0100

0677

0620

0420

0257

044

4185

821

1212

3076

454

122119864minus03

267

181

825119864minus10

15046

100

000100

000100

00100

068

006

80161

0100

Highpo

rosity

particles

0760

0500

0380

0380

0613

320

1422

1870

5325

701

703119864minus04

267

203

535119864minus10

15046

100

000100

000100

00100

076

0076

0200

0100

0780

0500

0390

0390

0639

294

1306

1675

4891

627

766119864minus04

267

208

597119864minus10

15046

100

000100

000100

00100

078

0078

0200

0100

0800

0500

040

0040

0066

7270

1202

1502

4500

563

832119864minus04

267

214

666119864minus10

15046

100

000100

000100

00100

080

0080

0200

0100

0820

0500

0410

0410

0694

249

1105

1349

4140

505

905119864minus04

267

219

742119864minus10

15046

100

000100

000100

00100

082

0082

0200

0100

0840

0500

0420

0420

0724

229

1018

1212

3814

454

982119864minus04

267

224

825119864minus10

15046

100

000100

000100

00100

084

0084

0200

0100

Capillary

1000

0380

0380

0620

1000

421

1870

1870

7005

701

535119864minus04

267

267

535119864minus10

15046

100

000100

000100

00100

100

0100

0263

0100

1000

0390

0390

0610

1000

377

1675

1675

6273

627

597119864minus04

267

267

597119864minus10

15046

100

000100

000100

00100

100

0100

0256

0100

1000

040

0040

0060

010

00338

1502

1502

5625

563

666119864minus04

267

267

666119864minus10

15046

100

000100

000100

00100

100

0100

0250

0100

1000

0410

0410

0590

1000

303

1349

1349

5051

505

742119864minus04

267

267

742119864minus10

15046

100

000100

000100

00100

100

0100

0244

0100

1000

0420

0420

0580

1000

273

1212

1212

4541

454

825119864minus04

267

267

825119864minus10

15046

100

000100

000100

00100

100

0100

0238

0100


0200400600800

100012001400160018002000

20 30 40 50 60 70






Capillary


y = 267x + 0

Ψ

120601

Line

High porosity

(a)

99111123135147159171183195207219231243255267

035 045 055 065 075 085 095


Capillary


y = 267x + 0

Pt

120576t

Φ = 10

Φ = 075

Φ = 062

Φ = 05

Φ = 075

Φ = 062

Φ = 05

Φ = 1

(b)

99111123135147159171183195207219231243255267

000 010 020 030 040 050 060 070 080 090 100


120576p

y = 160x + 107

Pt


(c)







0in his worked




Table2Cr

oss-referencefor

term

s119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


3minminus1cm

secminus

1cm

secminus

1cm

secminus

1

Nonporousp

articles

Gidding

srsquotradition

alno

nporou

scolum

n040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

1000010

00010

0010

0399

004

00100

0100

Guiocho

nrsquostradition

alspheric

alparticle(app

arent)

0362

1000

0362

000

0000

0187

830

2293

3106

858

120119864minus03

267

97436119864minus10

15046

1000010

00010

0010

0361

0036

0100

0100

Gidd

ingrsquos

table5

3-1

5060meshglassb

eads

0422

1000

0422

000

0000

0113

500

1184

1873

444

200119864minus03

267

113

844119864minus10

15046

1000010

00010

0010

0421

004

20100

0100

5060meshglassb

eads

040

910

00040

9000

0000

0126

560

1371

2097

513

179119864minus03

267

109

729119864minus10

15046

1000010

00010

0010

040

70041

0100

0100


ExA

irregular

particle

(app

arent)

040

010

00040

0000

0000

0225

1000

2500

2250

563

100119864minus03

444

178

400119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExA

correctedforp

article

irregularity

040

010

00040

0000

0000

0225

601

1502

2250

563

166119864minus03

267

107

400119864minus10

15046

078

00010

000

080010

0399

004

00100

0100

ExB

spheric

alparticle

(app

arent)

040

010

00040

0000

0000

0187

830

2075

2250

563

120119864minus03

369

148

482119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExB

corrected

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

Porous

particles

Gidding

srsquotradition

alpo

rous

column

060

0066

7040

00200

0333

203

900

1500

3375

563

111119864minus03

267

160

667119864minus10

15046

100

00010

00010

0010

0599

006

00150

0100

Gidd

ingrsquos

table5

3-1

3040meshalum

ina

0803

0498

040

00403

0672

271

1204

1499

4510

562

830119864minus04

267

214

667119864minus10

15046

100

00010

00010

0010

0801

0080

0201

0100

5060meshalum

ina

0837

0499

0417

0420

0721

235

1043

1246

3906

467

959119864minus04

267

224

803119864minus10

15046

100

00010

00010

0010

0835

0084

0201

0100

6080meshchromosorbW

(5DNP)

0766

0498

0382

0384

0621

316

1404

1833

5259

687

712119864minus04

267

204

545119864minus10

15046

100

00010

00010

0010

0764

0077

0201

0100

6080meshchromosorbW

(20

DNP)

0785

0495

0389

0396

064

8300

1333

1698

4991

636

750119864minus04

267

210

589119864minus10

15046

100

00010

00010

0010

0783

0079

0202

0100



05





119901







of 369 for 1198750






0 and 107 for 119875

119905


119905also






119905based upon


119905is even more



119905










0









119905is 267












0 119875

119905 120576

119905 and 120576

119901


0




119905and 120576


0and









119905below




2

1199011205762][150(1 minus 120576)










119891=

12057630180 (1 minus 120576




0of the


0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]




0180(1 minus 120576

0)2










119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

000

028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

2161

400

173119864minus03

267

144

729119864minus11

393119864minus11

1500

046

088

000

023

000

0205

000

41300

030

070

056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

0419

197

725

1142

4865

766

138119864minus03

149

95399119864minus11

253119864minus11

300

021

100

000

017

000

0170

00035

100

048

129

076

Colum

nF 2

rawdata

064

200581

03730

0269

0429

361

807

1258

4863

758

124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

000

017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

03800

0259

0418

1014

752

1177

4476

701

133119864minus03

168

107

384119864minus11

246119864minus11

1500

021

100

000

017

000

0170

00035

100

048

127

075

Colum

nF 1

corrected

06350

0630

040

000235

0392

197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

678

150119864minus03

150

98434119864minus11

285119864minus11

1500

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







120583119904=119876

A (5)





0 as follows

120583119894=120583119904

1205760

(6)





Δ119875

119871=1198750(1 minus 120576

0)2

120583119894120578

120576201198892119901

(7)


120583119905=119871

1199050

(8)










120576119905= 120576

0+ 120576

119894 (9)





120583119905120576119905= 120583

119904 (10)


119905into the




Δ119875

119871=1198750(1 minus 120576

0)2

120583119905120576119905120578

120576301198892119901

(11)



1198750(1 minus 120576

0)2

120583119904

120576301198892119901

=120583119905120576119905

1198960(119889

119901119898Ω

119901)2 (12)



120601 =Δ119875119889

2

119901

120583119905120578119871

(13)



120601 =1

1198960

(14)



Ψ =(1 minus 120576

119905Φ)

2

(120576119905Φ)

3 (15)


Φ =1205760

120576119905

(16)



Δ119875

119871=1198750(1 minus 120576

119905Φ)

2

120583119905120576119905120578

(120576119905Φ)

3

(119889119901)2

(17)


119905= 120576

0and thus 120583

119905= 120583

119894= 120583

119904120576

0and Φ = 1


and 1198750


1198750=

1

1198960Ψ

(18)

or

1198750=120601

Ψ (19)





119901 is varied










cannot be measured


119905



119905




119875119905= 119875

0120576119905 (20)






Table1Colum

nperm


119870119865

Particlepo

rosity

rang

e120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905

(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


cm3 m

inminus1

cmsecminus

1cm

secminus

1cm

secminus

1

Non

porous

particles

0380

1000

0380

000

0000

0160

711

1870

2662

701

141119864minus03

267

101

535119864minus10

15046

100

000100

000100

00100

038

0038

0100

0100

0390

1000

0390

000

0000

0147

653

1675

244

6627

153119864minus03

267

104

597119864minus10

15046

100

000100

000100

00100

039

0039

0100

0100

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

000100

000100

00100

040

004

00100

0100

0410

1000

0410

000

0000

0124

553

1349

2071

505

181119864minus03

267

109

742119864minus10

15046

100

000100

000100

00100

041

004

10100

0100

0420

1000

0420

000

0000

0115

509

1212

1907

454

196119864minus03

267

112

825119864minus10

15046

100

000100

000100

00100

042

004

20100

0100

Lowpo

rosity

particles

0507

0750

0380

0127

0204

213

948

1870

3549

701

106119864minus03

267

135

535119864minus10

15046

100

000100

000100

00100

051

0051

0133

0100

0520

0750

0390

0130

0213

196

871

1675

3261

627

115119864minus03

267

139

597119864minus10

15046

100

000100

000100

00100

052

0052

0133

0100

0533

0750

040

00133

0222

180

801

1502

2999

563

125119864minus03

267

142

666119864minus10

15046

100

000100

000100

00100

053

0053

0133

0100

0546

0750

0410

0136

0231

166

737

1349

2760

505

136119864minus03

267

146

742119864minus10

15046

100

000100

000100

00100

055

0055

0133

0100

0560

0750

0420

0140

0241

153

679

1212

2542

454

147119864minus03

267

149

825119864minus10

15046

100

000100

000100

00100

056

0056

0133

0100

Medium

porosity

particles

0613

0620

0380

0233

0376

258

1146

1870

4293

701

872119864minus04

267

164

535119864minus10

15046

100

000100

000100

00100

061

0061

0161

0100

0629

0620

0390

0239

0392

237

1053

1675

3946

627

949119864minus04

267

168

597119864minus10

15046

100

000100

000100

00100

063

0063

0161

0100

064

50620

040

00245

040

9218

969

1502

3629

563

103119864minus03

267

172

666119864minus10

15046

100

000100

000100

00100

064

0065

0161

0100

0661

0620

0410

0251

0426

201

892

1349

3340

505

112119864minus03

267

177

742119864minus10

15046

100

000100

000100

00100

066

006

60161

0100

0677

0620

0420

0257

044

4185

821

1212

3076

454

122119864minus03

267

181

825119864minus10

15046

100

000100

000100

00100

068

006

80161

0100

Highpo

rosity

particles

0760

0500

0380

0380

0613

320

1422

1870

5325

701

703119864minus04

267

203

535119864minus10

15046

100

000100

000100

00100

076

0076

0200

0100

0780

0500

0390

0390

0639

294

1306

1675

4891

627

766119864minus04

267

208

597119864minus10

15046

100

000100

000100

00100

078

0078

0200

0100

0800

0500

040

0040

0066

7270

1202

1502

4500

563

832119864minus04

267

214

666119864minus10

15046

100

000100

000100

00100

080

0080

0200

0100

0820

0500

0410

0410

0694

249

1105

1349

4140

505

905119864minus04

267

219

742119864minus10

15046

100

000100

000100

00100

082

0082

0200

0100

0840

0500

0420

0420

0724

229

1018

1212

3814

454

982119864minus04

267

224

825119864minus10

15046

100

000100

000100

00100

084

0084

0200

0100

Capillary

1000

0380

0380

0620

1000

421

1870

1870

7005

701

535119864minus04

267

267

535119864minus10

15046

100

000100

000100

00100

100

0100

0263

0100

1000

0390

0390

0610

1000

377

1675

1675

6273

627

597119864minus04

267

267

597119864minus10

15046

100

000100

000100

00100

100

0100

0256

0100

1000

040

0040

0060

010

00338

1502

1502

5625

563

666119864minus04

267

267

666119864minus10

15046

100

000100

000100

00100

100

0100

0250

0100

1000

0410

0410

0590

1000

303

1349

1349

5051

505

742119864minus04

267

267

742119864minus10

15046

100

000100

000100

00100

100

0100

0244

0100

1000

0420

0420

0580

1000

273

1212

1212

4541

454

825119864minus04

267

267

825119864minus10

15046

100

000100

000100

00100

100

0100

0238

0100


0200400600800

100012001400160018002000

20 30 40 50 60 70






Capillary


y = 267x + 0

Ψ

120601

Line

High porosity

(a)

99111123135147159171183195207219231243255267

035 045 055 065 075 085 095


Capillary


y = 267x + 0

Pt

120576t

Φ = 10

Φ = 075

Φ = 062

Φ = 05

Φ = 075

Φ = 062

Φ = 05

Φ = 1

(b)

99111123135147159171183195207219231243255267

000 010 020 030 040 050 060 070 080 090 100


120576p

y = 160x + 107

Pt


(c)







0in his worked




Table2Cr

oss-referencefor

term

s119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


3minminus1cm

secminus

1cm

secminus

1cm

secminus

1

Nonporousp

articles

Gidding

srsquotradition

alno

nporou

scolum

n040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

1000010

00010

0010

0399

004

00100

0100

Guiocho

nrsquostradition

alspheric

alparticle(app

arent)

0362

1000

0362

000

0000

0187

830

2293

3106

858

120119864minus03

267

97436119864minus10

15046

1000010

00010

0010

0361

0036

0100

0100

Gidd

ingrsquos

table5

3-1

5060meshglassb

eads

0422

1000

0422

000

0000

0113

500

1184

1873

444

200119864minus03

267

113

844119864minus10

15046

1000010

00010

0010

0421

004

20100

0100

5060meshglassb

eads

040

910

00040

9000

0000

0126

560

1371

2097

513

179119864minus03

267

109

729119864minus10

15046

1000010

00010

0010

040

70041

0100

0100


ExA

irregular

particle

(app

arent)

040

010

00040

0000

0000

0225

1000

2500

2250

563

100119864minus03

444

178

400119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExA

correctedforp

article

irregularity

040

010

00040

0000

0000

0225

601

1502

2250

563

166119864minus03

267

107

400119864minus10

15046

078

00010

000

080010

0399

004

00100

0100

ExB

spheric

alparticle

(app

arent)

040

010

00040

0000

0000

0187

830

2075

2250

563

120119864minus03

369

148

482119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExB

corrected

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

Porous

particles

Gidding

srsquotradition

alpo

rous

column

060

0066

7040

00200

0333

203

900

1500

3375

563

111119864minus03

267

160

667119864minus10

15046

100

00010

00010

0010

0599

006

00150

0100

Gidd

ingrsquos

table5

3-1

3040meshalum

ina

0803

0498

040

00403

0672

271

1204

1499

4510

562

830119864minus04

267

214

667119864minus10

15046

100

00010

00010

0010

0801

0080

0201

0100

5060meshalum

ina

0837

0499

0417

0420

0721

235

1043

1246

3906

467

959119864minus04

267

224

803119864minus10

15046

100

00010

00010

0010

0835

0084

0201

0100

6080meshchromosorbW

(5DNP)

0766

0498

0382

0384

0621

316

1404

1833

5259

687

712119864minus04

267

204

545119864minus10

15046

100

00010

00010

0010

0764

0077

0201

0100

6080meshchromosorbW

(20

DNP)

0785

0495

0389

0396

064

8300

1333

1698

4991

636

750119864minus04

267

210

589119864minus10

15046

100

00010

00010

0010

0783

0079

0202

0100



05





119901







of 369 for 1198750






0 and 107 for 119875

119905


119905also






119905based upon


119905is even more



119905










0









119905is 267












0 119875

119905 120576

119905 and 120576

119901


0




119905and 120576


0and









119905below




2

1199011205762][150(1 minus 120576)










119891=

12057630180 (1 minus 120576




0of the


0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]




0180(1 minus 120576

0)2










119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

000

028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

2161

400

173119864minus03

267

144

729119864minus11

393119864minus11

1500

046

088

000

023

000

0205

000

41300

030

070

056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

0419

197

725

1142

4865

766

138119864minus03

149

95399119864minus11

253119864minus11

300

021

100

000

017

000

0170

00035

100

048

129

076

Colum

nF 2

rawdata

064

200581

03730

0269

0429

361

807

1258

4863

758

124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

000

017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

03800

0259

0418

1014

752

1177

4476

701

133119864minus03

168

107

384119864minus11

246119864minus11

1500

021

100

000

017

000

0170

00035

100

048

127

075

Colum

nF 1

corrected

06350

0630

040

000235

0392

197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

678

150119864minus03

150

98434119864minus11

285119864minus11

1500

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





1198750(1 minus 120576

0)2

120583119904

120576301198892119901

=120583119905120576119905

1198960(119889

119901119898Ω

119901)2 (12)



120601 =Δ119875119889

2

119901

120583119905120578119871

(13)



120601 =1

1198960

(14)



Ψ =(1 minus 120576

119905Φ)

2

(120576119905Φ)

3 (15)


Φ =1205760

120576119905

(16)



Δ119875

119871=1198750(1 minus 120576

119905Φ)

2

120583119905120576119905120578

(120576119905Φ)

3

(119889119901)2

(17)


119905= 120576

0and thus 120583

119905= 120583

119894= 120583

119904120576

0and Φ = 1


and 1198750


1198750=

1

1198960Ψ

(18)

or

1198750=120601

Ψ (19)





119901 is varied










cannot be measured


119905



119905




119875119905= 119875

0120576119905 (20)






Table1Colum

nperm


119870119865

Particlepo

rosity

rang

e120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905

(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


cm3 m

inminus1

cmsecminus

1cm

secminus

1cm

secminus

1

Non

porous

particles

0380

1000

0380

000

0000

0160

711

1870

2662

701

141119864minus03

267

101

535119864minus10

15046

100

000100

000100

00100

038

0038

0100

0100

0390

1000

0390

000

0000

0147

653

1675

244

6627

153119864minus03

267

104

597119864minus10

15046

100

000100

000100

00100

039

0039

0100

0100

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

000100

000100

00100

040

004

00100

0100

0410

1000

0410

000

0000

0124

553

1349

2071

505

181119864minus03

267

109

742119864minus10

15046

100

000100

000100

00100

041

004

10100

0100

0420

1000

0420

000

0000

0115

509

1212

1907

454

196119864minus03

267

112

825119864minus10

15046

100

000100

000100

00100

042

004

20100

0100

Lowpo

rosity

particles

0507

0750

0380

0127

0204

213

948

1870

3549

701

106119864minus03

267

135

535119864minus10

15046

100

000100

000100

00100

051

0051

0133

0100

0520

0750

0390

0130

0213

196

871

1675

3261

627

115119864minus03

267

139

597119864minus10

15046

100

000100

000100

00100

052

0052

0133

0100

0533

0750

040

00133

0222

180

801

1502

2999

563

125119864minus03

267

142

666119864minus10

15046

100

000100

000100

00100

053

0053

0133

0100

0546

0750

0410

0136

0231

166

737

1349

2760

505

136119864minus03

267

146

742119864minus10

15046

100

000100

000100

00100

055

0055

0133

0100

0560

0750

0420

0140

0241

153

679

1212

2542

454

147119864minus03

267

149

825119864minus10

15046

100

000100

000100

00100

056

0056

0133

0100

Medium

porosity

particles

0613

0620

0380

0233

0376

258

1146

1870

4293

701

872119864minus04

267

164

535119864minus10

15046

100

000100

000100

00100

061

0061

0161

0100

0629

0620

0390

0239

0392

237

1053

1675

3946

627

949119864minus04

267

168

597119864minus10

15046

100

000100

000100

00100

063

0063

0161

0100

064

50620

040

00245

040

9218

969

1502

3629

563

103119864minus03

267

172

666119864minus10

15046

100

000100

000100

00100

064

0065

0161

0100

0661

0620

0410

0251

0426

201

892

1349

3340

505

112119864minus03

267

177

742119864minus10

15046

100

000100

000100

00100

066

006

60161

0100

0677

0620

0420

0257

044

4185

821

1212

3076

454

122119864minus03

267

181

825119864minus10

15046

100

000100

000100

00100

068

006

80161

0100

Highpo

rosity

particles

0760

0500

0380

0380

0613

320

1422

1870

5325

701

703119864minus04

267

203

535119864minus10

15046

100

000100

000100

00100

076

0076

0200

0100

0780

0500

0390

0390

0639

294

1306

1675

4891

627

766119864minus04

267

208

597119864minus10

15046

100

000100

000100

00100

078

0078

0200

0100

0800

0500

040

0040

0066

7270

1202

1502

4500

563

832119864minus04

267

214

666119864minus10

15046

100

000100

000100

00100

080

0080

0200

0100

0820

0500

0410

0410

0694

249

1105

1349

4140

505

905119864minus04

267

219

742119864minus10

15046

100

000100

000100

00100

082

0082

0200

0100

0840

0500

0420

0420

0724

229

1018

1212

3814

454

982119864minus04

267

224

825119864minus10

15046

100

000100

000100

00100

084

0084

0200

0100

Capillary

1000

0380

0380

0620

1000

421

1870

1870

7005

701

535119864minus04

267

267

535119864minus10

15046

100

000100

000100

00100

100

0100

0263

0100

1000

0390

0390

0610

1000

377

1675

1675

6273

627

597119864minus04

267

267

597119864minus10

15046

100

000100

000100

00100

100

0100

0256

0100

1000

040

0040

0060

010

00338

1502

1502

5625

563

666119864minus04

267

267

666119864minus10

15046

100

000100

000100

00100

100

0100

0250

0100

1000

0410

0410

0590

1000

303

1349

1349

5051

505

742119864minus04

267

267

742119864minus10

15046

100

000100

000100

00100

100

0100

0244

0100

1000

0420

0420

0580

1000

273

1212

1212

4541

454

825119864minus04

267

267

825119864minus10

15046

100

000100

000100

00100

100

0100

0238

0100


0200400600800

100012001400160018002000

20 30 40 50 60 70






Capillary


y = 267x + 0

Ψ

120601

Line

High porosity

(a)

99111123135147159171183195207219231243255267

035 045 055 065 075 085 095


Capillary


y = 267x + 0

Pt

120576t

Φ = 10

Φ = 075

Φ = 062

Φ = 05

Φ = 075

Φ = 062

Φ = 05

Φ = 1

(b)

99111123135147159171183195207219231243255267

000 010 020 030 040 050 060 070 080 090 100


120576p

y = 160x + 107

Pt


(c)







0in his worked




Table2Cr

oss-referencefor

term

s119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


3minminus1cm

secminus

1cm

secminus

1cm

secminus

1

Nonporousp

articles

Gidding

srsquotradition

alno

nporou

scolum

n040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

1000010

00010

0010

0399

004

00100

0100

Guiocho

nrsquostradition

alspheric

alparticle(app

arent)

0362

1000

0362

000

0000

0187

830

2293

3106

858

120119864minus03

267

97436119864minus10

15046

1000010

00010

0010

0361

0036

0100

0100

Gidd

ingrsquos

table5

3-1

5060meshglassb

eads

0422

1000

0422

000

0000

0113

500

1184

1873

444

200119864minus03

267

113

844119864minus10

15046

1000010

00010

0010

0421

004

20100

0100

5060meshglassb

eads

040

910

00040

9000

0000

0126

560

1371

2097

513

179119864minus03

267

109

729119864minus10

15046

1000010

00010

0010

040

70041

0100

0100


ExA

irregular

particle

(app

arent)

040

010

00040

0000

0000

0225

1000

2500

2250

563

100119864minus03

444

178

400119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExA

correctedforp

article

irregularity

040

010

00040

0000

0000

0225

601

1502

2250

563

166119864minus03

267

107

400119864minus10

15046

078

00010

000

080010

0399

004

00100

0100

ExB

spheric

alparticle

(app

arent)

040

010

00040

0000

0000

0187

830

2075

2250

563

120119864minus03

369

148

482119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExB

corrected

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

Porous

particles

Gidding

srsquotradition

alpo

rous

column

060

0066

7040

00200

0333

203

900

1500

3375

563

111119864minus03

267

160

667119864minus10

15046

100

00010

00010

0010

0599

006

00150

0100

Gidd

ingrsquos

table5

3-1

3040meshalum

ina

0803

0498

040

00403

0672

271

1204

1499

4510

562

830119864minus04

267

214

667119864minus10

15046

100

00010

00010

0010

0801

0080

0201

0100

5060meshalum

ina

0837

0499

0417

0420

0721

235

1043

1246

3906

467

959119864minus04

267

224

803119864minus10

15046

100

00010

00010

0010

0835

0084

0201

0100

6080meshchromosorbW

(5DNP)

0766

0498

0382

0384

0621

316

1404

1833

5259

687

712119864minus04

267

204

545119864minus10

15046

100

00010

00010

0010

0764

0077

0201

0100

6080meshchromosorbW

(20

DNP)

0785

0495

0389

0396

064

8300

1333

1698

4991

636

750119864minus04

267

210

589119864minus10

15046

100

00010

00010

0010

0783

0079

0202

0100



05





119901







of 369 for 1198750






0 and 107 for 119875

119905


119905also






119905based upon


119905is even more



119905










0









119905is 267












0 119875

119905 120576

119905 and 120576

119901


0




119905and 120576


0and









119905below




2

1199011205762][150(1 minus 120576)










119891=

12057630180 (1 minus 120576




0of the


0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]




0180(1 minus 120576

0)2










119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

000

028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

2161

400

173119864minus03

267

144

729119864minus11

393119864minus11

1500

046

088

000

023

000

0205

000

41300

030

070

056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

0419

197

725

1142

4865

766

138119864minus03

149

95399119864minus11

253119864minus11

300

021

100

000

017

000

0170

00035

100

048

129

076

Colum

nF 2

rawdata

064

200581

03730

0269

0429

361

807

1258

4863

758

124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

000

017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

03800

0259

0418

1014

752

1177

4476

701

133119864minus03

168

107

384119864minus11

246119864minus11

1500

021

100

000

017

000

0170

00035

100

048

127

075

Colum

nF 1

corrected

06350

0630

040

000235

0392

197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

678

150119864minus03

150

98434119864minus11

285119864minus11

1500

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Table1Colum

nperm


119870119865

Particlepo

rosity

rang

e120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905

(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


cm3 m

inminus1

cmsecminus

1cm

secminus

1cm

secminus

1

Non

porous

particles

0380

1000

0380

000

0000

0160

711

1870

2662

701

141119864minus03

267

101

535119864minus10

15046

100

000100

000100

00100

038

0038

0100

0100

0390

1000

0390

000

0000

0147

653

1675

244

6627

153119864minus03

267

104

597119864minus10

15046

100

000100

000100

00100

039

0039

0100

0100

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

000100

000100

00100

040

004

00100

0100

0410

1000

0410

000

0000

0124

553

1349

2071

505

181119864minus03

267

109

742119864minus10

15046

100

000100

000100

00100

041

004

10100

0100

0420

1000

0420

000

0000

0115

509

1212

1907

454

196119864minus03

267

112

825119864minus10

15046

100

000100

000100

00100

042

004

20100

0100

Lowpo

rosity

particles

0507

0750

0380

0127

0204

213

948

1870

3549

701

106119864minus03

267

135

535119864minus10

15046

100

000100

000100

00100

051

0051

0133

0100

0520

0750

0390

0130

0213

196

871

1675

3261

627

115119864minus03

267

139

597119864minus10

15046

100

000100

000100

00100

052

0052

0133

0100

0533

0750

040

00133

0222

180

801

1502

2999

563

125119864minus03

267

142

666119864minus10

15046

100

000100

000100

00100

053

0053

0133

0100

0546

0750

0410

0136

0231

166

737

1349

2760

505

136119864minus03

267

146

742119864minus10

15046

100

000100

000100

00100

055

0055

0133

0100

0560

0750

0420

0140

0241

153

679

1212

2542

454

147119864minus03

267

149

825119864minus10

15046

100

000100

000100

00100

056

0056

0133

0100

Medium

porosity

particles

0613

0620

0380

0233

0376

258

1146

1870

4293

701

872119864minus04

267

164

535119864minus10

15046

100

000100

000100

00100

061

0061

0161

0100

0629

0620

0390

0239

0392

237

1053

1675

3946

627

949119864minus04

267

168

597119864minus10

15046

100

000100

000100

00100

063

0063

0161

0100

064

50620

040

00245

040

9218

969

1502

3629

563

103119864minus03

267

172

666119864minus10

15046

100

000100

000100

00100

064

0065

0161

0100

0661

0620

0410

0251

0426

201

892

1349

3340

505

112119864minus03

267

177

742119864minus10

15046

100

000100

000100

00100

066

006

60161

0100

0677

0620

0420

0257

044

4185

821

1212

3076

454

122119864minus03

267

181

825119864minus10

15046

100

000100

000100

00100

068

006

80161

0100

Highpo

rosity

particles

0760

0500

0380

0380

0613

320

1422

1870

5325

701

703119864minus04

267

203

535119864minus10

15046

100

000100

000100

00100

076

0076

0200

0100

0780

0500

0390

0390

0639

294

1306

1675

4891

627

766119864minus04

267

208

597119864minus10

15046

100

000100

000100

00100

078

0078

0200

0100

0800

0500

040

0040

0066

7270

1202

1502

4500

563

832119864minus04

267

214

666119864minus10

15046

100

000100

000100

00100

080

0080

0200

0100

0820

0500

0410

0410

0694

249

1105

1349

4140

505

905119864minus04

267

219

742119864minus10

15046

100

000100

000100

00100

082

0082

0200

0100

0840

0500

0420

0420

0724

229

1018

1212

3814

454

982119864minus04

267

224

825119864minus10

15046

100

000100

000100

00100

084

0084

0200

0100

Capillary

1000

0380

0380

0620

1000

421

1870

1870

7005

701

535119864minus04

267

267

535119864minus10

15046

100

000100

000100

00100

100

0100

0263

0100

1000

0390

0390

0610

1000

377

1675

1675

6273

627

597119864minus04

267

267

597119864minus10

15046

100

000100

000100

00100

100

0100

0256

0100

1000

040

0040

0060

010

00338

1502

1502

5625

563

666119864minus04

267

267

666119864minus10

15046

100

000100

000100

00100

100

0100

0250

0100

1000

0410

0410

0590

1000

303

1349

1349

5051

505

742119864minus04

267

267

742119864minus10

15046

100

000100

000100

00100

100

0100

0244

0100

1000

0420

0420

0580

1000

273

1212

1212

4541

454

825119864minus04

267

267

825119864minus10

15046

100

000100

000100

00100

100

0100

0238

0100


0200400600800

100012001400160018002000

20 30 40 50 60 70






Capillary


y = 267x + 0

Ψ

120601

Line

High porosity

(a)

99111123135147159171183195207219231243255267

035 045 055 065 075 085 095


Capillary


y = 267x + 0

Pt

120576t

Φ = 10

Φ = 075

Φ = 062

Φ = 05

Φ = 075

Φ = 062

Φ = 05

Φ = 1

(b)

99111123135147159171183195207219231243255267

000 010 020 030 040 050 060 070 080 090 100


120576p

y = 160x + 107

Pt


(c)







0in his worked




Table2Cr

oss-referencefor

term

s119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


3minminus1cm

secminus

1cm

secminus

1cm

secminus

1

Nonporousp

articles

Gidding

srsquotradition

alno

nporou

scolum

n040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

1000010

00010

0010

0399

004

00100

0100

Guiocho

nrsquostradition

alspheric

alparticle(app

arent)

0362

1000

0362

000

0000

0187

830

2293

3106

858

120119864minus03

267

97436119864minus10

15046

1000010

00010

0010

0361

0036

0100

0100

Gidd

ingrsquos

table5

3-1

5060meshglassb

eads

0422

1000

0422

000

0000

0113

500

1184

1873

444

200119864minus03

267

113

844119864minus10

15046

1000010

00010

0010

0421

004

20100

0100

5060meshglassb

eads

040

910

00040

9000

0000

0126

560

1371

2097

513

179119864minus03

267

109

729119864minus10

15046

1000010

00010

0010

040

70041

0100

0100


ExA

irregular

particle

(app

arent)

040

010

00040

0000

0000

0225

1000

2500

2250

563

100119864minus03

444

178

400119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExA

correctedforp

article

irregularity

040

010

00040

0000

0000

0225

601

1502

2250

563

166119864minus03

267

107

400119864minus10

15046

078

00010

000

080010

0399

004

00100

0100

ExB

spheric

alparticle

(app

arent)

040

010

00040

0000

0000

0187

830

2075

2250

563

120119864minus03

369

148

482119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExB

corrected

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

Porous

particles

Gidding

srsquotradition

alpo

rous

column

060

0066

7040

00200

0333

203

900

1500

3375

563

111119864minus03

267

160

667119864minus10

15046

100

00010

00010

0010

0599

006

00150

0100

Gidd

ingrsquos

table5

3-1

3040meshalum

ina

0803

0498

040

00403

0672

271

1204

1499

4510

562

830119864minus04

267

214

667119864minus10

15046

100

00010

00010

0010

0801

0080

0201

0100

5060meshalum

ina

0837

0499

0417

0420

0721

235

1043

1246

3906

467

959119864minus04

267

224

803119864minus10

15046

100

00010

00010

0010

0835

0084

0201

0100

6080meshchromosorbW

(5DNP)

0766

0498

0382

0384

0621

316

1404

1833

5259

687

712119864minus04

267

204

545119864minus10

15046

100

00010

00010

0010

0764

0077

0201

0100

6080meshchromosorbW

(20

DNP)

0785

0495

0389

0396

064

8300

1333

1698

4991

636

750119864minus04

267

210

589119864minus10

15046

100

00010

00010

0010

0783

0079

0202

0100



05





119901







of 369 for 1198750






0 and 107 for 119875

119905


119905also






119905based upon


119905is even more



119905










0









119905is 267












0 119875

119905 120576

119905 and 120576

119901


0




119905and 120576


0and









119905below




2

1199011205762][150(1 minus 120576)










119891=

12057630180 (1 minus 120576




0of the


0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]




0180(1 minus 120576

0)2










119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

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028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

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173119864minus03

267

144

729119864minus11

393119864minus11

1500

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088

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023

000

0205

000

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030

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056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

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197

725

1142

4865

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138119864minus03

149

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253119864minus11

300

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129

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Colum

nF 2

rawdata

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200581

03730

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124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

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1166

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724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

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017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

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0259

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1177

4476

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133119864minus03

168

107

384119864minus11

246119864minus11

1500

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100

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000

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00035

100

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127

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Colum

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corrected

06350

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197

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1502

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267

170

399119864minus11

253119864minus11

300

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100

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100

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120

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Colum

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200623

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267

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358119864minus11

230119864minus11

500

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Colum

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corrected

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040

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1502

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6563

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267

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386119864minus11

248119864minus11

1000

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100

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00035

100

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120

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Colum

nF 4

corrected

06390

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104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

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120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

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164119864minus03

141

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310119864minus11

1500

021

100

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017

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00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

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260

787

1225

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127119864minus03

153

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236119864minus11

500

030

100

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012

032

018

Colum

nI 5rawdata

06540

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3683

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4531

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146119864minus03

151

99423119864minus11

277119864minus11

1000

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100

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012

031

018

Colum

nI 6rawdata

06550

0585

03830

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164

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150119864minus03

150

98434119864minus11

285119864minus11

1500

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018

Colum

nI 1corrected

06580

060

8040

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0430

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988

1502

3701

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101119864minus03

267

176

390119864minus11

256119864minus11

500

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100

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00104

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060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

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1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

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100

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021

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0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

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022

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0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

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100

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029

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0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

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040

000098

0163

124

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1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

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Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

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031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

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550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0200400600800

100012001400160018002000

20 30 40 50 60 70






Capillary


y = 267x + 0

Ψ

120601

Line

High porosity

(a)

99111123135147159171183195207219231243255267

035 045 055 065 075 085 095


Capillary


y = 267x + 0

Pt

120576t

Φ = 10

Φ = 075

Φ = 062

Φ = 05

Φ = 075

Φ = 062

Φ = 05

Φ = 1

(b)

99111123135147159171183195207219231243255267

000 010 020 030 040 050 060 070 080 090 100


120576p

y = 160x + 107

Pt


(c)







0in his worked




Table2Cr

oss-referencefor

term

s119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


3minminus1cm

secminus

1cm

secminus

1cm

secminus

1

Nonporousp

articles

Gidding

srsquotradition

alno

nporou

scolum

n040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

1000010

00010

0010

0399

004

00100

0100

Guiocho

nrsquostradition

alspheric

alparticle(app

arent)

0362

1000

0362

000

0000

0187

830

2293

3106

858

120119864minus03

267

97436119864minus10

15046

1000010

00010

0010

0361

0036

0100

0100

Gidd

ingrsquos

table5

3-1

5060meshglassb

eads

0422

1000

0422

000

0000

0113

500

1184

1873

444

200119864minus03

267

113

844119864minus10

15046

1000010

00010

0010

0421

004

20100

0100

5060meshglassb

eads

040

910

00040

9000

0000

0126

560

1371

2097

513

179119864minus03

267

109

729119864minus10

15046

1000010

00010

0010

040

70041

0100

0100


ExA

irregular

particle

(app

arent)

040

010

00040

0000

0000

0225

1000

2500

2250

563

100119864minus03

444

178

400119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExA

correctedforp

article

irregularity

040

010

00040

0000

0000

0225

601

1502

2250

563

166119864minus03

267

107

400119864minus10

15046

078

00010

000

080010

0399

004

00100

0100

ExB

spheric

alparticle

(app

arent)

040

010

00040

0000

0000

0187

830

2075

2250

563

120119864minus03

369

148

482119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExB

corrected

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

Porous

particles

Gidding

srsquotradition

alpo

rous

column

060

0066

7040

00200

0333

203

900

1500

3375

563

111119864minus03

267

160

667119864minus10

15046

100

00010

00010

0010

0599

006

00150

0100

Gidd

ingrsquos

table5

3-1

3040meshalum

ina

0803

0498

040

00403

0672

271

1204

1499

4510

562

830119864minus04

267

214

667119864minus10

15046

100

00010

00010

0010

0801

0080

0201

0100

5060meshalum

ina

0837

0499

0417

0420

0721

235

1043

1246

3906

467

959119864minus04

267

224

803119864minus10

15046

100

00010

00010

0010

0835

0084

0201

0100

6080meshchromosorbW

(5DNP)

0766

0498

0382

0384

0621

316

1404

1833

5259

687

712119864minus04

267

204

545119864minus10

15046

100

00010

00010

0010

0764

0077

0201

0100

6080meshchromosorbW

(20

DNP)

0785

0495

0389

0396

064

8300

1333

1698

4991

636

750119864minus04

267

210

589119864minus10

15046

100

00010

00010

0010

0783

0079

0202

0100



05





119901







of 369 for 1198750






0 and 107 for 119875

119905


119905also






119905based upon


119905is even more



119905










0









119905is 267












0 119875

119905 120576

119905 and 120576

119901


0




119905and 120576


0and









119905below




2

1199011205762][150(1 minus 120576)










119891=

12057630180 (1 minus 120576




0of the


0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]




0180(1 minus 120576

0)2










119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

000

028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

2161

400

173119864minus03

267

144

729119864minus11

393119864minus11

1500

046

088

000

023

000

0205

000

41300

030

070

056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

0419

197

725

1142

4865

766

138119864minus03

149

95399119864minus11

253119864minus11

300

021

100

000

017

000

0170

00035

100

048

129

076

Colum

nF 2

rawdata

064

200581

03730

0269

0429

361

807

1258

4863

758

124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

000

017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

03800

0259

0418

1014

752

1177

4476

701

133119864minus03

168

107

384119864minus11

246119864minus11

1500

021

100

000

017

000

0170

00035

100

048

127

075

Colum

nF 1

corrected

06350

0630

040

000235

0392

197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

678

150119864minus03

150

98434119864minus11

285119864minus11

1500

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Table2Cr

oss-referencefor

term

s119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119896119871

119863Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

120576119905Φ

(120576119905minus1205760)

120576119894

Δ119875119889119901

2Δ119875119889119901

2(1minus120576119905Φ)2120576119905(1minus1205760)2

1120601

1198750120576119905

119889119901

2120576119905

(119889119901119898Ω119901)

(1minus1205760)

120583119905120578119871

120583119904120578119871

(120576119905Φ)3

(1205760)3

120601Ψ

120601po

iseUnits

Non

eNon

eNon

eNon

eNon

epsi

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

cmNon

ecm


3minminus1cm

secminus

1cm

secminus

1cm

secminus

1

Nonporousp

articles

Gidding

srsquotradition

alno

nporou

scolum

n040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

1000010

00010

0010

0399

004

00100

0100

Guiocho

nrsquostradition

alspheric

alparticle(app

arent)

0362

1000

0362

000

0000

0187

830

2293

3106

858

120119864minus03

267

97436119864minus10

15046

1000010

00010

0010

0361

0036

0100

0100

Gidd

ingrsquos

table5

3-1

5060meshglassb

eads

0422

1000

0422

000

0000

0113

500

1184

1873

444

200119864minus03

267

113

844119864minus10

15046

1000010

00010

0010

0421

004

20100

0100

5060meshglassb

eads

040

910

00040

9000

0000

0126

560

1371

2097

513

179119864minus03

267

109

729119864minus10

15046

1000010

00010

0010

040

70041

0100

0100


ExA

irregular

particle

(app

arent)

040

010

00040

0000

0000

0225

1000

2500

2250

563

100119864minus03

444

178

400119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExA

correctedforp

article

irregularity

040

010

00040

0000

0000

0225

601

1502

2250

563

166119864minus03

267

107

400119864minus10

15046

078

00010

000

080010

0399

004

00100

0100

ExB

spheric

alparticle

(app

arent)

040

010

00040

0000

0000

0187

830

2075

2250

563

120119864minus03

369

148

482119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

ExB

corrected

040

010

00040

0000

0000

0135

601

1502

2250

563

166119864minus03

267

107

666119864minus10

15046

100

00010

00010

0010

0399

004

00100

0100

Porous

particles

Gidding

srsquotradition

alpo

rous

column

060

0066

7040

00200

0333

203

900

1500

3375

563

111119864minus03

267

160

667119864minus10

15046

100

00010

00010

0010

0599

006

00150

0100

Gidd

ingrsquos

table5

3-1

3040meshalum

ina

0803

0498

040

00403

0672

271

1204

1499

4510

562

830119864minus04

267

214

667119864minus10

15046

100

00010

00010

0010

0801

0080

0201

0100

5060meshalum

ina

0837

0499

0417

0420

0721

235

1043

1246

3906

467

959119864minus04

267

224

803119864minus10

15046

100

00010

00010

0010

0835

0084

0201

0100

6080meshchromosorbW

(5DNP)

0766

0498

0382

0384

0621

316

1404

1833

5259

687

712119864minus04

267

204

545119864minus10

15046

100

00010

00010

0010

0764

0077

0201

0100

6080meshchromosorbW

(20

DNP)

0785

0495

0389

0396

064

8300

1333

1698

4991

636

750119864minus04

267

210

589119864minus10

15046

100

00010

00010

0010

0783

0079

0202

0100



05





119901







of 369 for 1198750






0 and 107 for 119875

119905


119905also






119905based upon


119905is even more



119905










0









119905is 267












0 119875

119905 120576

119905 and 120576

119901


0




119905and 120576


0and









119905below




2

1199011205762][150(1 minus 120576)










119891=

12057630180 (1 minus 120576




0of the


0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]




0180(1 minus 120576

0)2










119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

000

028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

2161

400

173119864minus03

267

144

729119864minus11

393119864minus11

1500

046

088

000

023

000

0205

000

41300

030

070

056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

0419

197

725

1142

4865

766

138119864minus03

149

95399119864minus11

253119864minus11

300

021

100

000

017

000

0170

00035

100

048

129

076

Colum

nF 2

rawdata

064

200581

03730

0269

0429

361

807

1258

4863

758

124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

000

017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

03800

0259

0418

1014

752

1177

4476

701

133119864minus03

168

107

384119864minus11

246119864minus11

1500

021

100

000

017

000

0170

00035

100

048

127

075

Colum

nF 1

corrected

06350

0630

040

000235

0392

197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

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1198681-1198686

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050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials





05





119901







of 369 for 1198750






0 and 107 for 119875

119905


119905also






119905based upon


119905is even more



119905










0









119905is 267












0 119875

119905 120576

119905 and 120576

119901


0




119905and 120576


0and









119905below




2

1199011205762][150(1 minus 120576)










119891=

12057630180 (1 minus 120576




0of the


0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]




0180(1 minus 120576

0)2










119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









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119870119896

119871119863

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119889119901

120578119876

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Colum

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Colum

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Guiochon

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1198631ndash1198636(2006)

Colum

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(2007)

Colum

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Colum

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Colum

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Colum

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Guiochon

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1198651ndash1198654

(2008)

Colum

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06350

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197

725

1142

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138119864minus03

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Colum

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Colum

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134119864minus03

161

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128

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Colum

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133119864minus03

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Colum

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197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

678

150119864minus03

150

98434119864minus11

285119864minus11

1500

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials









119905below




2

1199011205762][150(1 minus 120576)










119891=

12057630180 (1 minus 120576




0of the


0= (1185)(1205763

01198892119901(1 minus 120576

0)2)rdquo [15 p 30]




0180(1 minus 120576

0)2










119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

000

028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

2161

400

173119864minus03

267

144

729119864minus11

393119864minus11

1500

046

088

000

023

000

0205

000

41300

030

070

056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

0419

197

725

1142

4865

766

138119864minus03

149

95399119864minus11

253119864minus11

300

021

100

000

017

000

0170

00035

100

048

129

076

Colum

nF 2

rawdata

064

200581

03730

0269

0429

361

807

1258

4863

758

124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

000

017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

03800

0259

0418

1014

752

1177

4476

701

133119864minus03

168

107

384119864minus11

246119864minus11

1500

021

100

000

017

000

0170

00035

100

048

127

075

Colum

nF 1

corrected

06350

0630

040

000235

0392

197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

678

150119864minus03

150

98434119864minus11

285119864minus11

1500

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials











119865) of 1198892





=














119888120576119879) where 120576

119879is the



119905) The





119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

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3390

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110119864minus03

267

165

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207119864minus10

1499

046

100

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0550

00150

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Colum

nD

6corrected

05760

0701

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0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

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055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

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356

1119

1735

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894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

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030

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0300

000

41300

030

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047

Colum

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rawdata

05400

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04320

0108

0190

470

1000

1853

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400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

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100

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027

000

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41300

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070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

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267

172

804119864minus11

519119864minus11

1500

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100

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0279

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Colum

nE 2

corrected

05400

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393119864minus11

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Guiochon

columns

1198651ndash1198654

(2008)

Colum

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rawdata

06350

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725

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129

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Colum

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rawdata

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200581

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166

107

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230119864minus11

500

021

100

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000

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100

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129

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Colum

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rawdata

064

100588

03770

0264

0424

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1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

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00035

100

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128

075

Colum

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rawdata

06390

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168

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1500

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127

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Colum

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197

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267

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253119864minus11

300

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Colum

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200623

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230119864minus11

500

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Colum

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267

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248119864minus11

1000

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Colum

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06390

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267

171

384119864minus11

246119864minus11

1500

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100

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100

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120

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Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

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eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

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005

013

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Colum

nH

2corrected

05420

0738

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267

145

823119864minus11

446119864minus11

1000

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100

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Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

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0396

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700

1117

4296

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163

102

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280119864minus11

1500

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100

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038

Colum

nH

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05170

0791

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900108

0183

433

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1191

2639

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162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

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0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

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017

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0170

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037

Colum

nI 2rawdata

06550

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6873

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1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

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164119864minus03

141

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310119864minus11

1500

021

100

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017

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037

Colum

nI 4rawdata

06430

0572

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260

787

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127119864minus03

153

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236119864minus11

500

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100

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018

Colum

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06540

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3683

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146119864minus03

151

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277119864minus11

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Colum

nI 6rawdata

06550

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03830

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150

98434119864minus11

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Colum

nI 1corrected

06580

060

8040

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0430

488

988

1502

3701

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101119864minus03

267

176

390119864minus11

256119864minus11

500

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100

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0196

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Colum

nI 2corrected

06550

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040

000255

0425

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984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

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100

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0207

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Colum

nI 3corrected

06550

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0425

1209

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102119864minus03

267

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474119864minus11

310119864minus11

1500

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Colum

nI 4corrected

06430

0622

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040

5260

966

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3617

563

104119864minus03

267

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367119864minus11

236119864minus11

500

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Colum

nI 5corrected

06540

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0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

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100

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020

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0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

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0803

040

000098

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1313

2801

563

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234

116126119864minus10

627119864minus11

1500

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Colum

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∘A(120578

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1307

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563

154119864minus03

232

116127119864minus10

630119864minus11

1500

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100

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029

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00104

050

005

013

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Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

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0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

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005

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Colum

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∘A(120578

=00104

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0714

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0161

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129

847

1504

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118119864minus03

273

154

108119864minus10

606119864minus11

1500

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100

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030

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00104

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Colum

nJ 1corrected

04980

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040

000098

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1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

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100

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0307

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050

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Colum

nJ 2corrected

04980

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040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

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031

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00104

050

005

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010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






119905was equal




119905(there is no



1 Note









2 Note that the



2









ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

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055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

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393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

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028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

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470

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267

144

729119864minus11

393119864minus11

1500

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088

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023

000

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000

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030

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056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

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197

725

1142

4865

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138119864minus03

149

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253119864minus11

300

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100

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100

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129

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Colum

nF 2

rawdata

064

200581

03730

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361

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124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

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017

000

0170

00035

100

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129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

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724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

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017

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00035

100

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128

075

Colum

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rawdata

06390

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4476

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133119864minus03

168

107

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1500

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100

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127

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Colum

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06350

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197

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1502

3572

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267

170

399119864minus11

253119864minus11

300

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Colum

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200623

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267

171

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230119864minus11

500

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100

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120

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Colum

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corrected

064

100624

040

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1502

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104119864minus03

267

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248119864minus11

1000

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00035

100

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120

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Colum

nF 4

corrected

06390

0626

040

000239

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1014

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1502

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563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

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120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

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018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

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164119864minus03

141

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310119864minus11

1500

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100

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Colum

nI 4rawdata

06430

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260

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127119864minus03

153

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236119864minus11

500

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012

032

018

Colum

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06540

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3683

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146119864minus03

151

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277119864minus11

1000

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285119864minus11

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Colum

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267

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256119864minus11

500

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Colum

nI 2corrected

06550

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102119864minus03

267

175

437119864minus11

286119864minus11

1000

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100

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024

060

037

Colum

nI 3corrected

06550

0611

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0425

1209

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3684

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102119864minus03

267

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474119864minus11

310119864minus11

1500

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Colum

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06430

0622

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040

5260

966

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563

104119864minus03

267

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236119864minus11

500

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029

018

Colum

nI 5corrected

06540

0612

040

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0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

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020

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0204

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050

012

029

018

Colum

nI 6corrected

06550

0611

040

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0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

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65654

1313

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563

153119864minus03

234

116126119864minus10

627119864minus11

1500

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100

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029

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050

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013

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Colum

nJ 2rawdata90

∘A(120578

=00104

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000098

0163

124

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1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

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030

000

0302

00104

050

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Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

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031

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0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

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040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




ble3Summaryexperim

entald

ata

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Naefe

andHalasz

columns

1198601(19

72)

Colum

nA1rawdata

07140

0560

040

000314

0523

782007

2811

4016

563

498119864minus04

500

357

908119864minus10

648119864minus10

2500

020

100

000135

0001350

00038

100

053

132

074

Colum

nA1corrected

07140

0532

03800

0334

0539

7813

3518

705002

701

749119864minus04

267

191

908119864minus10

648119864minus10

2500

020

100

000110

000110

100038

100

053

139

074

Endelean

dHalasz

columns

1198602(19

74)

Colum

nA2rawdata

08426

0475

040

00044

30738

11910

1080

4740

563

110119864minus03

192

162

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

033

016

Colum

nA2corrected

08426

0511

04309

0412

0723

11910

1080

3411

405

110119864minus03

267

225

435119864minus10

366119864minus10

3000

040

100

000

063

000

0629

00010

100

013

031

016

Guiochon

columns

1198612ndash1198614(19

98)

Colum

nB 2

rawdata

05639

0722

040

730157

0264

22771

1367

2931

520

130119864minus03

263

148

467119864minus10

263119864minus10

429

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 3

rawdata

05582

0704

03932

0165

0272

44764

1369

3382

606

131119864minus03

226

126

471119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 4

rawdata

05509

0710

03909

0160

0263

72784

1422

3422

621

128119864minus03

229

126

459119864minus10

253119864minus10

1328

500

100

000

060

000

0600

00165

98008

021

015

Colum

nB 3

corrected

05653

0723

040

860157

0265

44774

1369

2899

513

129119864minus03

267

151

465119864minus10

263119864minus10

838

500

100

000

060

000

0600

00165

98008

020

015

Colum

nB 4

corrected

05651

0723

040

830157

0265

72776

1374

2907

514

129119864minus03

267

151

464119864minus10

262119864minus10

1375

500

100

000

060

000

0600

00165

98008

020

015

Guiochon

columnC

(1999)

Colum

nCrawdata

05930

0673

03990

0194

0323

183

865

1459

3372

569

116119864minus03

257

152

109119864minus09

645119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Colum

nCcorrected

05930

0673

03990

0194

0323

190

900

1518

3372

569

111119864minus03

267

158

105119864minus09

620119864minus10

1000

046

100

000

097

000

0970

01990

059

006

015

010

Guiochon

columns

1198631ndash1198636(2006)

Colum

nD

1rawdata

07830

0456

03570

0426

0663

86694

886

7115

909

144119864minus03

975

76334119864minus10

261119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

013

Colum

nD

2rawdata

07230

0491

03550

0368

0571

88656

907

6726

930

152119864minus03

975

70353119864minus10

255119864minus10

1499

046

100

000

048

000

0481

00150

100

010

028

014

Colum

nD

3rawdata

06850

0506

03466

0338

0518

97685

1000

7025

1026

146119864minus03

975

67338119864minus10

231119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD

4rawdata

06560

0521

03415

0315

0478

103

696

1062

7143

1089

144119864minus03

975

64332119864minus10

218119864minus10

1499

046

100

000

048

000

0481

00150

100

010

029

015

Colum

nD5rawdata

06190

0545

03371

0282

0425

109

692

1118

7100

1147

144119864minus03

975

60334119864minus10

207119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

016

Colum

nD

6rawdata

05760

0587

03383

0238

0359

107

635

1103

6516

1131

157119864minus03

975

56364119864minus10

210119864minus10

1499

046

100

000

048

000

0481

00150

100

010

030

017

Colum

nD

1corrected

07830

0542

04243

0359

0623

86907

1158

3397

434

110119864minus03

267

209

334119864minus10

261119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

013

Colum

nD

2corrected

07230

0584

04221

0301

0521

88857

1186

3212

444

117119864minus03

267

193

353119864minus10

255119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

014

Colum

nD

3corrected

06850

0603

04129

0272

0463

97896

1307

3354

490

112119864minus03

267

183

338119864minus10

231119864minus10

1499

046

100

000

055

000

0550

00150

100

010

024

015

Colum

nD

4corrected

06560

0621

040

730249

0420

103

911

1388

3411

520

110119864minus03

267

175

332119864minus10

218119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

015

Colum

nD

5corrected

06190

0650

04025

0217

0362

109

905

1462

3390

548

110119864minus03

267

165

334119864minus10

207119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

016

Colum

nD

6corrected

05760

0701

04038

0172

0289

107

831

1442

3111

540

120119864minus03

267

154

364119864minus10

210119864minus10

1499

046

100

000

055

000

0550

00150

100

010

025

017

Guiochon

columns

1198641-1198642

(2007)

Colum

nE 1

rawdata

064

500594

03830

0262

0425

356

1119

1735

4371

678

894119864minus04

256

165

804119864minus11

519119864minus11

1500

046

100

000

030

000

0300

000

41300

030

079

047

Colum

nE 2

rawdata

05400

0800

04320

0108

0190

470

1000

1853

2161

400

100119864minus03

463

250

729119864minus11

393119864minus11

1500

046

100

000

027

000

0270

000

41300

030

070

056

Colum

nE 1

corrected

064

500594

040

000245

040

8356

969

1502

3628

563

103119864minus03

267

172

804119864minus11

519119864minus11

1500

046

100

000

028

000

0279

000

41300

030

075

047

Colum

nE 2

corrected

05400

0800

04320

0108

0190

470

577

1068

2161

400

173119864minus03

267

144

729119864minus11

393119864minus11

1500

046

088

000

023

000

0205

000

41300

030

070

056

Guiochon

columns

1198651ndash1198654

(2008)

Colum

nF 1

rawdata

06350

0586

03720

0263

0419

197

725

1142

4865

766

138119864minus03

149

95399119864minus11

253119864minus11

300

021

100

000

017

000

0170

00035

100

048

129

076

Colum

nF 2

rawdata

064

200581

03730

0269

0429

361

807

1258

4863

758

124119864minus03

166

107

358119864minus11

230119864minus11

500

021

100

000

017

000

0170

00035

100

048

129

075

Colum

nF 3

rawdata

064

100588

03770

0264

0424

670

748

1166

4643

724

134119864minus03

161

103

387119864minus11

248119864minus11

1000

021

100

000

017

000

0170

00035

100

048

128

075

Colum

nF 4

rawdata

06390

0595

03800

0259

0418

1014

752

1177

4476

701

133119864minus03

168

107

384119864minus11

246119864minus11

1500

021

100

000

017

000

0170

00035

100

048

127

075

Colum

nF 1

corrected

06350

0630

040

000235

0392

197

954

1502

3572

563

105119864minus03

267

170

399119864minus11

253119864minus11

300

021

100

000

019

000

0195

00035

100

048

120

076

Colum

nF 2

corrected

064

200623

040

000242

0403

361

964

1502

3611

563

104119864minus03

267

171

358119864minus11

230119864minus11

500

021

100

000

019

000

0186

00035

100

048

120

075

Colum

nF 3

corrected

064

100624

040

000241

0402

670

963

1502

360

6563

104119864minus03

267

171

386119864minus11

248119864minus11

1000

021

100

000

019

000

0193

00035

100

048

120

075

Colum

nF 4

corrected

06390

0626

040

000239

0398

1014

960

1502

3594

563

104119864minus03

267

171

384119864minus11

246119864minus11

1500

021

100

000

019

000

0192

00035

100

048

120

075


Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

678

150119864minus03

150

98434119864minus11

285119864minus11

1500

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Table3Con

tinued

119870119865

Particlecolum

ndescrip

tion

120576119905

Φ1205760

120576119894

120576119901

Δ119875

1206011206010

ΨΨ0

1198960

1198750

119875119905

119870119896

119871119863

Ω119901

119889119901119898

119889119901

120578119876

120583119904

120583119894

120583119905

Units

Non

eNon

eNon

eNon

eNon

ebar

Non

eNon

eNon

eNon

eNon

eNon

eNon

ecm

2cm

2cm

cmNon

ecm


3 minminus1cm

secminus1cm

secminus1cm

secminus1

Guiochon

columns

1198671-1198672serie

s(2010)

Colum

nH

1rawdata

05320

0744

03960

0136

0225

120

563

1057

3125

587

178119864minus03

180

96122119864minus10

652119864minus11

1500

046

100

000

026

000

0262

00104

050

005

013

009

Colum

nH

2rawdata

05420

0686

03720

0170

0271

61747

1379

4152

766

134119864minus03

180

98823119864minus11

446119864minus11

1000

046

100

000

025

000

0248

00054

050

005

013

009

Colum

nH

1corrected

05320

0752

040

000132

0220

120

799

1502

2993

563

125119864minus03

267

142

122119864minus10

652119864minus11

1500

046

100

000

031

000

0313

00104

050

005

013

009

Colum

nH

2corrected

05420

0738

040

000142

0237

61814

1502

3049

563

123119864minus03

267

145

823119864minus11

446119864minus11

1000

046

100

000

026

000

0259

00054

050

005

013

009

Guiochon

columns

1198673-1198674serie

s(2010)

Colum

nH

3rawdata

06270

060

903820

0245

0396

463

700

1117

4296

685

143119864minus03

163

102

447119864minus11

280119864minus11

1500

021

100

000

018

000

0177

00036

050

024

063

038

Colum

nH

4rawdata

05170

0791

040

900108

0183

433

616

1191

2639

511

162119864minus03

233

121

580119864minus11

300119864minus11

1500

021

100

000

019

000

0189

00036

050

024

059

047

Colum

nH

3corrected

06270

0638

040

000227

0378

463

942

1502

3527

563

106119864minus03

267

167

447119864minus11

280119864minus11

1500

021

100

000

021

000

0205

00036

050

024

060

038

Colum

nH

4corrected

05170

0791

040

900108

0183

433

699

1353

2639

511

143119864minus03

265

137

580119864minus11

300119864minus11

1500

021

100

000

020

000

0201

00036

050

024

059

047

Guiochon

columns

1198681-1198686

(2010)

Colum

nI 1rawdata

06580

0562

03700

0288

0457

488

741

1127

5156

784

135119864minus03

144

95390119864minus11

256119864minus11

500

021

100

000

017

000

0170

00104

050

024

065

037

Colum

nI 2rawdata

06550

0576

03770

0278

044

6873

661

1009

4745

724

151119864minus03

139

91437119864minus11

286119864minus11

1000

021

100

000

017

000

0170

00104

050

024

064

037

Colum

nI 3rawdata

06550

0588

03850

0270

0439

1209

610

931

4341

663

164119864minus03

141

92474119864minus11

310119864minus11

1500

021

100

000

017

000

0170

00104

050

024

062

037

Colum

nI 4rawdata

06430

0572

03680

0275

0435

260

787

1225

5153

801

127119864minus03

153

98367119864minus11

236119864minus11

500

030

100

000

017

000

0170

00104

050

012

032

018

Colum

nI 5rawdata

06540

0583

03810

0273

044

144

3683

1044

4531

693

146119864minus03

151

99423119864minus11

277119864minus11

1000

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 6rawdata

06550

0585

03830

0272

044

164

6665

1016

4438

678

150119864minus03

150

98434119864minus11

285119864minus11

1500

030

100

000

017

000

0170

00104

050

012

031

018

Colum

nI 1corrected

06580

060

8040

000258

0430

488

988

1502

3701

563

101119864minus03

267

176

390119864minus11

256119864minus11

500

021

100

000

020

000

0196

00104

050

024

060

037

Colum

nI 2corrected

06550

0611

040

000255

0425

873

984

1502

3684

563

102119864minus03

267

175

437119864minus11

286119864minus11

1000

021

100

000

021

000

0207

00104

050

024

060

037

Colum

nI 3corrected

06550

0611

040

000255

0425

1209

984

1502

3684

563

102119864minus03

267

175

474119864minus11

310119864minus11

1500

021

100

000

022

000

0216

00104

050

024

060

037

Colum

nI 4corrected

06430

0622

040

000243

040

5260

966

1502

3617

563

104119864minus03

267

172

367119864minus11

236119864minus11

500

030

100

000

019

000

0188

00104

050

012

029

018

Colum

nI 5corrected

06540

0612

040

000254

0423

443

982

1502

3679

563

102119864minus03

267

175

423119864minus11

277119864minus11

1000

030

100

000

020

000

0204

00104

050

012

029

018

Colum

nI 6corrected

06550

0611

040

000255

0425

646

984

1502

3684

563

102119864minus03

267

175

434119864minus11

285119864minus11

1500

030

100

000

021

000

0207

00104

050

012

029

018

Guiochon

columns

1198691-1198692

(2011)

Colum

nJ 1rawdata90

∘A(120578

=00054

P)04980

0803

040

000098

0163

65654

1313

2801

563

153119864minus03

234

116126119864minus10

627119864minus11

1500

046

100

000

029

000

0287

00054

050

005

013

010

Colum

nJ 2rawdata90

∘A(120578

=00104

P)04980

0803

040

000098

0163

124

651

1307

2801

563

154119864minus03

232

116127119864minus10

630119864minus11

1500

046

100

000

029

000

0287

00104

050

005

013

010

Colum

nJ 1rawdata160

∘A(120578

=00054

P)05630

0714

04020

0161

0269

71896

1592

3099

550

112119864minus03

289

163

102119864minus10

573119864minus11

1500

046

100

000

030

000

0302

00054

050

005

012

009

Colum

nJ 2rawdata160

∘A(120578

=00104

P)05630

0714

04020

0161

0269

129

847

1504

3099

550

118119864minus03

273

154

108119864minus10

606119864minus11

1500

046

100

000

030

000

0302

00104

050

005

012

009

Colum

nJ 1corrected

04980

0803

040

000098

0163

65748

1502

2801

563

134119864minus03

267

133

126119864minus10

627119864minus11

1500

046

100

000

031

000

0307

00054

050

005

013

010

Colum

nJ 2corrected

04980

0803

040

000098

0163

124

748

1502

2801

563

134119864minus03

267

133

127119864minus10

630119864minus11

1500

046

100

000

031

000

0308

00104

050

005

013

010

Colum

nJ 1corrected

05630

0714

04020

0161

0269

71827

1470

3099

550

121119864minus03

267

150

102119864minus10

573119864minus11

1500

046

100

000

029

000

0290

00054

050

005

012

009

Colum

nJ 2corrected

05630

0714

04020

0161

0269

129

827

1470

3099

550

121119864minus03

267

150

108119864minus10

606119864minus11

1500

046

100

000

030

000

0299

00104

050

005

012

009


050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




050

100150200250300350400

045 050 055 060 065 070 075 080 085



Pt

120576t



J1 J2 H4

H1H2

D6

B2 B3 B4

J3 J4

E2

C

H3

D5 D4

E1

D2

A1

D1

A2



0

500

1000

1500

2000

2500

20 25 30 35 40 45 50 55 60 65 70 75 80

Linear (line)

Ψ




J1 J2

J3 J4E2

E1

A1

A2

H4 H1

C

120601

H2H3I1 I2 I3 I4 I5

F1 F2 F3 F4

D1 D2 D3 D4 D5 D6






B2 C E

1 H

4 J

1and J






18 However two



0 The spherical







0




0value of 268 is





3and B




4are














Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials















Greek1205760













1198750



























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials























Similarly




















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials


















119888)









119888asymp







0for this data set







1and





119905 not 119875

0 Thus



0



119905 both of




0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






0 When this data is










18rdquo [3 p 1]



1through F


0are based




119905are greater




119905are



18rdquo [24] In


1andH








0





3andH



0



0and 137 for 119875

119905






value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







value of 167 for 119875119905



1ndashI







119905 which fairly






1and J


0(which












0 they jettison










0is 267 and accord-


10 Conclusions








0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials









0must be




0





0= 180) and Ergun (119875

0= 150) [28]14


0is a


0










119890


119901 The










Acknowledgment



Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Endnotes





Δ119875 (psi) =15119906 (cms) 120578 (cP) 119871 (cm)

1198960119889119901

2(120583m2)

(587c)


Δ119875 =15 [010 cms] [10 cP] [15 cm]

[10 times 10minus3] [102]= 225 psi (587d)








0[6]



0[10 11]








0


0 He did



0(or as










References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials






References





































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials










CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



review article a reconciliation of packed column

Documents