prediction of colloid detachment in a model porous media: hydrodynamics

*Corresponding author. Tel.: #1-860-486-3548; fax: #1-860-486-2298.

E-mail address: [email protected] (D. Grasso)1Present address: Department of Civil Engineering, University of

Texas, Austin, TX 78712, USA.

Chemical Engineering Science 55 (2000) 1523}1532

Prediction of colloid detachment in a model porous media:hydrodynamics

John Bergendahl!,1, Domenico Grasso!,",*!Department of Chemical Engineering, University of Connecticut, 261 Glenbrook Road, Storrs, CT 06269-2037, USA"Environmental Engineering Program, University of Connecticut, 261 Glenbrook Road, Storrs, CT 06269-2037, USA

Received 2 February 1999; accepted 21 June 1999

Abstract

Understanding the mobility of colloids through porous media is important in both engineered and natural applications. This studyemployed a model system to explore physically based colloid detachment. Polystyrene colloids were attached in the primaryminimum to glass beads in a packed column, and a residually attached fraction was subsequently detached via hydrodynamic shear.Colloid fractions released from the surfaces in the porous media were experimentally quanti"ed. A #owrate of 75 ml/min detached50% of the residual colloid fraction from the surface. The residual colloid fraction released was predicted with a model incorporatingan interaction energy distribution and system physics. In this model, detachment is realized when the applied rolling moment fromhydrodynamic shear overcomes the resistance associated with rolling. With the exception of one parameter, the hysteresis loss factor,system characteristics were described a priori. Using the hysteresis loss factor and interaction energy distribution developed fromextended-DLVO theory, the detachment of the residual colloid fraction from the packed bed was well predicted. This workdecomposes colloid detachment into the constitutive mechanisms dependent upon thermodynamics and hydrodynamics. ( 2000Elsevier Science Ltd. All rights reserved.

Keywords: Colloid detachment; Mobilization; Hydrodynamics; Porous media; Particle; Packed bed

1. Introduction

Conditions causing colloid detachment from surfacesin porous media are important in determining the occur-rence of permeability loss in aquifers, turbidity increasesin groundwater withdrawal wells, and facilitated trans-port of hydrophobic compounds from contaminatedsites. Colloid detachment from packed beds has receivedsigni"cant research attention (Kallay, Barouch& Matijevic, 1987; Vaidyanathan & Tien, 1988; To-biason, 1989; Rijnaarts, Norde, Bouwer, Lyklema & Zeh-nder, 1993; Elimelech, 1994; Liu, Johnson & Elimelech,1995; Rijnaarts, Norde, Bouwer, Lyklema & Zehnder,1996). A model to quantitatively predict removal withthermodynamic changes has recently been presented(Bergendahl and Grasso, 1999). But until now, a model

quantifying detachment with hydrodynamic perturba-tions has not been available. This paper presents a math-ematical model to predict hydrodynamic conditionsconducive for incipient detachment of colloids not other-wise mobilized by chemistry changes in packed beds.

Because of high surface area to volume ratio, collo-idal-sized particles are predominantly a!ected by sur-face and hydrodynamic forces. Detachment of colloidsfrom surfaces in porous media can arise from perturba-tions in aqueous chemistry (i.e. ionic strength and/orpH) or hydrodynamics. In this work, polystyrene latexcolloids were attached to glass beads in the primary energyminimum and subsequently detached with hydrodynamicperturbations. The laminar shear on the attached colloidswas determined using a constricted tube model. Colloidrolling friction was calibrated for the system at a given setof conditions, and used with extended-DLVO theory toquantitatively predict the #uid #ow rate required to de-tach colloids at various conditions. This theoretical deri-vation e!ectively decouples surface energetics fromsystem hydrodynamics, allowing discrete considerationof each in determining colloid detachment.

0009-2509/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 4 2 2 - 4

Nomenclature

a#0--0*$

colloid radius, lma#0/5!#5

contact radius of colloid and glass sur-face, lm

A132

Hamaker constant between surfaces1 and 2 across medium 3, J

A#0-6./

cross-sectional area of the column, lm2

dc

diameter of the constrictions, lmd%&&%#5*7%

e!ective pore diameter, lmdg

average diameter of the glass spheres,lm

d.!9

maximum pore diameter, lmd0

distance of closest approach of surfaces,nm

dz

pore diameter as a function of lengthalong pore, z, lm

E'-!44

, EPS

Young's modulus of elasticity for glassand polystyrene, respectively, J/m2;stress/strain

f coe$cient of sliding frictionFD

drag force on attached colloid, NFL

lift force on attached colloid, N*G

.*/depth of primary minimum of interactionenergy, J or kT

*GABd0

Lewis AB interaction energy at d0,

mJ m~2

h pore length, lmk Boltzmann's constant, J/KK

*/5%3!#5*0/elastic interaction constant, J ) lm~2

M!11-*%$

applied moment on sphere from externalforces, N lm

M3%4*45!/#%

moment resisting rolling, N lmN

103%number of pores in column cross-section

NRe

Reynold's numberP normal force, NQ #uid #owrate in the packed bed,

ml min~1

Lv

Lrhydrodynamic shear on attachedcolloid, s~1

¹ temperature, Kv#0--0*$

#uid velocity at colloid, m s~1

v103%

#uid velocity in pore based on e!ectivepore diameter, m s~1

vz

#uid velocity in pore, m s~1

= interaction energy per unit area,J lm~2

z length along pore, lm

Greek letters

b hysteresis loss factore porosityi'-!44

, iPS

Poisson's ratio for glass and polystyrene,respectively; transverse strain/longitudi-nal strain

l #uid kinematic viscosity, cm2 s~1

o #uid density, gm ml~1

k #uid absolute viscosity, Pa skR

coe$cient of rolling friction

2. Background

The detachment of colloids from surfaces in porousmedia may occur from one of the following disturbancesto the system:

1. Thermodynamics: A physicochemical change producinga net repulsive surface interaction. These surface inter-action energies are comprised of van der Waals,electrostatic, and other non-DLVO energies, andthe magnitudes are functions of the aqueous andsurface chemistry. This detachment mechanism hasbeen addressed in detail by Bergendahl and Grasso(1999).

2. Hydrodynamics: An increase in yuid shear on attachedcolloids. Detachment of particles with hydrodynamicshear has been the subject of much research, and hasbeen found to be dependent on the #ow characteristicsof the system as well as the surface interaction energy.This paper addresses colloid detachment due to hy-drodynamic shear.

Many researchers have studied particle mobilizationfrom #at substrates (Cleaver & Yates, 1973; Hubbe,1985). Das, Schechter & Sharma (1994) found completeremoval of glass and polystyrene particles from #at glasssurfaces with hydrodynamic shear. Similarly, Sharma,Chamoun, Sita Rama Sarma & Schechter (1992) re-ported a high fraction of colloids released from #at glassand copper surfaces with increasing #uid #ow rate. HighpH and low ionic strengths also contributed to thedetachment of the particles from the surfaces in thesestudies.

Visser, (1970,1976) reported that the percent removalof carbon black particles from a #at cellophane surfaceincreased as both the wall shear stress and pH increased.Although the mechanism of detachment is still somewhatelusive, the removal e$ciency of particles from #at surfa-ces has been correlated with the wall shear stress.

However, the detachment of particles from sphericalsubstrates in porous media has not been explored in asmuch detail as that for #at surfaces. In situ colloid mobil-ization in environmental applications has been noted by

1524 J. Bergendahl, D. Grasso / Chemical Engineering Science 55 (2000) 1523}1532

Fig. 1. Construct for porous media with laminar #ow using the con-stricted tube model.

many investigators. Backhus, Ryan and Groher (1993)performed turbidity measurements in groundwaterpumped from sampling wells at di!erent pumping rates.An increase in turbidity was measured with increasingpumping rate. It was hypothesized to be a result of thedetachment of particles from the soil grains as a result ofthe increased #uid shear in the aquifer. Fogler and co-workers (Khilar & Fogler, 1984; Kia, Fogler & Reed,1987; Mohan & Fogler, 1997) have studied permeabilityreductions in sandstone cores with pH and ionic strengthchanges. The reduction in permeability was thought to bedue to capture of mobilized "nes in pore throats and thetrends were explained with DLVO theory.

McDowell-Boyer (1992) performed particle detach-ment experiments with quartz and feldspar sand (dia-meters ranging from 350 to 500 lm) in packed-bedlaboratory columns. She reported an increase in thepercent of 1.46 lm diameter polystyrene latex particlesmobilized with increasing #owrate, showing that colloidsmay be removed with hydrodynamic shear. However,Ryan and Gschwend (1994) noted no signi"cant e!ect ontotal mass fraction of colloid release from quartz grainswith #owrate increases, although the detachment ratewas greater at higher #owrates. This indicated a hy-drodynamic impact on the mass transfer rate of thecolloids from the quartz grain surfaces to the bulk #uid#ow.

Particle detachment in deep bed "lters under highsurface loading has been studied by others. Bai and Tien(1997) deposited particles in porous media increasing thehydraulic gradient signi"cantly. They reported hy-drodynamic particle detachment at high hydraulicgradients in the porous media. They also noted greaterremoval with #uid #ow shock. Where Payatakes, Parkand Petrie (1981) performed visual experiments on par-ticle pore clogging and re-entrainment in porous media,they observed large aggregate detachment with increased#uid shear.

Particle detachment has also been reported duringbatch mixing processes. Bergendahl and Grasso (1998)measured increases in colloid concentration with time inan end-over-end batch leaching apparatus. The mecha-nism of colloid detachment was hypothesized to be roll-ing for the expected surface energetics. The rolling ofthe colloids from the parent material was thought to beattributable to the mechanical agitation inherent in thebatch test.

3. Theoretical development

Various external forces are exerted on particles at-tached to porous media in #ow systems. These forcesmay vary as a function of system geometry (#at, tubular,porous, etc.), and may manifest at di!erent magnitudes.Hydrodynamic drag force from the #uid pressure

gradient, and lift force from the #uid velocity gradientparallel to the surface, experienced in these systems arediscussed in various monographs (Sa!man, 1965; Gold-man, Cox & Brenner, 1967; O'Neill, 1968; Wang, 1990;Tsai, Pui & Liu, 1991; Bergendahl & Grasso, 1998).Physicochemical surface forces resulting from electros-tatic, van der Waals, and other surface interactions alsoplay a signi"cant role in these systems (Raveendran& Amirtharajah, 1995; Bergendahl, Butkus & Grasso,1997).

Packed beds of granular media have been representedby many di!erent geometrical models: sphere-in-shell(Happel, 1958; Payatakes, Rajagopalan, & Tien, 1974),capillary tube (Tien, 1989), and constricted tube (Paya-takes, Tien, & Turian, 1973). For this work, the con-stricted tube model was selected as the best representationof the void space between spheres in packed beds (Fig. 1).The average diameter of the constrictions in the porousmedia model can be found through (Chan & Ng, 1988)

dc"

dg

2.5658(1)

with an e!ective pore diameter of (Chan and Ng, 1988)

d%&&%#5*7%

"

dc

0.470. (2)

The maximum pore size can be estimated from (Paya-takes et al., 1973)

d.!9

"dc2.141. (3)

The pore diameter changes along the pore length havebeen described by a parabolically shaped constrictedtube (Tien, 1989)

dz"2G

d.!92

#C4Adc2!

d.!92 B A0.5!

z

hB2

DH. (4)

The number of pores in a cross-section of the bed issimply

N103%

"

A#0-6./

e(p/4)d2

%&&%#5*7%

. (5)

J. Bergendahl, D. Grasso / Chemical Engineering Science 55 (2000) 1523}1532 1525

Fig. 2. Cumulative interaction energy distribution for residual PS col-loid fraction on glass beads at I"0.01 M; gamma distribution withshape parameter"1.66, Hamaker constant, A

132"3.79]10~21 J,

Lewis AB interaction energy at d0, *GAB

d0"!2.13 mJ m~2 (Adapted

from Bergendahl and Grasso, 1999).

The #uid velocity at any point along the pore is then

vz"

Q/N103%

(p/4)d2z

. (6)

Assuming laminar #ow with a parabolic #ow pro"le,the #uid velocity at an attached colloid anywhere alongthe pore can be calculated

v#0--0*$

"2Q/N

103%(p/4)d2

zC1!A

dz/2!a

#0--0*$dz/2 B

2

D. (7)

The concomitant shear experienced by a colloid at thepore wall is

Lv

Lr"

Q/N103%

(p/4)d2z

4(dz/2!a

#0--0*$)

(dz/2)2

. (8)

Alternatively, the e!ective pore velocity can be calculated

v103%

"

Q/N103%

(p/4)d2%&&%#5*7%

(9)

and the Reynold's number determined (Dybbs & Ed-wards, 1984)

NRe

"

o ) v103%

) d%&&%#5*7%

ke

1!e. (10)

The adhesion energy for the PS}water}glass interac-tion was estimated with extended-DLVO theory and veri-"ed with experimental data (Bergendahl & Grasso, 1999).For detachment to occur, the hydrodynamic forceon an attached colloid must overcome the maximumenergy gradient associated with the primary minimum.In spite of the simplicity and ideality of this system,surface interactions are commonly heterogeneous anda distribution of site energies existed. This was repre-sented by a gamma distribution with a shape factor of1.66 (Bergendahl & Grasso, 1999), and is illustrated inFig. 2.

The #uid #ow in porous media results in lift and dragforces on colloids attached to pore walls. For laminar#ow, the lift and drag forces can be estimated with thefollowing correlations:

FL"

81.2ka3#0--0*$

(Lv/Lr)3@2

l1@2

(adapted from Sa!man, 1965). (11)

(Note: The Sa!man derivation does not account for #uid#ow modi"cation as a result of wall e!ects).

FD"10.205pkA

Lv

LrBa2#0--0*$

(Goldman et al., 1967; O'Neill, 1968). (12)

For hydrodynamic detachment of attached colloids,lifting, sliding or rolling are detachment mechanisms that

remove colloids from surfaces. Through a summation ofexternal forces and moments on an attached colloid, themechanism causing incipient motion can be determined(Wang, 1990; Tsai et al., 1991; Bergendahl & Grasso,1998). Coupling the external forces and moments withthe interaction energy between the colloid and the sur-face, the point at which lifting occurs can be found(Bergendahl & Grasso, 1998):

=(

FL

32

p a#0--0*$

(13)

Similarly, sliding along the surface can occur when(Bergendahl & Grasso, 1998)

=(

FD/f#F

L32

p a#0--0*$

(14)

Although system dependent, rolling is often the pri-mary detachment mechanism for hydrodynamic detach-ment of colloids (Tsai et al., 1991; Bergendahl &Grasso, 1998). Incipient motion from rolling was deter-mined to be the predominant removal mechanism forthis system (Bergendahl, 1999). Rolling can only occurwhen the resistance to rolling is overcome by the appliedmoment from hydrodynamic forces. Incipient rolling oc-curs when the applied moment, M

!11-*%$, is equal to the

rolling resistance (Johnson, 1985)

M3%4*45!/#%

"kRPa

#0--0*$. (15)

The coe$cient of rolling friction, kR, is proportional

to a hysteresis loss factor, b (Johnson, 1985). A de-formed sphere will dissipate energy when rolling alonga surface. The amount of energy dissipated is a functionof the hysteresis loss factor. The hysteresis loss factor is


Table 1Porous media properties

Porosity e Cross-sectional areaof bed A

#0-6./

Average graindiameter d

g

Constrictiondiameter d

c

Maximum porediameter d

.!9

E!ective porediameter d

%&&%#5*7%

Number of poresin bed cross-section N

103%(cm2) (lm) (lm) (lm) (lm)

0.4 5.726 512.5 200 427.6 425 1615

material dependent (Johnson, 1985), and highly variable.Expanding the coe$cient of rolling friction

M3%4*45!/#%

"Ab2 a

#0/5!#53 p a

#0--0*$BPa

#0--0*$. (16)

The applied moment from the hydrodynamic drag is

M!11-*%$

"A10.205pkALv

LrB a2#0--0*$B a

#0--0*$. (17)

Equating the applied moment to the rolling resistance todetermine a requisite incipient mobilization force, yields

10.205pk ALv

LrB a3#0--0*$

"Ab2 a

#0/5!#53 p a

#0--0*$B Pa

#0--0*$. (18)

To obtain the interaction force in terms of interactionenergy (per area), the Derjaguin approximation,P"2 p a

#0--0*$= (Israelachvili, 1992), was used

10.205pk ALv

LrB a3#0--0*$

"Ab2 a

#0/5!#53 p a

#0--0*$B 2 p a2

#0--0*$=.

(19)

From the work of Johnson, Kendall and Roberts (1971),the contact radius, a

#0/5!#5, can be estimated as

a3#0/5!#5

"0.636=p a2

#0--0*$K

*/5%3!#5*0/

, (20)

where

K*/5%3!#5*0/

,

4

3p ((1!i2'-!44

/pE'-!44

)#(1!i2PS

/pEPS

)).

(21)

Combining Eqs. (19) and (20), and using the Langbeinapproximation for the interaction area, =+*G

.*//

(2 p a#0--0*$

d0) (Israelachvili, 1992)

Lv

Lr"

2bDG.*/

3 ) 10.205d0p2k a3

#0--0*$

)G0.63(3DG

.*/)a

#0--0*$d0K

*/5%3!#5*0/H

1@3,

(22)

which can be simpli"ed to

Lv

Lr"

1

12.381

b*G4@3.*/

d4@30

p2 k a8@3#0--0*$

K1@3*/5%3!#5*0/

. (23)

To predict the shear required to mobilize a certainfraction of attached colloids: (1) the primary minimumdepth, *G

.*/, was found from the gamma distribution

(Fig. 2); and, (2) Eq. (23) was used to estimate the neces-sary #uid shear to overcome *G

.*/.

4. Materials and methods

The experimental protocol for this study on the hy-drodynamic detachment of colloids from a packed bed ofglass beads is detailed elsewhere (Bergendahl & Grasso,1999). The physical properties of the packed bed of glassbeads are listed in Table 1. Dual peristaltic pumps (ColeParmer, Chicago, IL; pump heads in parallel) with anin-line pulsation dampener, were used to inject an aque-ous solution of varying chemistry up-#ow through a bedof 425}600 lm diameter soda lime glass beads (SigmaChemical Company, St. Louis, MO). The colloids were1.0 lm diameter (standard deviation"0.017 lm) poly-styrene latex microspheres from Interfacial DynamicsCorporation (Portland, OR) with carboxyl surfacegroups having a surface charge density of 27.0 lC cm~2

(as reported by Interfacial Dynamics Corporation). Thecolloidal solutions were sonicated 60 s prior to use. Theglass beads were cleaned as described in Bergendahl andGrasso (1999). Aqueous solutions were prepared froma Milli-Q water system (Millipore Corp., Bedford, MA)and were deaerated with 15 cmHg vacuum prior to use.

A spectrophotometer (Varian Techtron, Victoria, Aus-tralia; 500 nm, 5 cm pathlength cell) provided continuousoptical density readings, which were converted to colloidconcentrations (Bergendahl & Grasso, 1999). The glasscolumn had an inner diameter of 25 mm and a length of155 mm and was obtained from Ace Glass, Vineland, NJ.After wet "lling the column with glass beads, the porositywas 0.4.

The colloids were attached in the primary minimum(Bergendahl & Grasso, 1999) with a solution chemistry ofpH"3.5 and I"0.1 M NaCl at 5 ml min~1 for 10 porevolumes. This ionic strength was below the experi-mentally determined critical coagulation concentration,which was found to be 0.158$0.004 M NaCl. Followingthe attachment phase, the column was "rst #ushed withidentical solution with no colloids, and then the aquaticmatrix was changed to various combinations of pH


Table 2Flow domain parameters

Fluid#owrate Q

E!ective porevelocity v

103%

Reynold'snumber N

Re!

Minimum hydrodynamic

shearLv

Lr"

(ml min~1) (mm s~1) (s~1)

5 0.36 0.1 6.725 1.82 0.5 33.550 3.64 1.0 67.175 5.46 1.5 100.6

100 7.28 2.1 134.2

!Using the e!ective pore diameter and the e!ective pore velocity."Based on maximum pore diameter.

Fig. 3. Pore diameter and #uid shear at 75 ml min~1. Column cross-sectional area"5.726 cm2, grain diameter"512.5 lm (average), andporosity"0.4.

values and ionic strengths. The #owrate in the column wasthen sequentially and incrementally increased from 5 to 25,50, 75 ml min~1, and "nally 100 ml min~1 with constantsolution chemistry. A "nal rinse with deionized water ad-justed to pH 11.0 removed remaining colloids. Experimentsshowed a 94% average total colloid recovery. This recoverycompares well with those reported by others: Ryan,Elimelech, Ard, Harvey and Johnson (1999) reported re-coveries of 37}103% with pH increases in well-controlled"eld tests with arti"cial silica colloids, and Hahn (1995)found up to 95% recovery of polystyrene colloids with ionicstrength reductions in laboratory column experiments.

The morphology of the attached colloids was investi-gated by imaging individual glass beads, after attachingcolloids, with a scanning electron microscope (AMRAY,Inc., Bedford, MA, Model 1000). The column was careful-ly disassembled and the glass beads were placed on two-sided carbon tape mounted on a stub. The SEM wasoperated at 20 kV and magni"cations up to 5000].In#uent and e%uent particle distributions were also con-ducted to verify singlet attachment and detachment.

5. Results and discussion

5.1. Flow parameters

The pore diameter increased from the minimum con-striction diameter of 200 lm to the maximum porediameter of 427.6 lm, and is illustrated in Fig. 3 as afunction of length along the pore, z. Table 2 summarizespore velocities and Reynold's numbers for various #ow-rates. The pore velocity varied from 0.36 to 7.28 mm s~1

yielding Reynold's numbers from 0.1 to 2.1. The min-imum hydrodynamic shear rates (at the maximum porediameter) are also presented.

5.2. Colloid detachment runs

Results from a typical attachment and detachment runare illustrated in Fig. 4. As expected, a signi"cant portion

of the attached colloids were removed from the substrateas a result of the initial chemistry changes. The fractionthermodynamically removed by #uid matrix changes wasin agreement with extended-DLVO theory, and consis-tent with the data reported in Bergendahl and Grasso(1999). Mass removal corresponding to various #owrateswere determined by a trapezoid integration technique(Shenk, 1979), with *t"5 s (Fig. 5).

Fig. 5 illustrates that the colloids detach over a rangeof #owrates. The colloids did not detach in an `all ornonea step-wise fashion as implied by traditional stabilitymodels, but rather in a distributed fashion. Similar re-moval distributions with hydrodynamic shear have beenreported by others. Hubbe (1985) performed detachmentexperiments on colloids attached to #at surfaces andfound a distribution of detachment e$ciency as hy-drodynamic shear increased. While there may be some#ow variations in the packed bed, the detachment distri-bution is attributed primarily to varying interaction ener-gies between the colloids and glass bead surfaces as notedin Fig. 2.

After attachment of the colloids, the glass beads wereimaged with scanning electron microscopy to view


Fig. 4. Results of typical attachment and detachment experiment: col-loids are attached for 20 pore volumes at pH 3.5 and I"0.1 M, #ushedfor 25 pore volumes at pH 7 and I"1 mM, and then sequentiallydetached with hydrodynamic shear as noted. A "nal #ush (starting atPV"145) was conducted with deionized water adjusted to pH 11 torecover remaining colloids.

Fig. 5. Cumulative removal of residual colloid fraction as a function of#owrate, (a) I"1 mM NaCl, (b) I"0.01 M NaCl, and (c) I"0.1M NaCl.

the morphology of the attached colloids. The colloidswere primarily deposited individually on the glass surfa-ces, although minor clumping was identi"ed in localsurface areas. Colloid}colloid interaction energy was re-pulsive at all conditions (Bergendahl & Grasso, 1999),and colloid aggregation in solution or on the surface wasnot expected. In addition, colloid distributions in boththe in#uent and e%uent were monodisperse with modesin the 0.89}1.02 lm size range (one channel width of theparticle counter).

5.3. Removal predictions

From Fig. 5, it can be seen that the #owrate resultingin median (50%) removal of colloids remaining afterchemistry changes (residual colloid fraction) was75 ml min~1 for all aquatic matrices. This system behav-ior is evidence that constant non-DLVO interactionsgoverned detachment of colloids not removed by aque-ous chemistry changes. Removal distributions for theresidual colloid fraction were insensitive to aqueouschemistry (pH or ionic strength) for this system, and weredependent on #owrate only. At 75 ml min~1, the min-imum hydrodynamic shear on the attached colloids was100.6 s~1 (Fig. 3). In various pore regions, the shear maybe greater due to higher #uid velocity (corresponding tosmaller pore diameters, see Fig. 3). In these areas ofhigher shear, the colloids can translate to lower sheardomains. When the energy associated with the shearovercomes adhesional energy, detachment is realized.

The estimated shear in this system corresponding tomedian removal of the residual colloid fraction from thebed (100.6 s~1), is similar to shear values found for signif-icant detachment in other hydrodynamic systems. Be-

rgendahl and Grasso (1998) reported colloid removalfrom parent material in soil leaching tests with a 55 s~1

hydrodynamic shear rate. Indeed, shear rates greaterthan 60 s~1 are commonly not recommended for #oc-culation operations because of the potential to separateaggregates (Amirtharajah & O'Melia, 1990).

Net repulsive interactions between colloids and glasssurfaces were thermodynamically induced with initial


Fig. 6. Depth of primary energy minimum of attachment of PS latexcolloids removed by hydrodynamic shear in packed bed of glass beads(hysteresis loss factor, b"1.77]10~3).

Fig. 7. Cumulative removal of residual colloid fraction by hy-drodynamic shear in packed bed of glass beads with column innerdiameter"25 mm, porosity"0.4, glass bead diameter"425}600 lm,and 1.0 lm polystyrene latex colloids with carboxyl surface groups. Thebackground electrolyte was NaCl. Prediction uses d

0"0.158 nm,

K*/5%3!#5*0/

"4.014]109 N/m2 (Bergendahl, 1999), and hysteresis lossfactor, b"1.77]10~3.aquatic matrix changes. A signi"cant fraction of the col-

loids were mobilized and removed from the porous me-dia with the initial chemistry change (Fig. 4). After steadystate was achieved, the residual colloid fraction musthave had negative primary interfacial energy minimaproducing attractive conditions. This attractive interac-tion ranged from approximately 0 to !2000 kT (Fig. 2).From the gamma distribution reported by Bergendahland Grasso (1999), 50% removal corresponded to anattractive primary minimum of !1841 kT (Fig. 2). Fromthe interaction energy at 50% removal, the hysteresis lossfactor, b, at 75 ml min~1 was predicted (b"1.77]10~3).The attractive *G

.*/that the hydrodynamic shear can

overcome to detach the colloids was then predicted(Fig. 6).

This method is predicated on correlating incipientrolling from hydrodynamic drag to hysteresis energy loss(Johnson, 1985). Many others have used a similar tech-nique to ascertain the incipient moment inducing move-ment (Wang, 1990; Tsai et al., 1991). However, someprevious techniques (Wang, 1990; Tsai et al., 1991) havedetermined the incipient moment about an edge of thecontact radius of a deformed colloid with the assumptionthat material reformation does not take place. The poten-tial for the front edge of the contact radius to elasticallydeform (in the direction of rolling), and the rear edge toreform to its original shape, is ignored in these alternativetheories. In the approach used in this work, the deforma-tion of the front edge, and reformation of the rear edge isaddressed through the hysteresis loss factor.

To determine the requisite #owrate to remove a givencolloid fraction, the gamma distribution (Fig. 2) wasemployed. Fig. 7 shows the cumulative fraction removedas the #owrate is increased in the bed. The data collectedfrom experiments is shown as well as our model predic-tion. Fig. 7 indicates a very good model prediction of

residual colloid fraction removed as a function of #ow-rate. The agreement of the prediction to the experimentaldata indicates a relative insensitivity of residual colloidfraction behavior to solution chemistry.

Real surfaces are expected to be rough, and this rough-ness may a!ect the surface energetics. Tabor (1977) mea-sured a reduction in adhesion energy between a smoothrubber and a hard, #at surface as the roughness increased.Bhattacharjee, Ko and Elimelech (1998) studied the e!ectof roughness on interaction energy, and found a reductionin the attachment energy barrier and the primary minimumdepth with random asperities. While surface asperities ofa scale considerably less than the colloid radius wille!ectively prevent the surfaces from achieving direct con-tact over the entire contact area, larger asperities mayincrease the hydrodynamic drag required for detachmentby hindering rolling (larger moment arm) (Ryan &Elimelech, 1996). With the experiments reported here,SEM images indicated very smooth and spherical surfa-ces, so roughness was not considered. However, to extendthis model to real, natural surfaces, roughness must beincorporated for accurate removal predictions.

6. Summary

The objective of this work was to develop a predictivetool for determining the hydrodynamic shear that willdetach residual colloidal fractions in porous media. Poly-styrene latex colloids were attached in the primary inter-action energy minimum to glass beads in a column.A hydrodynamic shear of 100.6 s~1 in the packed bed


removed and mobilized 50% of the colloids that were nototherwise removed by alteration of the aquatic matrix.

Balancing the rolling moment derived from the #uidshear and the rolling resistance, the hydrodynamic de-tachment of colloids in the packed bed was characterizedwith one material parameter, the hysteresis loss factor forrolling, b, determined to be 1.77]10~3 for polystyrene.Using this parameter and a gamma distribution of theresidual colloid fraction interaction energy, detachmentas a function of #owrate was exceptionally well predicted.This work has e!ectively decoupled surface energeticsand hydrodynamics in the prediction of colloid detach-ment from porous media.

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prediction of colloid detachment in a model porous media: hydrodynamics

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