blocking and ripening of colloids in porous media and their implications for bacterial transport

Colloids and Surfaces

A: Physicochemical and Engineering Aspects 160 (1999) 291–308

Blocking and ripening of colloids in porous media and theirimplications for bacterial transport

Terri A. Camesano *, Kenneth M. Unice, Bruce E. LoganDepartment of Ci6il and En6ironmental Engineering, The Pennsyl6ania State Uni6ersity, 212 Sackett Building, Uni6ersity Park,

PA 16802, USA

Received 5 January 1999; received in revised form 12 March 1999; accepted 15 March 1999

Abstract

A model accounting for the dynamics of colloid deposition in porous media was developed and applied to systemscontaining similarly charged particles and collectors. Colloid breakthrough and intracolumn retention data confirmedthat blocking reduced overall colloidal adhesion to soil. The surface coverage at which blocking occurred varied forthe type of colloid, as shown by changes in the clean-bed collision efficiency, a0, and the excluded area parameter, b.Excluded area parameters were relatively high due to unfavorable interactions between particles and collectors, andranged from 11.5 for one bacterium (Pseudomonas putida KT2442) to 13.7 and 24.1 for carboxylated latexmicrospheres with differing degrees of charged groups on their surfaces. Differences in b values for the three colloidswere correlated with electrophoretic mobility, with the most negatively charged colloid (carboxylated latex; CLmicrospheres) having the highest b. No correlation between hydrophobicity and a0 or b was found. Besides usingcolloidal particles capable of blocking, the addition of chemical additives to the soil has been suggested as a meansfor reducing attachment of colloids to porous media. Dextran addition caused an order-of-magnitude reduction in theoverall a (for carboxylated-modified latex; CMLs). This reduction was not attributed to blocking, but to the sorptionof dextran to the soil which lowered a0. The filtration-based numerical model used to fit the a0 and b parameters wasused to demonstrate that blocking could result in significantly enhanced bacterial transport in field situations. © 1999Elsevier Science B.V. All rights reserved.

Keywords: Blocking; Bacterial transport; Dextran; Adhesion

www.elsevier.nl/locate/colsurfa

1. Introduction

An understanding of colloid deposition andtransport in porous media is important for many

subsurface applications, such as dispersal of bac-teria for in situ bioaugmentation, predicting thefacilitated transport of contaminants, and for theprevention of drinking water contamination withmobile microbes. Solutions to an advection–dis-persion equation for colloid transport and/or col-loid filtration models are typically used toquantify the deposition of colloids in porous me-

* Corresponding author. Tel.: +1-814-8654851; fax: 1-814-8637304.

E-mail address: [email protected] (T.A. Camesano)

0927-7757/00/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S0927 -7757 (99 )00156 -9

T.A. Camesano et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 160 (1999) 291–308292

dia [1–5]. Model calculations are performed byassuming that the rate of colloid deposition isindependent of previously attached colloids. How-ever, this assumption is only valid for initial depo-sition rates, when the particles are deposited ontoclean collectors. The deposition rate may decreaserapidly as particles start to accumulate on thecollectors [6]. One explanation for this drop indeposition rate is that as the fraction of thesurface covered by colloids increases, depositedcolloids may prevent the further attachment ofcolloids due to a process termed blocking [7].When blocking is occurring, an attached particlereduces the area available for deposition by anamount that is greater than the projected area ofthe particle [6]. In some systems, an alternateprocess (filter ripening) occurs when attached par-ticles can act as additional collectors for attach-ment by forming multilayer films [6,8,9].

In a prior bacterial transport study, injectinghigher concentrations of Burkholderia cepacia G4into porous media columns led to an enhance-ment in transport which was attributed to block-ing [10]. This occurred even when the fractionalsurface coverage in portions of the column wasmuch lower than that previously reported todemonstrate blocking. Ripening accounted for thedeposition of Pseudomonas fluorescens P17 inporous media columns [10], as multilayer deposi-tion appeared to occur at a surface coverage thatwas B1% (assuming homogeneous spherical col-lectors). It is well-known that injection concentra-tion affects bacterial retention in soils [11,12], butthese previous studies have not considered block-ing as an explanation.

In this study, we developed a filtration-basedmodel explicitly accounting for blocking thatcould be used to predict the effect of influentcolloid concentration on the deposition of colloidsin porous media. Using the model and columnexperimental data, it was demonstrated thatblocking occurred to differing extents for severaldifferent colloids. The area excluded by each col-loid was directly related to the electrophoreticmobility of the colloid, but no correlation wasobserved with hydrophobicity. A chemical addi-tive (dextran) was used to demonstrate that it waspossible to decrease a0 without causing blocking

to occur. Finally, the model was used to demon-strate that blocking can result in enhanced trans-port of bacteria in porous media.

1.1. De6elopment of colloid transport model

The transport of an aqueous suspension ofcolloids in one dimension is modeled as:

(C(t

=KL

(2C(x

−u(C(x

−k C+kd Cs (1)

where C is colloid concentration; u, the porevelocity; KL, the dispersion coefficient; k, thefiltration (decay) constant; x, the distance; t, thetime; kd, the detachment rate constant and Cs, theconcentration of deposited colloids. Cs is a func-tion of time, as in:

dCs

dt= (k C−kd Cs) (2)

Eqs. (1) and (2) were solved simultaneouslyusing a flux-averaged type inlet condition and ano-flux outlet boundary condition at x=L, andwith C=Cin at t=0 [13,14]. The Peclet number inthese experiments (Pe=u L/KL) was large (981),indicating that dispersion was negligible.

The filtration constant, k, can be determinedfrom filtration theory [1,2] as:

k=3(1−n)h

2dc

a u (3)

where n is the column porosity; dc,the collectordiameter; u, the pore velocity; h, the single mediacollector efficiency [2] and a, the overall collisionefficiency. Eq. (3) can be written in simplifiedform by using the filtration coefficient, l=3/2(1−n)h/dc, such that:

k=a l u (4)

When the fraction of the collector surface areacovered by deposited colloids is small comparedwith the surface area available for deposition, a isconstant and equal to a0, defined as the clean-bedcollision efficiency. As more colloids are depositedon the soil grains and the collectors become par-tially covered, the rate of deposition is no longerconstant, resulting in a change in a, which is theonly adjustable parameter [15].

T.A. Camesano et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 160 (1999) 291–308 293

The collision efficiency was determined experi-mentally in column studies by neglecting disper-sion, desorption and concentration effects andmeasuring deposition in the column at low massloadings. The collision efficiency is calculated as afunction of distance by slicing the column into1-cm sections and applying a filtration model[1,16] as:

ai=−2dc ln(1−FR,i)

3(1−n)h Li

(5)

where ai is the collision efficiency of slice i ; Li,the length of slice i and FR,i is the fraction ofparticles retained in slice i. The dimensionlesscollision number, j(=l L), was used to scalecolumn length based on collision frequencies [16].

1.2. The dynamic blocking function

The dynamic blocking function represents thetransient nature of the particle deposition rate [17]and can be modeled linearly or non-linearly. Thelinear Langmuirian model for the dynamic block-ing function for the deposition of colloids inporous media, B(u), is:

B(u)=umax−u

umax

(6)

where u is the fractional surface coverage andumax is the maximum surface coverage [18]. Byintroducing an excluded area parameter, b(=1/umax), the collision efficiency can be expressed as[19–21]:

a=a0(1−b u) (7)

Similarly, the collision efficiency per slice is:

ai=a0(1−b ui) (8)

where a is the observed or apparent collisionefficiency; a0, the clean-bed collision efficiency; ai,the observed or apparent collision efficiency perslice and ui, the fractional coverage of slice i.Since the surface coverage decreases along thelength of the column and umax and a0 are assumedto be constant during the initial stages of deposi-tion, ai should increase with column length whenblocking is occurring.

The Langmuirian model is based on a linearrelationship between concentration and attach-ment. The solution to the convection–diffusionequation including Langmuirian kinetics forpacked bed geometry has been previously pre-sented [18]. Johnson and Elimelech [18] havedemonstrated that a non-linear model is moreappropriate for the attachment of positivelycharged colloids to negatively charged glass mi-crospheres because the Langmuirian model doesnot adequately describe surface exclusion effectsof colloids that are much larger than themolecules the Langmuir isotherm was developedto model. In addition, deposition of colloids ontoporous media is non-linear due to hydrodynamicscattering, surface heterogeneities, and non-uni-formly accessible surfaces [4,22,23].

Previously, a multilayer deposition model wasdeveloped and applied to particle deposition inpacked beds, in which there are two collisionefficiencies to account for the bare and coveredareas of the collectors [20]. However, this model isbased on the assumption of uniform surface cov-erage on the collectors, which is often not the casewhen soils are used as the porous media. Songand Elimelech [23] have demonstrated that thismultilayer deposition model can be used to de-scribe the deposition of colloids onto non-uni-formly charged collectors, but under theseconditions there is a non-linear dependence of thedeposition rate on the surface coverage.

These facts imply that a non-linear modelshould be used for the dynamic blocking function.However, the model proposed by Johnson andElimelech [18] to overcome the limitations of theLangmuirian model for colloid deposition studies,called the random sequential adsorption model(RSA) [24,25] has only been applied to colloidalsystems in which the colloids and the media are ofopposite charge and the surface coverage is nearthe jamming limit (umax). In previous bacterialtransport studies and for the microspheres used inthis study, the colloids and collectors have anoverall negative charge. In addition, surface cov-erages in the types of experiments we are inter-ested in can be much lower than the jamminglimit for hard spheres (umax=0.546) [18]. There-fore, the linear Langmuirian model is used in this


work, although heterogeneity of the surface dic-tates a non-linear relationship between surfacecoverage and blocking. For low coverages, thedifferences between the Langmuir and RSAmodel become minimal [18].

1.3. Modeling colloid deposition

For each experiment performed, Eqs. (1) and(2) were solved simultaneously using a CrankNicholson finite difference technique, as describedin detail elsewhere [14]. This model was used tosimulate an experiment, and the fractional reten-tion of colloids per theoretical slice of the columnwas calculated using Eq. (2). Particle storage wasbased on the liquid volume of a model slice,calculated as:

Vslice=p

4d2 n Dx (9)

where Vslice is the liquid volume of a model sliceand d is the column diameter.

The cumulative number of particles stored in acolumn slice, S, at each time step is calculated byaveraging the storage concentration at the en-trance and exit of each slice [14]. Once N, the totalnumber of bacteria or microspheres, and S, thestorage of colloids in that slice (per ml of liquid),have been calculated, the fraction of particlesretained in each slice, FR,i, may be calculated by:

FR,i1 =

Sil

Nl�5i−1

i=1

(1−FR,il )n (10)

where the superscript l represents the number oftime steps.

Once the fraction of colloids retained has beencalculated for the time step of interest, the colli-sion efficiency per slice, ai, may be calculated foreach slice using Eq. (5). Therefore, a break-through curve of the colloid concentration overtime and a calculation of the collision efficiencyper slice as a function of collision number (j=l L) were obtained for each simulation, referredto as ‘model’ a. The overall collision efficiencywas also calculated using the total fractional re-tention of colloids in the model column and Eq.(3), which is referred to as ‘experimental’ a.

The fractional coverage per slice, ui,sph, wascalculated assuming spherical collectors and col-loids as:

ui,sph=V S am

ac nc

(11)

where V is the available liquid volume in the slice;am, the projected surface area per microbe orparticle; ac, the surface area per collector and nc,is the number of collectors.

Since the soil is heterogeneous and the collec-tors are not spherical, assuming that the collectorsare spherical results in a substantial underestima-tion of the available surface area. A comparisonwas made between the surface coverage based onassuming spherical collectors (usph) and the sur-face coverage calculated from measured values ofthe specific surface area obtained from the desorp-tion of nitrogen gas from the soil grains.

To model blocking using Eq. (8), a value for a0

is needed. Values for a0 were determined from lowparticle concentration experiments, in whichblocking was not occurring because the cumula-tive mass loading was low enough to consider thesoil a clean-bed. These values of a0 were used insubsequent model runs to find b values. Experi-mental breakthrough curve data was fit to theo-retical breakthrough curve data using aSIMPLEX method of minimizing the least-squares error [14].

1.4. Illustrati6e simulations

A series of simulations were performed to pre-dict the distance bacteria could travel for varyingbacterial injections and degrees of blocking. Typi-cal parameters [10] were used in the simulations(kd=0, n=0.37, dp=1 mm, u=12.1 m d−1, dc=127 mm, 10 PV bacterial injection and 10 PVrinse) and a0, b, and N were varied. After asimulation, an overall or cumulative collision effi-ciency, acum, was calculated. This value of acum

was then used to determine the distance for 2-logremoval of cells, L2 (C/C0=0.01) in:

L2= −log(0.01)

l acum

(12)


2. Experimental methods

2.1. Microspheres, cultures, and media

Two types of microspheres differing in chargedensities were used in these experiments: fluores-cent carboxylated latex microspheres (CL; Poly-sciences) with a 0.97 mm diameter, and fluorescentcarboxylated (modified) latex microspheres(CML; Interfacial Dynamics) with diameters from0.97 to 1.0 mm. Microspheres with negativecharges but differing degrees of surface chargewere chosen to mimic bacterial cells, which overallare negatively charged, but to different extents.Microspheres were added to low ionic strength(IS) water (Milli-Q) and washed twice in low ISwater by centrifuging at 5000×g for 15–20 minat 15°C, and resuspended in sterile 10−3 M KClsolution. In some experiments, a dextran solution(MW=17 200; 1.96 g l−1 in 10−3 M KCl) wasadded to the microsphere suspension to determinethe effect of dextran on colloid retention.

The bacterium studied was Pseudomonas putidaKT2442, provided by D.F. Dwyer (Department ofCivil Engineering, The University of Minnesota).KT2442 is an aerobic, rod-shaped, gram-negative,motile bacterium, microscopically verified asmotile during experiments in low IS water, withan average equivalent diameter of 1.08 mm asmeasured using a microscope (Olympus BH-2)and image analysis system (Galai ScanArray).KT2442 was chosen for transport experimentsbecause it is the parent strain of a geneticallyengineered microbe capable of degrading tolueneand 4-ethyl benzoate [26]. KT2442 was grown inM9 buffer with an added mineral salt solutionand 5 mM benzoate [26]. Since KT2442 is resis-tant to the antibiotic rifampicin, 50 mg l−1 of thischemical was added to help prevent contamina-tion of the culture [26]. KT2442 was grown untillate-log phase (absorbance �0.5 at 560 nm) anddiluted to either 107 or 108 cells ml−1 in low ionicstrength (IS) water. The bacterial solution wasradiolabelled with 3H-leucine and excess radiola-bel was removed by a filtering procedure as de-scribed in Martin et al. [16]. The final (influent)cell concentration was determined by acridine or-ange direct counting [27].

2.2. Column experiments

The soil used in these studies was a southernArizona soil, with an average equivalent diameterof 127 mm [10]. Soils were packed dry and withoutpre-treatment into 7×1.5 cm glass columns (Om-nifit). The surface area of �2 g of Arizona soilwas measured in triplicate from the desorption ofnitrogen gas and application of Brunauer–Emmett–Teller (BET) isotherms in a surface areaanalyzer (Quantachrome Monosorb Surface AreaAnalyzer). The BET surface area was used only tocompare with the surface area calculated by as-suming spherical collectors. In the modeling, b

values were calculated from the surface area afterassuming spherical collectors, not using the BETsurface area.

In fluorescent microsphere experiments, thecolumn was rinsed with 3 pore volumes (PV) of10−3 M KCl, followed by a 10 PV injection ofparticles suspended in KCl (or dextran and KCl,as noted) and a 5 PV KCl rinse. When dextranwas used, 10 PV of dextran in KCl was added tothe column before the microsphere/dextran solu-tion to pre-equilibrate the soil. The effluent wascontinuously sampled after colloid injection usinga fraction collector (Gilson).

The column media was extruded from thecolumn at the conclusion of each experiment andsliced into 1 cm increments to determine deposi-tion as a function of column length. Each 1 cmincrement was divided into quarters, placed in apre-weighed scintillation vial, and weighed again.Two of the quarters from each cm were amendedwith 10 ml of 0.1% v/v Tween 80 solution in lowIS water, and sonicated for \2 min to extract themicrospheres from the soil. After the samplessettled (\12 h), a liquid sample was taken fromthe top of the vial.

Effluent samples and the supernatant from thesoil samples were filtered onto 0.2 mm, black,polycarbonate filters (Poretics) and microsphereswere enumerated under blue light. In experimentsin which \108 ml−1 CMLs were used, effluentconcentration profiles were determined spec-trophotometrically at 450 nm (Shimadzu UV-1601).


In bacterial transport experiments, 10 PV ofAGW followed by 10 PV of low IS water wasinjected to equilibrate the column. Then, 10 PV ofradiolabeled KT2442 suspended in low IS waterwas injected, followed by a 10 PV low IS waterrinse. The column contents were extruded at theconclusion of the experiment and sliced into 1 cmsegments. Each 1 cm segment was sliced into fivefractions and all sections were analyzed usingscintillation counting.

Although colloids can be accurately detected inliquids, extracting colloids from soil remainsproblematic. In a similar study, all of the radioac-tivity associated with bacteria could not be recov-ered even after applying a correction factor whenheterogeneous Arizona soil was used as thecolumn media [10]. In the present study, a spike-correction factor was applied to all of the KT2442experiments, but the mass balances were still notcomplete for all experiments.

In general, the percentage of colloids that couldbe recovered from the soil and counted under themicroscope increased as the injected number ofcolloids increased. Uncorrected mass recoveriesranged from � 45% for low injections (NB109)to �90% for higher injections (N\1010). Sinceenumeration of microspheres and bacteria fromliquids is accurate, we assumed that all of thecolloidal mass that was not counted in the effluentwas attached to the soil and forced each of themass balances to sum to 100% by applying con-stant correction factors to the number of micro-spheres (or bacteria) retained in each slice of soil[10].

2.3. Colloid characterization

The bacterial adhesion to hydrocarbons(BATH) [28] test was applied to KT2442 and themicrospheres to determine the relative hydropho-bicity of each species. Triplicate samples wereprepared and analyzed as described previously[29].

Water contact angles (f) on lawns of micro-spheres and bacteria deposited on aluminum ox-ide filters (Anotec) were measured using amicroscope with a goniometric eyepiece (Rame-Hart). These filters were chosen because they re-

mained flat when dried; cellulose acetate andpolycarbonate filters curled when dried. The im-precision in measuring contact angle was greaterfor the bacterial lawns than microsphere lawns,and so KT2442 measurements were performed sixtimes while microsphere measurements were per-formed in triplicate.

Electrophoretic mobility of microspheres orbacteria suspended in 0.007 M phosphate bufferwas analyzed in triplicate using an electrophoresisinstrument (Coulter Delsa 440).

For the two types of microspheres, a coagula-tion jar test was performed with and withoutdextran to determine colloid–colloid collision effi-ciencies, ac, using a procedure described elsewhere[10].

We also tried to characterize the adsorption ofdextran to the soil using adsorption isothermexperiments. However, the adsorption of dextranto the soil was so poor that in the concentrationrange chosen, 0.0025 g dextran per g soil–0.025 gdextran per g soil, dextran concentrations couldnot be reliably detected using a total organiccarbon analyzer (Shimadzu TOC 5000A).

3. Results

3.1. Column experiments

Appreciable blocking was observed for CL mi-crospheres at injections \109 particles (Fig. 1).Although there is scatter in the data for the lowerconcentrations, both breakthrough data and in-tracolumn data support blocking for these col-loids. The overall collision efficiency decreasedfrom 0.085 to 0.012 as the number of injected CLmicrospheres increased from 8.2×107 to 2.4×1010 (Table 1), which is within the range of exper-imental error for these conditions, noting that theamount of error in the low concentration experi-ments is greater than the error in the higherconcentration experiments because it is moredifficult to accurately count low numbers of mi-crospheres under the microscope. The clean-bedcollision efficiency for these experiments, a0, wastaken as the overall a value at a mass of depositedmicrospheres where blocking was assumed to be


negligible (8.19×107 total microspheres, a0=0.082, a=0.085), corresponding to usph=0.003.When determining a0, blocking was turned off inthe model.

For CML microspheres at N=8.8×109, thecolumn media still behaved as if it were ‘clean’, asevidenced by a nearly constant breakthrough con-

centration, and this experiment was used to deter-mine a0 (Fig. 2). After injecting a higherconcentration of microspheres (N=4.9×1010),substantial blocking occurred (b=13.7) and theoverall a decreased from 0.096 to 0.013 (Table 1;Fig. 2).

Blocking was also observed for P. putida

Fig. 1. (A) Breakthrough data and (B) intracolumn collision efficiencies measured (symbols) and model predictions (lines) forcarboxylated latex microspheres (CL) at three different microsphere injections (N). For modeling of experimental data, b=24.1,a0=0.082, and kd (desorption coefficient)=0. The collision number is defined in Eq. (10).


Table 1Summary of retention in colloid experiments

Experimental a Model a baN (total number of particles) a0 usphb uc

0.085 0.086 –8.1×107 0.082CLs 0.003 B0.0019.0×108 0.074 0.074 24.1 0.082 0.034 0.002

0.033 0.0281.2×1010 24.1 0.082 0.262 0.0120.012 0.014 24.12.3×1010 0.082 0.226 0.011

8.7×109CMLs 0.096 0.096 – 0.096 0.379 0.0184.9×1010 0.013 0.013 13.7 0.096 0.487 0.024

0.087 0.087 –5.7×108d 0.125KT2442 0.029 0.0026.1×108 0.088 0.076 11.5 0.125 0.045 0.002

0.034 0.031 11.5 0.1251.2×1010 0.352 0.024

a No blocking was included in the model for ‘clean-bed’ experiments, indicated by a dashed line.b The measured fractional retention of colloids was used to calculate the fractional surface coverage, assuming that all collectors

are spheres of diameter 127 mm.c The measured fractional retention of colloids was used to calculate fractional surface coverage, using the measured value of 4.92

m2 g−1 as the specific area of Arizona soil.d This experiment was a spike injection over 1.22 PV. All other injections were spread over 10 PV.

KT2442 at the two cell loadings tested (Fig. 3).Desorption (kd=10−4 s−1) was included in thesesimulations because of the tailing observed in thebreakthrough curves. The overall a decreasedfrom 0.088 to 0.034 when the number of injectedbacteria was increased from 6.1×108 to 1.2×1010 cells (Table 1). The a0 for this bacterium wasobtained from an experiment in which a spike ofbacteria at N=5.7×108 cells ml−1 was injectedover 1.22 pore volumes (data not shown).

3.2. Dextran

Polymer coatings such as dextran have beenused to prevent the adsorption of proteins tovarious surfaces, including quartz, and are used ascoatings in many biotechnological applications[30,31]. Therefore, it was hypothesized that apply-ing dextran could decrease the adhesion of nega-tively charged colloids to soil.

The addition of dextran to CL microspherescaused a decrease in the overall a from 0.085 to0.070, which was not significant (Table 2). Withina 95% confidence interval, the average break-through concentrations or a values for these twoexperiments were not statistically different, as cal-culated following the procedure of Jewett et al.[32]. The lack of a significant effect caused bydextran addition may be due in part to the

difficulty in accurately counting low numbers ofmicrospheres under the microscope. Therefore, itis unknown if dextran affects a0 at very lowcolloid loadings.

For CML microspheres at a higher loading(N=8.8×109), an order-of-magnitude decreasein the overall a from 0.096 to 0.009 was observed(Table 2). In order to determine the reason for thedecrease in a, model simulations for dextran withCML microspheres were performed in two ways.First, it was assumed that dextran did not changea0, but caused blocking. In that case, a0 was usedfrom the dextran-free experiment (0.096) and a b

value of 177 was found to fit the cumulative a

value obtained experimentally. Second, it was as-sumed that dextran changed a0, but did not causeblocking, producing a0=0.009 when blockingwas eliminated from the model. Based on theagreement or disagreement of the breakthroughcurve simulations, it appears that dextran did notcause blocking, but changed a0 (Fig. 4).

3.3. Colloidal properties

Based on the BATH test, both microspheresand the bacteria had the same hydrophobicity.However, contact angle measurements indicatedthat KT2442 was slightly less hydrophobic (f=


24.5) than either of the microspheres (f=39–40;Table 3). Others have found that contact anglesyielded more accurate estimates of cell surfacehydrophobicity than BATH tests [33]. The elec-trophoretic mobilities show that CL microspheresare the most negatively charged, followed byCML microspheres and KT2442 (Table 3).

Particles can be blocking only if they do notstick to one another under the experimental con-ditions examined. A coagulation jar test for CLand CML microspheres confirmed that the colloidsuspensions were stable. Colloid–colloid collisionefficiencies were all on the order of 10−5 or less,with and without dextran (Table 3).

Fig. 2. (A) Breakthrough data and (B) intracolumn collision efficiencies measured (symbols) and model predictions (lines) forcarboxylated-modified latex microspheres (CML). The lower injection data was modeled assuming no blocking. The experiment atN=8.8×109 was used to define a0=0.096. For the experiment at higher loading with blocking occurring, b was calculated as 13.7.


Fig. 3. (A) Breakthrough data and (B) intracolumn collision efficiencies measured (symbols) and model predictions (lines) for P.putida KT2442 in low IS water at two bacterial injections, N (b=11.5, k2=10−4 s−1). A spike injection was used to determine thata0 =0.125 (data not shown).

3.4. Predicted colloid transport

Simulations were performed to determine thecontrolling parameter (clean-bed collision effi-ciency, excluded area parameter, or total numberof injected colloids) with regard to colloid trans-

port (Fig. 5). For a low injection of colloids(N=6.38×108), the transport distance is essen-tially controlled by the magnitude of a0, andincreasing b has little effect on how far the col-loids can move. When high concentrations ofcolloids (N=4.55×1010) are injected, a0 becomes


less important as the collectors rapidly fill up withcells. Therefore, increasing b substantially in-creases the transport distance of colloids. Theincrease in distance transported can be seen bycomparing the distance to 2-log removal (calcu-lated using Eq. (12)). For example, for equal a0

values (assume a0=0.1) a bacterial suspensionwith a b value of 18 would only travel 2 m beforea 2-log reduction in cell concentration, while abacterial suspension with a b value of 80 couldtravel 10 m before the same decrease in cellconcentration due to soil retention.

3.5. Surface co6erages

The measured specific surface area for Arizonasoil is 4.92 m2 g−1, while a value of �0.002 m2

g−1 was calculated by assuming spherical homo-geneous collectors. The measured value representsthe surface area available to nitrogen gasmolecules. Bacteria will not be able to sample allof the available area measured because of theirsize, yet the assumption of spherical collectorsclearly leads to a large underestimation of theavailable surface area of the soil grains. Whensurface coverages were recalculated using themeasured surface areas, u was more than anorder-of-magnitude lower than usph. This means

that blocking and ripening are occurring at evenlower surface coverages than previously believedto be possible.

4. Discussion

4.1. Concentration effect

The observation that injecting high concentra-tions of bacteria reduced overall deposition inporous media columns was first reported by Gan-non et al. [11]. In their study, the normalizedbreakthrough concentration of the bacteriumPseudomonas sp. KL2 was B0.02 when the in-jected number of cells was 7×1010 cells, butreached 0.7 when 3×1011 cells were injected (0.01M NaCl solutions). Gannon et al. [11] hypothe-sized that when the number of cells injected in-creased, a greater fraction of the favorablecollector sites were filled and the remaining bacte-ria could move through the medium without sig-nificant retention. They examined thisconcentration effect with KL2 in further detail byapplying a model that accounted for the maxi-mum percentage of the surface that could becovered [34].

Table 2Summary of retention in microsphere experiments with dextran

N (total number of particles) Experimental a usphbModel a ba a0 uc

0.0860.0858.1×107 0.082CL, controlc – 0.003 B0.0010.070 B0.0015.6×107 (dextran)CL 0.0020.08224.10.085

8.7×109d 0.096 0.096CML, control – 0.096 0.379 0.0180.0698.6×109 (dextran)e B0.0010.009 0.009 (177)f 0.096CML

0.009 0.069 B0.0018.6×109 (dextran)e,gCML 0.009 0.009 –

a No blocking was included in the model for ‘clean-bed’ experiments, indicated by a dashed line.b The measured fractional retention of colloids was used to calculate the fractional surface coverage for the whole column,

assuming that all collectors are spheres of diameter 127 mm.c The measured fractional retention of colloids was used to calculate fractional surface coverage, using the measured value of 4.92

m2 g−1 as the specific area of Arizona soil.d The control experimental solutions do not contain dextran, and are reproduced from Table 1 for comparison with dextran

experiments.e These results represent the average results of two experiments.f This represents the excluded area parameter if dextran did not alter a0 and blocking occurred. Results without blocking in the

model (one line below) more accurately reflect the physical phenomena.g Same experimental data as one line above, but blocking was not allowed,therefore, experimental a=a0.

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291–

308302

Table 3Physical and chemical properties of colloids

Diameter (mm) a0 Relative hydrophobicity ac (withdextran)Water contact ac (no dextran)Electrophoretic mobilityangle (f) (mm cm V−1 s−1)(H ; %)

0.97 0.082CLs 3596 40.390.0 −4.2490.03 9.68×10−6 1.35×10−5

0.97–1.0 0.096 3795CMLs 39.090.0 −3.8990.14 7.23×10−5 3.95×10−5

1.0KT2442 0.125 3499a 24.593.4 −1.6990.12 NDb NDb

a Rogers, 1997.b ND, not determined.


Fig. 4. The effect of dextran on CML and CL microspheres. When blocking was allowed, b=177 for CMLs and b=24.1 for CLsusing a0 values derived from dextran-free experiments. An alternate model simulation is shown for the CML experiment whenblocking was not allowed, but a0 was set equal to a0 that was determined in the dextran-free experiments. When there is no blocking,a0= the overall experimental a (a0=0.009).

In another study, a concentration effect wasobserved on bacterial transport [12], but this ef-fect was not mathematically modeled. Using datafor the experiment with the highest concentrationof cells, we calculate usph=0.93 by assuming uni-form spherical collectors and assuming the diame-

ter of the bacteria is 1 mm. The maximumfractional surface area that can be covered is 0.54for hard spheres, and lower maximum values arelikely for ‘soft’ particles such as bacteria. Possibly,ripening was occurring in Bai et al.’s [12] experi-ments since fractional surface coverages exceed


the maximum that would be possible if the cellswere only attaching to the soil grain surfaces.Ripening has also been observed for Arthrobactersp. strain DSM 6687 [35] and P. fluorescens P17[10]. If cell–cell adhesion occurs, but to a lesserextent than cell–surface adhesion, then it may be

possible to have both ripening and blocking oc-curring simultaneously. For uniformly chargedcollectors and colloids, this would be impossible.However, bacteria and soil, while overall nega-tively charged, may each have positively chargedregions on their surfaces, or at least regions that

Fig. 5. Simulations were performed using the following parameters: 10 PV injection, 10 PV rinse, dp=1 mm, dc=127 mm, u=4.5m d−1, KL=10−4 cm2 s−1, kd=0, as described in text.


are less negatively charged than the average sur-face charge, and this heterogeneity could allowsimultaneous blocking and ripening to occur,since different regions could have different a

values.The existence of different a values for covered

and uncovered portions of the collectors has neverbeen explicitly examined using bacteria. However,it has been demonstrated that the multilayer de-position model [20] including individual collisionefficiencies corresponding to bare and coveredsurfaces can be applied to colloid deposition stud-ies in which the collectors are heterogeneous [23].Collisions with bare surfaces almost always re-sulted in attachment, while collisions with coveredsurfaces resulted in very low attachment probabil-ities. We were only able to measure average colli-sion efficiencies and obtain average b values.Therefore, b may actually be much higher thanthe values we calculate by averaging the proper-ties of heterogeneous soil grains.

The possibility must also be considered that theavailable surface area in these experiments wasmuch higher than the values we calculated assum-ing spherical collectors, and so the surface cover-age observed in experiments by Bai et al. [12]could have actually been lower than 0.93. Even ifthe available surface area was much higher, themodel proposed above in which there are two a

values, one for bare and one for covered surfaces,could still hold.

4.2. Factors affecting a0 and b

The colloid loading at which blocking begins tooccur depends on hydrodynamic conditions andphysical and chemical properties of the colloidand surface [17,35,36]. Flow velocity, column size,and packing were constant for all experiments andthe three colloids were all nearly the same sizehere. KT2442 experiments were done in low ISwater (B10−5 M), while the microsphere experi-ments were performed in 10−3 M KCl solution.Blocking should be greatest at low ionic strengths[6,36–39], yet there are other differences betweenthe bacteria and the microspheres that make itimpossible to isolate the effect of solution chem-istry on blocking from these experiments. There-

fore, our discussion of the differences in a0 and b

focuses on the different chemical properties of thecolloids.

For bacteria, a0 has been correlated with thetype of cell coating [35]. However, we did not finda correlation between a0 and cell surface proper-ties as measured using contact angle, partitioningin the BATH test, or electrophoretic mobility.Bacteria can have contact angles ranging fromB20 to over 100° [40], and those with contactangles between 20 and 50° are classified as rela-tively hydrophobic [40]. The microspheres andKT2442 have nearly the same hydrophobicity,and lie in the middle of this hydrophobicity spec-trum. The slightly higher a0 value observed forKT2442 could be due in part to the capsularmaterial surrounding the bacterium. An India inkstain showed that KT2442 does have some capsu-lar material (not shown), which likely contributedto its greater attachment to soil under ‘clean’column conditions. We speculate that polymerson the bacterial surface may have led to thishigher a0 value, as studies have demonstrated arelationship between polymers and attachment[30,31,35].

Increases in the excluded area parameter, b,and the extent of blocking have been correlatedwith increased electrostatic repulsion [9,35,38–40].All three colloids examined here can be consid-ered blocking because of the observed decrease inoverall retention when the injected concentrationwas increased. The extent of blocking increasedfor the three colloids with bCL\bCML\bKT2442,and was directly related to increased negativesurface charge (Table 3). CL microspheres exhib-ited blocking at a lower loading than CML micro-spheres due to increased electrostatic repulsion.

The range of b values observed is similar orhigher than values previously reported, and thecorresponding surface coverages are lower thanthe values where blocking has been previouslyreported to occur. An injection of 6.1×108 cellsresulted in blocking with KT2442, correspondingto usph=0.045 (experimentally derived from re-tention data and assuming spherical collectors).This is slightly lower than the result observed fora similarly sized injection of B. cepacia G4 underthe same hydrodynamic conditions, where block-


ing was observed at usph=0.056 [10]. The value ofb obtained for KT2442 (11.5) is in the same rangeas the previously reported b for a blockingRhodococcus strain (12.0), as compared with a b

of 1.6 for non-blocking P. putida mt2 [21].

4.3. Surface co6erage of soil collectors

The soil was heterogeneous in size, shape, andcomposition, and had a much larger surface areathan that predicted assuming spherical collectors.Properties of the soil will clearly affect a0 and b.Song and Elimelech have suggested that for nega-tively charged soil grains and colloids, all attach-ment occurs on positively charged patches on thesoil grains [23]. Soil heterogeneity is thereforeresponsible for the bulk of attachment thatoccurs.

In the literature, collectors are assumed spheri-cal when calculating surface coverages [9,20,23].Based on this assumption, it appears that surfacecoverages of at least 3–4% are necessary for theeffects of blocking to begin to be seen [9,10].However, since we have seen how the surface areais actually much greater, it appears that blockingand ripening effects can be observed at concentra-tions orders-of-magnitude lower than previouslybelieved to be possible. Soil heterogeneity willplay an important role in determining the surfacecoverage necessary for blocking to begin.

4.4. Adsorption of polysaccharide to soil

The presence of dextran caused a decrease in a0

for CML microspheres, but did not cause block-ing (Fig. 4). The failure of the adsorptionisotherm experiment in this study and previouswork with dextran in saturated column experi-ments demonstrate that dextran does not substan-tially sorb to Arizona soil [14]. Although sorptionand desorption of dextran are small, there muststill be interactions that we cannot account forbetween dextran and soil, and between dextranand the microspheres. The pKa of the glucoseunits that make up dextran is 12.28 [41]. There-fore, at neutral pH, the sugar units in dextran arepredominately found in protonated form. Themicrospheres have carboxylic acid functional

groups on them, with pKa=5, and are thereforedissociated at neutral pH [42]. Perhaps hydroxylgroups from the dextran are forming hydrogenbonds with R�COO− groups on the micro-spheres. Since hydrogen bonds have energies �10–40 kJ mol−1, they are much stronger than vander Waals bonds (�1 kJ mol−1) [43]. Thestrength of hydrogen bonds in water means thatthese types of interactions cannot be neglected asa potential source of association between the mi-crospheres and the dextran. Steric interactionscaused by the adsorption of dextran to the soilmay also have contributed to the reduced a valuesobserved when dextran was applied. In our exper-iments, it appeared that the microspheres associ-ated with the dextran and then were unable toattach to the soil, either through steric hindranceor other mechanisms.

4.5. Implications for colloid transport

Decreasing a from 0.1 to 0.005 increases thedistance that cells can be transported before a2-log reduction in concentration by only �4 m(Fig. 5A). Greater transport is possible throughproper manipulation of a0, b, and N, as shown bythese simulations. In order for blocking to be-come important, the number of cells injected hasto be large. However, it is difficult to specify thecell concentration or number of pore volumes ofcells that must be injected because a0, b, and Neach play a role in determining how far the bacte-ria will travel in the subsurface. The low cellinjection used in our simulation (N=6.38×108

or 4.4×107 cells per dry g soil) was not highenough to produce blocking, while the higherinjection (N=4.55×1010 or 3.09×109 cells perdry g soil) was sufficient to cause blocking. Usinga concentration that is high enough to produceblocking can be advantageous in enhancing thetransport of bacteria in porous media. However,a0 and b values will vary considerably for differ-ent strains even under similar experimental condi-tions due to differences in cell chemical andphysical properties [35].

It may be easier to control b than a0 by alteringhydrodynamic conditions in the column. The ex-tent of blocking increases when Pe is increased


[36,39]. Therefore, by increasing the flow velocity,it should be possible to increase b. The clean-bedcollision efficiency is also a function of hy-drodyamics. While motile bacteria exhibit en-hanced transport at low fluid velocities,non-motile and immobile colloids are less retainedin porous media at high fluid velocities [10,44,45].Therefore, at high velocities, the fewest colloidsshould be retained due to both a velocity effectand enhanced blocking.

Using a bacterial strain with a050.005 andb]65 would be best for increasing the overalltransport distance for bioremediation throughbioaugmentation, since the cells could travelgreater than 12 m before a 2-log reduction in cellconcentration (Fig. 5B). Although b values of thismagnitude have not been reported, they are verylikely to be possible when colloids and collectorsare similarly charged.

5. Conclusions

A blocking model for colloidal deposition un-der unfavorable conditions was developed andapplied to latex microspheres and bacteria at lowsurface coverages. A linear model for blockingwas used in which the excluded area parameter, b,could be calculated for different colloids. Thebacteria and microspheres studied exhibitedblocking, due to their negative charge, the rela-tively low ionic strength of the suspending phases,and the heterogeneity of the soil. The model wasused to illustrate the effect of blocking on bacte-rial transport. Using a concentration of cells thatis great enough to produce blocking can be ad-vantageous in enhancing the transport of bacteriain bioaugmentation experiments. It may also bepossible to use dextran to lower a0 for bacteria,and thus further enhance bacterial transport inporous media.

Acknowledgements

This publication was made possible in whole bygrant number ES-04940 from the National Insti-tute of Environmental Health Sciences, NIEHS.

Its contents are solely the responsibility of theauthors and do not necessarily represent officialviews of the funding agency. We thank D. Allara,and A. Hooper for assistance with contact anglemeasurements, J. van Tassel for help with elec-trophoresis and soil surface area measurements, J.Chorover for useful discussions, and A. DeSantisfor helpful discussions, suggestions, and labora-tory assistance. The review of this manuscript byM. Elimelech is also gratefully acknowledged.

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blocking and ripening of colloids in porous media and their implications for bacterial transport

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