Straining and Attachment of Colloids in Physically Heterogeneous Porous Media
Scott A. Bradford,* Mehdi Bettahar, Jirka Simunek, and Martinus Th. van Genuchten

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

ABSTRACT

Many soil column and batch experiments have been
conducted to quantify fundamental properties and processes that control colloid transport and fate in the subsurface, including sedimentation (Wan et al., 1995), hydrodynamics (Wang et al., 1981; Tan et al., 1994), ionicstrength (Abu-Sharar et al., 1987), pH (Suarez et al.,1984), chemical heterogeneity (Song and Elimelech,
1994; Song et al., 1994), hydrophobicity (Bales et al.,1993), and surfactants (Ryan and Gschwend, 1994). The
primary mechanism of colloid mass removal by the soil
is typically ascribed to colloid attachment. Attachment
is the removal of colloids from solution via collision
with and fixation to the solid phase, and is dependent
on colloid–colloid, colloid–solvent, and colloid–porous
media interactions. According to traditional clean-bed
attachment theory (first-order attachment), colloid removal by a filter bed decreases exponentially withdepth. Colloid attachment theory also predicts an optimum particle size for transport for a given aqueousporous medium system (Yao et al., 1971; Rajagopalan
and Tien, 1976). Smaller particles are predicted to be
removed more efficiently by diffusive transport, andlarger particles by sedimentation and interception.
Experimental observations of colloid transport are
not always in agreement with colloid attachment theory(Tufenkji et al., 2003). For example, researchers havereported enhanced colloid retention at the soil surface(Camesano and Logan, 1998) and that the spatial distribution of retained colloids does not follow a simple
exponential decrease with depth (Bolster et al., 1999;
Redman et al., 2001; Bradford et al., 2002). Some ofthese discrepancies have been attributed to soil surface
roughness (Kretzschmar et al., 1997; Redman et al.,2001), charge heterogeneity (Johnson and Elimelech,
1995), and variability in colloid characteristics (Bolster
et al., 1999). A time-dependent attachment rate has also
been reported to occur as a result of differences in theattachment behavior of colloids on clean porous media
and on media already containing attached colloids(Johnson and Elimelech, 1995). Blocking and ripeningrefer to decreasing and increasing attachment withtime, respectively.
Some of the discrepancies between colloid transport
data and attachment theory may also be due to the factthat attachment theory does not account for straining.
Straining is the trapping of colloid particles in downgradient pore throats that are too small to allow particle
passage (McDowell-Boyer et al., 1986). The magnitude
of colloid retention by straining depends on both colloid
and porous medium properties. Straining occurs when
colloids are retained in dead-end pores that are smaller
than some critical size. Colloid transport may still occur
in pores that are larger than this critical size. Sakthivadi-

Colloid transport studies were conducted in water-saturated physically heterogeneous systems to gain insight into the processes controlling transport in natural aquifer and vadose zone (variably saturated)systems. Stable monodispersed colloids (carboxyl latex microspheres)and porous media (Ottawa quartz sands) that are negatively charged
were employed in these studies. The physically heterogeneous systems
consisted of various combinations of a cylindrical sand lens embeddedin the center of a larger cylinder of matrix sand. Colloid migration was
found to strongly depend on colloid size and physical heterogeneity. A
decrease in the peak effluent concentration and an increase in thecolloid mass removal in the sand near the column inlet occurred whenthe median grain size of the matrix sand decreased or the size of thecolloid increased. These observations and numerical modeling of thetransport data indicated that straining was sometimes an importantmechanism of colloid retention. Experimental and simulation results
suggest that attachment was more important when the colloid size
was small relative to the sand pore size. Transport differences between
conservative tracers and colloids were attributed to flow bypassingof finer-textured sands, colloid retention at interfaces of soil texturalcontrasts, and exclusion of colloids from smaller pore spaces. Colloid
retention in the heterogeneous systems was also influenced by spatial
variations in the pore water velocity. Parameters in straining andattachment models were successfully optimized to the colloid transport data. The straining model typically provided a better descriptionof the effluent and retention data than the attachment model, especially for larger colloids and finer-textured sands. Consistent withpreviously reported findings, straining occurred when the ratio of thecolloid and median grain diameters was ⬎0.5%.

I

norganic, organic, and microbiological colloids exist
in natural and contaminated aquifer and vadose zone
environments. These colloid particles can be released
into soil solution and groundwater through a variety ofhydrologic, geochemical, and microbiological processes(MacCarthy and Zachara, 1989; Ryan and Elimelech,
1996). Knowledge of the processes that control colloidtransport and fate is required to assess the contamination potential and to protect drinking water supplies
from pathogenic microorganisms (Bitton and Harvey,1992), to develop engineered bioaugmentation and bioremediation strategies (Wilson et al., 1986), and to devise
microbially enhanced oil recovery systems (MacLeod etal., 1988). Furthermore, the high surface area of colloids
facilitates the sorption of many organic and inorganic
contaminants. Colloids can then act as a mobile solid
phase that accelerates the transport of sorbed contaminants (Kretzschmar et al., 1999; Ouyang et al., 1996).

S.A. Bradford, M. Bettahar, J. Simunek, and M.Th. van Genuchten,
George E. Brown, Jr. Salinity Laboratory, USDA, ARS, 450 West Big
Springs Road, Riverside CA 92507-4617. Received 1 May 2003. Special
Section: Colloids and Colloid-Facilitated Transport of Contaminantsin Soils. *Corresponding author (sbradford@ussl.ars.usda.gov).
Published in Vadose Zone Journal 3:384–394 (2004).
 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

Abbreviations: PV, pore volume.

384

385

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

www.vadosezonejournal.org

vel (1966, 1969) and Herzig et al. (1970) developed geometric relations between the effective diameter of colloids and soil grain-size distribution characteristics topredict mass removal by straining. Matthess and Pekdeger (1985) generalized this rule to porous media madeup of a distribution of grain sizes. Colloid transport datafrom Harvey et al. (1993) and Bradford et al. (2002)
indicate that straining was more pronounced than predictions based on the criteria given by Matthess and
Pekdeger (1985). Harvey et al. (1993) observed a trendof increasing colloid retention with increasing colloid
size and hypothesized that this straining behavior was
due to migration of clay particles to one end of thecolumn (decreasing the pore size at this location). Bradford et al. (2002) reported that effluent colloid concentration curves and the final spatial distributions ofretained colloids by the porous media were highly dependent on the colloid size and soil grain-size distribution. Relative peak effluent concentrations decreased
and mass removal of colloids near the column inlet
increased when colloid size increased and soil mediangrain size decreased. These observations were attributed
to colloid straining since conventional attachment andblocking models could not describe this behavior. Bradford et al. (2003) employed an irreversible depth-dependent straining coefficient to successfully model straining.
Laboratory-scale studies that explore the role of subsurface heterogeneity on colloid transport are important
to bridge the gap in knowledge between field-scale andhomogeneous soil column studies. This is especially true
for larger-sized colloids, which may undergo size exclusion in heterogeneous systems (Ryan and Elimelech,
1996) as well as straining (Bradford et al., 2002). Relatively few laboratory-scale studies have been conducted
to explore the influence of heterogeneity on colloid
migration in porous media (Saiers et al., 1994; Silliman,
1995), although laboratory-scale studies have examined
the influence of fractures on colloid migration (Reimus,
1995; Cumbie and McKay, 1999). Saiers et al. (1994)
measured the transport behavior of colloidal silica(mean colloid diameter of 0.091 ␮m) in systems composed of a coarse (mean grain size of 870 ␮m) soil lensembedded in a finer (mean grain size of 360 ␮m) soil
matrix. These authors found that colloid transport andattachment could be adequately described with an advection–dispersion transport model that accounted for firstorder kinetic attachment–detachment. Silliman (1995)
measured the transport behavior of a distribution oflatex microspheres (diameters ranging from 2 to 90 ␮m)
in various configurations of three coarse-textured sands(mean grain diameters equal to 3400, 2030, and 925 ␮m).
Results from this study showed significant colloid retention at media contacts where water moved from larger
to smaller diameter sands. Silliman (1995) attributed thisobservation to attachment leading to increased straining
since colloid attachment decreases the effective pore size
at a particular location and reversing the direction ofwater flow liberated large numbers of colloids.
The objective of this work was to investigate processes
controlling the transport and fate of colloids in physicalheterogeneous subsurface systems. Colloid transport ex-

periments were conducted in physically heterogeneous
systems consisting of various combinations of a cylindrical soil lens embedded in the center of a larger cylinderof matrix soil. These studies were performed under saturated conditions, but have implications for the variably
saturated vadose zone. Transport and retention was assessed by measuring temporal changes in colloid effluent concentrations and studying the final spatial distribution of colloids remaining in the soil columns. The
data were interpreted with the aid of conservative tracer(bromide) studies conducted simultaneously on thesame soil columns, and numerical modeling of the experimental systems. Special attention will be given to
the role of colloid straining in physical heterogeneous
systems.
MATERIALS AND METHODS
Many of the experimental materials, procedures, and protocols employed in this study were used also for homogeneous
soil column experiments described by Bradford et al. (2002).
Yellow-green fluorescent latex microspheres (Interfacial Dynamics Company, Portland, OR) were used as model colloid
particles in the experimental studies (excitation at 490 nm,
and emission at 515 nm). Two size diameters of colloid particles (dp), 1.0 and 3.2 ␮m, were employed. These microspheres
had carboxyl surface functional groups grafted onto latex particle surfaces by the manufacturer to create a negatively
charged hydrophobic colloid surface with a particle densityof 1.055 g cm⫺3 (provided by the manufacturer) and an equilibrium contact angle (air–water–lawn of colloids) of 115.2⬚ (measured with a Tantec Contact Angle Meter, Tantec Inc.,
Schaumburg, IL). Specific physical and chemical characteristics for the 1.0-␮m particles include: surface charge density of
27 ␮C cm⫺2 (provided by manufacturer) and zeta potentialof ⫺83.5 mV (measured with a Zetasizer 3000, Malvern Instruments, Inc., Southborough, MA). In contrast, the 3.2-␮m particles had a surface charge density of 11.9 ␮C cm⫺2 and a zeta
potential of ⫺85.5 mV. The initial influent concentration (Ci)for the 1.0- and 3.2-␮m colloids was equal to 3.86 ⫻ 1010 Nc
L⫺1 (where Nc denotes number of colloids) and 1.18 ⫻ 109 Nc
L⫺1, respectively.
The aqueous phase chemistry (pH, ionic strength, and composition) of the tracer, resident, and eluant solutions utilized in
the soil column experiments was chosen to create a stabilized
monodispersed suspension with the selected colloids. The initial resident and eluant solutions consisted of 0.001 M NaClwith its pH buffered to 6.98 using NaHCO3 (5 ⫻ 10⫺5 M ).
The colloid-conservative tracer solution consisted of 0.001 M
NaBr with its pH buffered to 6.73 using NaHCO3 (5 ⫻ 10⫺5 M)
and the previously indicated initial colloid concentration. The
aqueous solvent for all experimental solutions consisted ofdeionized water.
Aquifer material used for the soil column experiments consisted of various sieve sizes of Ottawa (quartz) sand (U.S.
Silica, Ottawa, IL). The porous media were selected to encompass a range in grain sizes and were designated by their mediangrain size (d50) as 710, 360, 240, and 150 ␮m. Specific propertiesof the 710-, 360-, 240-, and 150-␮m sands, include: uniformity
index (d60/d10; here x% of the mass is finer than dx) of 1.21,
1.88, 3.06, and 2.25; and intrinsic permeability of 4.08 ⫻ 10⫺10,
6.37 ⫻ 10⫺11, 1.12 ⫻ 10⫺11, and 4.68 ⫻ 10⫺12 m2, respectively.
The pore size distribution for these Ottawa sands can be estimated from capillary pressure–saturation curves presented by
Bradford and Abriola (2001). Ottawa sands typically consistedof 99.8% SiO2 (quartz) and trace amounts of metal oxides,

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

386

VADOSE ZONE J., VOL. 3, MAY 2004

were spheroidal in shape, and had rough surfaces. The vast
majority of the sands possessed a net negative charge at aneutral pH.
Aluminum soil columns, 10 cm long and with a 5-cm inside
diameter, were used in the transport studies. The columns
were equipped with standard fittings at both of their ends. A
stainless-steel wire screen (105-␮m mesh spacing) was placedat the soil surfaces to avoid sand displacement. Tubing to andfrom the columns, fittings, and column o-rings were composedof chemically resistant materials such as teflon, viton, andstainless steel.
The heterogeneous systems consisted of two soil types, asoil cylinder (2.3-cm diameter, 6 cm long) lens embedded in
the center of a second soil referred to as the matrix. The soilcolumns were wet packed with the various porous media, withthe water level kept above the soil surface. Care was taken
to ensure uniform packing by thoroughly mixing small quantities of the appropriate sieve size before addition to the columns. After each incremental addition of soil, the added soil
was gently mixed with the lower surface layer of soil and thenvibrated to minimize settling and layering, and to liberate any
entrapped air. After filling the soil column to a height of 2 cm
with the matrix soil, a stainless-steel cylinder of 2.3-cm internal
diameter was gently placed in the middle of the soil column.
The sand forming the heterogeneity (lens) was filled inside
the cylinder while matrix soil was added to the space separating the outer column and interior cylinder to the same height as
the soil lens. When the interior cylinder was filled to a heightof 6 cm (8 cm above the base of the column), the interior
cylinder was gently removed from the column and the remaining column space was filled with matrix soil. Table 1
provides porosity (ε) values for each experimental soil column.
The porosity was determined according to the method of Danielson and Sutherland (1986) using the measured soil bulk
density and assuming a specific solid density of 2.65 g cm⫺3.
Before initiating a carboxyl colloid tracer experiment thesoil columns containing Ottawa sand were flushed with several
cycles of deionized water and 0.026 M NaCl to remove mostof the natural colloids particles from the porous media. The
soil columns were flushed as follows: initial resident solution
was 0.026 M NaCl, 2 pore volume (PV) flush with deionizedwater, 2 PV flush with 0.026 M NaCl solution, 2 PV flush with
deionized water, and finally a 4 PV flush with eluant solution.
Here the 0.026 M NaCl solution promotes clay aggregationand the deionized water promotes clay mobilization (Bettahar
et al., 1998). This treatment produced persistently low effluent
concentrations of natural colloids in the column effluent.
A Masterflex L/S multihead drive pump (Barnant Company, Barrington, IL) was used to pump colloid and bromide
Table 1. Soil column properties (porosity, ε; and Darcy watervelocity, qw) and the recovered effluent (Me), soil (Ms), andtotal colloid mass fraction (Mt).
Soilmatrix

Soil
lens

dp

ε

qw

Me

Ms

Mt

710
710
710
710
710
710
360
240
150
360
240
150

360
240
150
360
240
150
710
710
710
710
710
710

␮m
1.0
1.0
1.0
3.2
3.2
3.2
1.0
1.0
1.0
3.2
3.2
3.2

0.323
0.328
0.329
0.320
0.320
0.339
0.309
0.307
0.329
0.318
0.321
0.328

cm min⫺1
0.121
0.109
0.127
0.126
0.102
0.129
0.095
0.117
0.106
0.120
0.108
0.115

0.613
0.614
0.636
0.607
0.505
0.536
0.585
0.532
0.435
0.297
0.221
0.148

0.218
0.198
0.198
0.491
0.583
0.499
0.242
0.315
0.431
0.594
0.831
1.109

0.831
0.812
0.834
1.098
1.088
1.035
0.827
0.847
0.866
0.891
1.052
1.257

tracer or eluant solution upward through the vertically oriented columns at a steady rate. The average Darcy velocity(q) for the various soil column experiments is given in Table 1.
The colloid and bromide tracer solutions were pumped
through the columns for about 81 min, after which a threeway valve was used to switch the pumped solution to theeluant for a total experimental time of 250 min. A total of 50
effluent samples were collected and analyzed for colloid andbromide concentration using a Turner Quantech Fluorometer(Barnstead/Thermolyne, Dubuque, IA) and an Orion 720a
pH/ISE meter (Orion Research Inc., Beverly, MA), respectively. The analytic protocol was sensitive to concentrations
over approximately two orders of magnitude below the initial
colloid and bromide concentrations. Concentrations of the
3.2-␮m colloids were slightly influenced by background interference from natural colloids (⬍3% of C/Ci).
Following completion of the colloid transport experiments,
the spatial distribution of colloids in a soil column was determined. The end fitting was removed and the saturated sandwas carefully excavated into 20-mL scintillation vials from thecolumn outlet to inlet. Excess eluant solution was added to
the vials. The vials were slowly shaken for 4 h using a Eberbach
shaker (Eberbach Corporation, Ann Arbor, MI) to liberate retained colloids. The concentration of the colloids in the excess aqueous solution was measured with a Turner Quantech
Fluorometer using the same experimental protocol as followed
for the effluent samples. These concentrations were corrected
for colloid release efficiency (determined from batch experiments) and natural background colloids (determined from
replicate “blank” soil columns). Additional details on the experimental protocols and procedures that were used to determine the spatial distribution of retained colloids are given by
Bradford et al. (2002).
A colloid mass balance was conducted at the end of eachsoil column experiment using effluent concentration data andthe final spatial distribution of retained colloids in the sands.
The calculated number of effluent and soil colloids was normalized by the total number of injected particles into a column.
Table 1 presents the calculated effluent (Me), soil (Ms), andthe total (Mt ⫽ Me ⫹ Ms) colloid mass fractions recovered forthe experimental systems. To account for mass balance errors
in the experimental data, the concentration of colloids retainedin the sand was multiplied by (1 ⫺ Me)/Ms. This approachassumes that the colloid mass balance error occurs primarilyon the solid phase.

THEORY AND MODEL
Clean-bed colloid attachment–detachment theory has frequently been used to describe colloid interactions with porous
media as (e.g., Bolster et al., 1999; Tufenkji et al., 2003):

⳵(␳bSatt)⫽ ␪w kattC ⫺ ␳b kdet Satt⳵t

[1]Here t is time (T), ␳b (M L⫺3) is the soil bulk density, Satt
(Nc M⫺1—Nc denotes number of colloids) is the solid phase
concentration of attached colloids, ␪w is the volumetric watercontent, katt (T⫺1) is the first-order colloid attachment coefficient, kdet (T⫺1) is the first-order colloid detachment coefficient, and C (Nc L⫺3) is the liquid phase colloid concentration.
Colloid filtration theory is incorporated into the katt term as(e.g., Logan et al., 1995):

katt ⫽

3(1 ⫺ ␪w)
␩␣v
2d50

[2]

where ␩ is the collector (porous medium) efficiency, ␣ is the387

www.vadosezonejournal.org

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

colloid sticking efficiency, d50 (L) is the median porous medium
grain diameter, and v (L T⫺1) is the pore water velocity. In
this work the value of ␩ is calculated using the following
correlation written in terms of dimensionless variables (Loganet al., 1995; Rajagopalan and Tien, 1976):
15/8
⫺2/3
␩ ⫽ 4 A1/3
⫹ As N1/8
s NPe
Lo N R ⫹0.4
0.00338 As N G1.2N⫺R[3]

Here As is the Happel correction factor, NPe is the Peclet
number, NLo is London-van der Waals attractive forces number, NR is the interception number, and NG is the gravitional
number. The first, second, and third terms on the right-handside of Eq. [3] denote contributions due to diffusion, interception, and sedimentation, respectively (Logan et al., 1995). The
value of ␣ in Eq. [2] represents the fraction of particles colliding with the porous medium that remains attached and therefore reflects the net effect of repulsive and attractive forces
between colloids and solid surfaces. The value of ␣ is usuallyderived from experimental breakthrough curves (Pieper et al.,
1997; Ryan et al., 1999) or from fitted values of katt and calculated values of ␩ (Bales et al., 1991; Redman et al., 1997).
Straining is modeled according to a slightly modified formof the approach described in Bradford et al. (2003). The massbalance equation for strained colloids is given as:

⳵(␳bSstr)⫽ ␪wkstr␺strC
⳵t[4]

where kstr (T⫺1) is the straining coefficient, ␺str is a dimensionless colloid straining function, and Sstr (Nc m⫺1) is the solid
phase concentration of strained colloids. The value of ␺str isa function of distance and is described as␺str ⫽ H(z ⫺ zo)

d50 ⫹ z ⫺ z0 ⫺␤
d50

冢

冣

[5]

where ␤ is a parameter that controls the shape of the colloid
spatial distribution, H(z ⫺ zo) is the Heaviside function, z (L)is depth, and zo (L) is the depth for the column inlet (matrixsand) or textural interface (lens sand). Equation [5] assumes
that colloid mass retention by straining occurs primarily at
the column inlet or textural interface because colloids are
retained in dead-end pores that are smaller than some criticalsize. The number of dead-end pores is hypothesized to decrease with increasing distance because size exclusion and/or
limited transverse dispersivity tend to keep mobile colloids
within the larger networks, thus bypassing smaller pores. Bradford et al. (2003) found that the value of ␤ ⫽ 0.432 gave agood description of the spatial distribution of retained colloids
when significant straining occurred. For the remainder of thismanuscript ␤ will be fixed to this value. In contrast to theattachment–detachment model given by Eq. [1] through [3],the straining model does not include a dependence on velocity.
Additional studies are warranted to quantify the velocity dependence of the straining coefficient.
Mathematical modeling of water flow and bromide andcolloid transport in the experimental systems was conductedusing a modified version of the HYDRUS-2D computer code
(Simunek et al., 1999). To simulate the three-dimensional flow
and transport process that occurred in the heterogeneous systems considered in this work, the code was run in axisymmetric(r-z) mode. This code was modified to account for colloid
attachment and detachment (Eq. [1]–[3]), and straining (Eq.
[4] and [5]). Although attachment and straining are likely tooccur simultaneously in natural systems, these processes wereconsidered separately in this work to facilitate the determination of unique parameter estimates in the heterogeneous sys-tems. The incomplete characterization of the velocity dependence of colloid retention parameters (especially straining
parameters) also hindered the simultaneous description of
attachment and straining.
Bradford et al. (2003) presented a method to predict the
influence of size and anion exclusion on colloid transport. The
influence of exclusion becomes more apparent with increasingtransport distances. Because of the relatively small transportdistances considered in this work (10 cm), exclusion was not
simulated. Bromide and colloids are therefore both assumed
to be transported at the same pore water velocity.
To minimize the number of parameters that were fitted tothe heterogeneous systems, the detachment coefficient and thebromide and colloids hydrodynamic longitudinal dispersivities(␭HBR and ␭H) that were used in the simulations were takenfrom homogeneous soil column studies that employed thesame sands and colloids (Bradford et al., 2002). Table 2 summarizes these parameter values. The transverse dispersivity
was set equal to one-tenth of the longitudinal dispersivity.
Bradford et al. (2002) discussed differences in the bromide
and colloid dispersivity for a particular sand. The detachment
coefficients (Table 2) were quite low and had only a minor
influence on the homogeneous colloid transport experiments.
HYDRUS-2D is coupled to a nonlinear least squares optimization routine based upon the Marquardt–Levenberg algorithm (Marquardt, 1963) to facilitate the estimation of colloidtransport parameters from experimental data. Each model
simulation was obtained by simultaneously fitting two parameters to effluent and retention data collected from a heterogeneous colloid transport experiment. Sticking efficiencies (independent of velocity) for the matrix and lens sands were fitted
for the attachment model (Eq. [1]–[3]). Attachment coefficients were not directly fitted, so that the velocity dependenceof katt could be characterized (Eq. [2] and [3]). Straining coefficients for the matrix and lens sands were fitted for the straining
model (Eq. [4] and [5]).

RESULTS AND DISCUSSION
Transport in Heterogeneous Systems:
710-␮m Matrix
We first discuss the water flow and transport of bromide and colloids through the physically heterogeneous
systems consisting of a finer-textured sand (360, 240,
and 150 ␮m) lens embedded in the center of 710-␮m
matrix sand. In these systems the finer-textured lens has
a lower intrinsic permeability than the coarser-textured
710-␮m matrix. Figure 1 presents the simulated aqueous
phase velocity distribution in the 710-␮m matrix–360␮m lens system. The higher permeability of the matrix
Table 2. Transport parameters (bromide dispersivity, ␭BR
H ; colloid
dispersivity, ␭H; and detachment coefficient, kdet) that wereobtained from homogeneous soil column data (Bradford etal., 2002).
Soil
type

dp

␭BR
H

710
710
360
360
240
240
150
150

␮m
1.00
3.20
1.00
3.20
1.00
3.20
1.00
3.20

0.061
0.076
0.070
0.103
0.074
0.053
0.080
0.179

␭H

kdet ⫻ 104

0.237
0.239
0.158
0.288
0.179
0.361
0.071
0.299

min⫺1
0.75
4.10
6.65
2.87
10.0
3.75
12.4
12.0

cm

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

388

VADOSE ZONE J., VOL. 3, MAY 2004

Fig. 1. Simulated aqueous phase velocity distribution in the 710-␮m
matrix–360-␮m lens system. A cross-section view from the column
center (left) to the column boundary (right) is shown.

leads to significant flow bypassing of the finer-textured
lens material. An estimate of the volume fraction ofwater that passes through the lens was calculated fromthe ratio of the transmissivity (product of the crosssectional area and hydraulic conductivity) for the lensmaterial and the total column to be 4.0, 0.7, and 0.3%
for the 360-, 240-, and 150-␮m lens systems, respectively.
Hence, more than 96% of the water flows through the710-␮m matrix sand in these systems.
Figure 2 shows a plot of the effluent concentration
curves (relative concentration, C/Ci, as a function ofpore volume) for bromide in the indicated 710-␮m matrix systems. Observe that the initial breakthrough ofbromide occurs slightly before one pore volume (about
0.85–0.9 PV), due to flow bypassing of the lens. The
somewhat asymmetric shape (approach to peak effluent
concentration, and tailing) of the bromide breakthroughcurve is also controlled by the degree of water bypassing(Fig. 1). In general, the transport behavior of bromide
in the various 710-␮m matrix systems is quite similar
because comparable amounts of water bypass the various soil lenses. Variations in the bromide (and colloid)
pulse volume occurred as a result of differences in theFig. 2. Observed and simulated (710-␮m matrix–360-␮m lens) effluent concentration curves of bromide in the indicated 710-␮m matrix systems.

Darcy velocity for the columns (Table 1). Figure 2 alsopresents the simulated effluent concentration curve forbromide in the 710-␮m matrix–360-␮m lens system. The
predicted bromide effluent concentration curve is very
similar to the observed data. This suggests that the bromide transport parameters and the simulated aqueous
phase flow field (Fig. 1) accurately characterize the experimental conditions.
Figures 3a and 3b present plots of the 1.0-␮m colloid
effluent concentration curves and the spatial distributions of retained colloids in the indicated 710-␮m matrix
systems. The relative effluent concentrations are plotted
as a function of pore volumes in Fig. 3a. In Fig. 3b thenormalized concentration (number, Nc, divided by the
total number added to the column, Ntc) per gram of dry
sand is plotted as a function of dimensionless depth fromthe column inlet. The beginning and ending locations forthe lens sand are denoted with solid horizontal lines infigures of the colloid spatial distributions. The 1.0-␮m
colloid transport behavior is very similar for the different heterogeneous systems. This observation is consistent with the similar water flow and bromide transport
shown in Fig. 1 and 2, respectively. Similar to bromide(Fig. 2), the earlier colloid breakthrough occurs as aresult of flow bypassing of the finer-textured lenses (Fig.
1). Figure 3b indicates that the majority of the colloid
mass removal occurs near the inlet interface of the matrix and the fine-textured lens. This likely occurs as a

Fig. 3. (a) The effluent concentration curves and (b) the final spatial
distributions of 1.0-␮m colloids in the indicated 710-␮m matrix
systems.

389

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

www.vadosezonejournal.org(Eq. [4] and [5]) models, and statistical parameters (coefficient of linear regression, and standard error) for the
goodness of parameter fit. Uncertainty in the estimatedcolloid transport parameters in the finer-textured lenssand is quite large due to flow bypassing of this material.
Both the attachment and straining models provide a
reasonable description of the effluent concentration
curve and the spatial distribution of retained colloids.
Analysis of homogeneous transport data for 1.0-␮m colloids in the 710-␮m sand by Bradford et al. (2003),
however, indicates that attachment is likely the dominant retention process.
Figures 5a and 5b present plots of the 3.2-␮m colloid
effluent concentration curves and the spatial distributions of retained colloids in the indicated 710-␮m matrix
systems. As for the 1.0-␮m colloids (Fig. 3a) and bromide (Fig. 2), the transport and retention behavior forthe 3.2-␮m colloids is similar for the different soil heterogeneities. We again attribute this to the fact that mostof the water flows through the 710-␮m matrix material(⬎96%) and bypasses much of the finer-textured lens(Fig. 1). Comparison of Fig. 3 and 5 reveals lower effluent concentrations and greater mass retention near thecolumn inlet for the 3.2-␮m colloids than for the 1.0-␮m
colloids. Figures 6a and 6b present plots of the observed
and simulated 3.2-␮m colloid effluent concentration
curves and the spatial distributions of retained colloids
in the 710-␮m matrix–360-␮m lens system. Fitted parameters from the attachment and straining models are
summarized in Table 3. Considerable uncertainty in theestimated transport parameters for the finer-textured
lens sand occurred as a result of flow bypassing. The
attachment model provides an adequate description of
the effluent concentration curve, but does not satisfactorily describe the spatial distribution of retained colloids.
The straining model provides a slightly improved characterization of the spatial distribution. Data analysis by
Bradford et al. (2003) indicates that transport of 3.2-␮mcolloids in homogeneous 710-␮m sand was controlled bystraining. This hypothesis was supported by the systematic trends of increasing colloid retention with increasing
colloid size or decreasing median sand grain size, theFig. 4. Observed and simulated (parameters for the attachment andstraining models are given in Table 3) (a) effluent concentration
curves and (b) the final spatial distributions of 1.0-␮m colloids inthe 710-␮m matrix–360-␮m lens system.

result of variations in colloid retention with changes in
the aqueous flow field in this region (Fig. 1) or due toenhanced retention in the finer-textured sand lens.
Figures 4a and 4b present plots of the observed andsimulated (attachment and straining models) 1.0-␮m
colloid effluent concentration curves and the spatial distributions of retained colloids in the 710-␮m matrix–360-␮m lens system. Table 3 shows fitted parametervalues for the attachment (Eq. [1]–[3]) and straining

Table 3. Fitted parameters (sticking efficiency, ␣; and straining coefficient, kstr) from the attachment (Eq. [1]–[3]) and straining (Eq.
[4] and [5]) models.
Figure

Model

dp

4

Attach␮m
1.04Strain1.0

6

Attach3.2

6Strain3.2

10

Attach1.010Strain1.0

12

Attach3.2

12Strain3.2† Denotes matrix sand.
‡ Denotes lens sand.

Sand

Symbol

Units

Fit

SE

r2

710†
360‡
710†
360‡
710†
360‡
710†
360‡
710‡
150†
710‡
150†
710‡
150†
710‡
150†

␣
␣
kstr
kstr
␣
␣
kstr
kstr
␣
␣
kstr
kstr
␣
␣
kstr
kstr

–
–
min⫺1
min⫺1
–
–
min⫺1
min⫺1
–
–
min⫺1
min⫺1
–
–
min⫺1
min⫺1

0.173
0.491
0.065
2.000
0.160
0.043
0.108
0.441
0.001
0.266
0.000
0.323
0.031
0.867
0.021
1.160

0.012
0.218
0.005
1.053
0.010
0.052
0.007
0.244
0.241
0.041
0.073
0.023
0.624
0.123
0.179
0.054

0.969
0.978
0.924
0.932
0.743
0.938
0.855
0.988

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

390

VADOSE ZONE J., VOL. 3, MAY 2004

Fig. 5. (a) The effluent concentration curves and (b) the final spatial
distributions of 3.2-␮m colloids in the indicated 710-␮m matrix
systems.

inability of conventional attachment or blocking theory
to accurately characterize the colloid spatial distribution, and the wide variability (a factor of 24) in fitted
sticking efficiencies for a given porous medium and forcolloids that had similar surface charges but different
sizes.
It should also be mentioned that the 3.2-␮m colloids
in the 710-␮m matrix–360-␮m lens system exhibitedslightly earlier colloid breakthrough (Fig. 5) comparedwith bromide (Fig. 2). This observation is attributed tosize exclusion and/or the greater dispersivity of colloid
particles compared with bromide (Table 2). This behavior, however, was not observed for the 710-␮m matrix
systems containing 240- or 150-␮m lens, presumably due
to greater flow bypassing of the finer-textured lenssands.

Fig. 6. Observed and simulated (parameters for the attachment andstraining models are given in Table 3) (a) effluent concentration
curves and (b) the final spatial distributions of 3.2-␮m colloids inthe 710-␮m matrix–360-␮m lens system.

preferentially through the lens and tends to bypass alarge volume of finer-textured matrix material adjacentto the lens in the middle region of the column. An
estimate of the volume fraction of water that passes
through the lens was calculated from the ratio of thetransmissivity for the lens material and the total column
to be 63.0, 90.7, and 95.7% for the 360-, 240-, and 150-␮m

Transport in Heterogeneous
Systems—710-␮m Lens
This section discusses water flow, and the transportof bromide and colloids, through the physical heterogeneous systems consisting of a 710-␮m sand lens embedded in the center of the finer-textured (360, 240, and150-␮m) matrix sand. In these systems the finer-textured
matrix sand has a lower water permeability than thecoarser-textured 710-␮m lens. Figure 7 presents the simulated aqueous phase velocity distribution in the 710-␮mlens–360-␮m matrix system. Notice that water flows

Fig. 7. Simulated aqueous phase velocity distribution in the 710-␮mlens–360-␮m matrix system. A cross-section view from the column
center (left) to the column boundary (right) is shown.

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

www.vadosezonejournal.org

matrix systems, respectively. Hence, the trend of decreasing water permeability with decreasing mediangrain size of the matrix material promotes increased
bypassing of the matrix material near the lens in these
physically heterogeneous systems.
Figure 8 presents plots of the effluent concentration
curves for bromide in the indicated 710-␮m lens systems.
Due to pronounced flow bypassing in these systems(Fig. 7), the bromide breakthrough occurs considerably
earlier than one pore volume (between 0.6 and 0.85),
and the effluent curves are asymmetrically shaped (slowapproach to peak effluent concentration and tailing).
Differences in the bromide effluent curves occur primarily as a result of the variations in the volume of water thatis transported in the 710-␮m lens material. A simulated
effluent concentration curve for bromide in the 360-␮m
matrix–710-␮m lens system is also presented in Fig. 8.
The observed and predicted bromide effluent concentration curves exhibit reasonable agreement, indicatingthat the bromide transport parameters and simulatedaqueous phase flow field (Fig. 7) are accurately characterized.
Figure 9a presents the effluent concentration curves
for 1.0-␮m colloids in the indicated heterogeneous
710-␮m lens systems. The peak effluent concentration
decreases with decreasing matrix grain size (360 ⬎ 240 ⬎150 ␮m). The spatial distributions of retained 1.0-␮m
colloids in the various 710-␮m lens systems are shownin Fig. 9b. The 150-␮m matrix system has the highest
colloid concentrations at the column inlet and then decreases rapidly to a low constant concentration withincreasing dimensionless depth. The spatial distributionof colloids in the 360-␮m matrix system has a much
more gradual shape and higher colloid concentrations
directly below the inlet lens–matrix interface (at a dimensionless depth of 0.3) compared with the 150-␮m
matrix system. The 240-␮m matrix systems exhibit intermediate behavior to the 360- and 150-␮m matrix systems. Both effluent and spatial distribution data areconsistent with straining, which increases in magnitudeand frequency with decreasing grain size of the sand.

Fig. 8. Observed and simulated (710-␮m lens–360-␮m matrix) effluent concentration curves of bromide in the indicated 710-␮mlens systems.

391

Fig. 9. (a) The effluent concentration curves and (b) the final spatial
distributions of 1.0-␮m colloids in the indicated 710-␮m lenssystems.

Figures 10a and 10b present plots of the observed andsimulated 1.0-␮m colloid effluent concentration curves
and the spatial distributions of retained colloids in the150-␮m matrix–710-␮m lens system. Table 3 summarizes the fitted parameters from the attachment andstraining models. The sticking efficiency for the 150-␮m
matrix sand was 266 times greater than that for the710-␮m lens sand. This difference is physically unrealistic because ␣ is theoretically the same for similar Ottawa
sands and colloids. In comparison with the attachment
model, the straining model provides an improved characterization of the effluent concentration curve and thespatial distribution. This observation suggests that straining is an important mechanism of colloid retention for
the 1.0-␮m colloids in this system. Straining also likely
influences the retention of 1.0-␮m colloids in the other710-␮m lens systems (360- and 240-␮m matrix sands),
but to a lesser extent due to the larger median grain
size of the matrix sand in these systems. Attachment isanticipated to have a greater role in colloid retention
for coarser-textured sands and/or smaller colloids.
Figure 11a presents the effluent concentration curves
for the 3.2-␮m colloids in the heterogeneous 710-␮mlens systems. As for the 1-␮m colloids (Fig. 9a), the
3.2-␮m colloids follow a trend of decreasing peak effluent concentration with decreasing matrix grain size(360 ⬎ 240 ⬎ 150 ␮m). The corresponding 3.2-␮m col-

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

392

VADOSE ZONE J., VOL. 3, MAY 2004

Fig. 10. Observed and simulated (parameters for the attachment andstraining models are given in Table 3) (a) effluent concentration
curves and (b) the final spatial distributions of 1.0-␮m colloids inthe 710-␮m lens–150-␮m matrix system.

loid spatial distribution plots are shown in Fig. 11b. The
heterogeneous 710-␮m lens systems exhibits high concentrations in the sand near the inlet and then rapidly
decreases to a constant low value with increasing distance until a dimensionless depth of around 0.6. A second minor increase in colloid retention occurs near theinterface of the lens and matrix sands in the 240- and150-␮m matrix systems (dimensionless depth of around0.6). For a particular matrix sand and 710-␮m lens system, comparison of Fig. 9 and 11 reveals lower effluent
concentrations and greater mass retention near the column inlet for the 3.2-␮m colloids than for the 1.0-␮m
colloids. This observation is consistent with straining
behavior, which is more pronounced for larger colloids(Bradford et al., 2002).
Figures 12a and 12b present plots of the observed andsimulated 3.2-␮m colloid effluent concentration curves
and the spatial distributions of retained colloids in the150-␮m matrix–710-␮m lens system. Table 3 summarizes the fitted parameters from the attachment andstraining models. The difference in the fitted sticking
efficiencies for the 150-␮m matrix (28 times greater)and 710-␮m lens sands was physically unrealistic since␣ is theoretically the same for similar Ottawa sandsand colloids. Similar to Fig. 10b, the straining model
provided an improved description of both the effluent

Fig. 11. (a) The effluent concentration curves and (b) the final spatial
distributions of 3.2-␮m colloids in the indicated 710-␮m lenssystems.

concentration curve and the spatial distribution compared with the attachment model. This observation suggests that straining is an important mechanism of colloid
retention for the 3.2-␮m colloids in this system, as wellas the other 710-␮m lens systems (360- and 240-␮m
matrix sands).

SUMMARY
Colloid transport studies were conducted in watersaturated physically heterogeneous systems to gain insight into the processes controlling transport in naturalaquifer and vadose zone (variably saturated) systems.
Attachment is typically assumed to be the dominantmechanism of colloid retention in porous media. The
experimental results and analysis in this manuscript indicate that straining is also sometimes an important mechanism of colloid retention, especially for decreasing median grain size and increasing colloid size. Straining was
found to be greatest in sand adjacent to the column
inlet, whereas attachment likely occurred throughout
the system at a lower rate. Results from this study wereconsistent with the finding reported in Bradford et al.
(2003) that straining was a significant mechanism of
colloid retention for values of (dp /d50) ⬎ 0.005. This
work also underlines the importance of aqueous phasevelocity distribution, retention at interfaces of texturalcontrast, and exclusion in heterogeneous systems. Additional research is warranted to better characterize theReproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

www.vadosezonejournal.org

Fig. 12. Observed and simulated (parameters for the attachment andstraining models are given in Table 3) (a) effluent concentration
curves and (b) the final spatial distributions of 3.2-␮m colloids inthe 710-␮m lens–150-␮m matrix system.

dependence of attachment and, especially, straining onthese factors. The potential role of attachment as ameans to initiate straining also needs to be examined.
REFERENCES
Abu-Sharar, T.M., F.T. Bingham, and J.D. Rhoades. 1987. Stabilityof soil aggregates as affected by electrolyte concentration and composition. Soil Sci. Soc. Am. J. 51:309–314.
Bales, R.C., S.R. Hinkle, T.W. Kroeger, and K. Stocking. 1991. Bacteriophage adsorption during transport through porous media: Chemical perturbations and reversibility. Environ. Sci. Technol. 25:2088–
2095.
Bales, R.C., S. Li, K.M. Maguire, M.T. Yahya, and C.P. Gerba. 1993.
MS-2 and poliovirus transport in porous media: Hydrophobic effects and chemical perturbations. Water Resour. Res. 29:957–963.
Bettahar, M., O. Razakarisoa, F. van Dorpe, and M. Baviere. 1998.
Influence of a surfactant contamination technique on the hydraulicconductivity of a controlled aquifer polluted by diesel. Rev. Sci.
L’Eau 11:85–100.
Bitton, G., and R.W. Harvey. 1992. Transport of pathogens throughsoil. p. 103–124. In R. Mitchell (ed.) New concepts in environmental
microbiology. Wiley-Liss, New York.
Bolster, C.H., A.L. Mills, G.M. Hornberger, and J.S. Herman. 1999.
Spatial distribution of bacteria experiments in intact cores. Water
Resour. Res. 35:1797–1807.
Bradford, S.A., and L.M. Abriola. 2001. Dissolution of residual tetrachloroethylene in fractional wettability porous media: Incorporation of interfacial area estimates. Water Resour. Res. 37:1183–1195.
Bradford, S.A., S.R. Yates, M. Bettahar, and J. Simunek. 2002. Physical factors affecting the transport and fate of colloids in saturated
porous media. Water Resour. Res. 38(12):1327 DOI: 10.1029/
2002WR001340.

393

Bradford, S.A., J. Simunek, M. Bettahar, M.Th. van Genuchten, and
S.R. Yates. 2003. Modeling colloid attachment, straining, and exclusion in saturated porous media. Environ. Sci. Technol. 37:2242–
2250.
Camesano, T.A., and B.E. Logan. 1998. Influence of fluid velocity
and cell concentration on the transport of motile and nonmotile
bacteria in porous media. Environ. Sci. Technol. 32:1699–1709.
Cumbie, D.H., and L.D. McKay. 1999. Influence of diameter on particle transport in a fractured shale saprolite. J. Contam. Hydrol. 37:
139–157.
Danielson, R.E., and P.L. Sutherland. 1986. Porosity. In A. Klute(ed.) Methods soil analysis. Part 1. 2nd ed. SSSA Book Ser. 5.
ASA and SSSA, Madison, WI.
Harvey, R.W., N.E. Kinner, D. MacDonald, D.W. Metge, and A.
Bunn. 1993. Role of physical heterogeneity in the interpretation ofsmall-scale laboratory and field observations of bacteria, microbialsized microsphere, and bromide transport through aquifer sediments. Water Resour. Res. 29:2713–2721.
Herzig, J.P., D.M. Leclerc, and P. LeGoff. 1970. Flow of suspension
through porous media: Application to deep filtration. Ind. Eng.
Chem. 62:129–157.
Johnson, P.R., and M. Elimelech. 1995. Dynamics of colloid depositionin porous media: Blocking based on random sequential adsorption.
Langmuir 11:801–812.
Kretzschmar, R., M. Borkovec, D. Grolimund, and M. Elimelech.
1999. Mobile subsurface colloids and their role in contaminanttransport. Adv. Agron. 66:121–193.
Kretzschmar, R., K. Barmettler, D. Grolimund, Y.-D. Yan, M. Borkovec, and H. Sticher. 1997. Experimental determination of colloid
deposition rates and collision efficiencies in natural porous media.
Water Resour. Res. 33:1129–1137.
Logan, B.E., D.G. Jewett, R.G. Arnold, E.J. Bouwer, and C.R.
O’Melia. 1995. Clarification of clean-bed filtration models. J. Environ. Eng. 121:869–873.
MacCarthy, J.F., and J.M. Zachara. 1989. Subsurface transport ofcontaminants. Environ. Sci. Technol. 23:496–502.
MacLeod, F.A., H.M. Lappin-Scott, and J.W. Costerton. 1988. Plugging of a model rock system by using starved bacteria. Appl. Environ. Microbiol. 54:1365–1372.
Marquardt, D.W. 1963. An algorithm for least-squares estimation of
nonlinear parameters. J. Soc. Indust. Appl. Math. 11:431–441.
Matthess, G., and A. Pekdeger. 1985. Survival and transport of pathogenic bacteria and viruses in groundwater. p. 472–482. In C.H.
Ward et al. (ed.) Ground water quality. John Wiley, New York.
McDowell-Boyer, L.M., J.R. Hunt, and N. Sitar. 1986. Particle transport through porous media. Water Resour. Res. 22:1901–1921.
Ouyang, Y., D. Shinde, R.S. Mansell, and W. Harris. 1996. Colloidenhanced transport of chemicals in subsurface environments: A
review. Crit. Rev. Environ. Sci. Technol. 26:189–204.
Pieper, A.P., J.N. Ryan, R.W. Harvey, G.L. Amy, T.H. Illangasekare,and D.W. Metge. 1997. Transport and recovery of bacteriophage
PRD1 in a sand and gravel aquifer: Effect of sewage-derived organic matter. Environ. Sci. Technol. 31:1163–1170.
Rajagopalan, R., and C. Tien. 1976. Trajectory analysis of deep-bed
filtration with the sphere-in-a-cell porous media model. AIChE
J. 22:523–533.
Redman, J.A., S.B. Grant, T.M. Olson, M.E. Hardy, and M.K. Estes.
1997. Filtration of recombinant Norwalk virus particles and bacteriophage MS2 in quartz sand: Importance of electrostatic interactions. Environ. Sci. Technol. 31:3378–3383.
Redman, J.A., S.B. Grant, T.M. Olson, and M.K. Estes. 2001. Pathogen filtration, heterogeneity, and the potable reuse of wastewater.
Environ. Sci. Technol. 35:1798–1805.
Reimus, P.W. 1995. The use of synthetic colloids in tracer transport
experiments in saturated rock fractures. LA-13004-T. Los Alamos
National Laboratory, Los Alamos, NM.
Ryan, J.N., and M. Elimelech. 1996. Colloid mobilization and transport
in groundwater. Colloids Surf. A 107:1–56.
Ryan, J.N., M. Elimelech, R.A. Ard, R.W. Harvey, and P.R. Johnson.
1999. Bacteriophage PRD1 and silica colloid transport and recovery
in an iron oxide-coated sand aquifer. Environ. Sci. Technol. 33:63–73.
Ryan, J.N., and P.M. Gschwend. 1994. Effect of solution chemistry
on clay colloid release from an iron oxide-coated aquifer sand.
Environ. Sci. Technol. 28:1717–1726.

Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved.

394

VADOSE ZONE J., VOL. 3, MAY 2004

Saiers, J.E., G.M. Hornberger, and C. Harvey. 1994. Colloidal silica
transport through structured, heterogeneous porous media. J. Hydrol. (Amsterdam) 163:271–288.
Sakthivadivel, R. 1966. Theory and mechanism of filtration of noncolloidal fines through a porous medium. Rep. HEL 15-5. Hydraul.
Eng. Lab., Univ. of Calif., Berkeley, CA.
Sakthivadivel, R. 1969. Clogging of a granular porous medium bysediment. Rep. HEL 15-7. Hydraul. Eng. Lab., Univ. of Calif.,
Berkeley, CA.
Silliman, S.E. 1995. Particle transport through two-dimensional, saturated porous media: Influence of physical structure of the medium.
J. Hydrol. (Amsterdam) 167:79–98.
Simunek, J., M. Sejna, and M.Th. van Genuchten. 1999. The HYDRUS-2D software package for simulating two-dimensional movement of water, heat, and multiple solutes in variably saturated
media. Version 2.0, IGWMC- TPS- 53. International Ground Water
Modeling Center, Colorado School of Mines, Golden, CO.
Song, L.F., and M. Elimelech. 1994. Transient deposition of colloidal
particles in heterogeneous porous media. J. Colloid Interface Sci.
167:301–313.
Song, L.F., P.R. Johnson, and M. Elimelech. 1994. Kinetics of colloid

deposition onto heterogeneously charged surfaces. Environ. Sci.
Technol. 28:1164–1171.
Suarez, D.L., J.D. Rhoades, R. Lavado, and C.M. Grieve. 1984. Effectof pH on saturated hydraulic conductivity and soil dispersion. Soil
Sci. Soc. Am. J. 48:50–55.
Tan, Y., J.T. Cannon, P. Baveye, and M. Alexander. 1994. Transport ofbacteria in an aquifer sand—Experiments and model simulations.
Water Resour. Res. 30:3243–3252.
Tufenkji, N., J.A. Redman, and M. Elimelech. 2003. Interpreting deposition patterns of microbial particles in laboratory-scale column
experiments. Environ. Sci. Technol. 37:616–623.
Wan, J., T.K. Tokunaga, and C.-F. Tsang. 1995. Bacterial sedimentation through a porous medium. Water Resour. Res. 31:1627–1636.
Wang, D.S., C.P. Gerba, and J.C. Lance. 1981. Effect of soil permeability
on virus removal through soil. Appl. Environ. Microbiol. 42:83–88.
Wilson, J.T., L.E. Leach, M. Henson, and J.N. Jones. 1986. In situ
biorestoration as a ground water remediation technique. Ground
Water Monit. Rev. 6:56–64.
Yao, K., M.T. Habibian, and C.R. O’Melia. 1971. Water and wastewater filtration: Concepts and applications. Environ. Sci. Technol. 5:1105–1112.