Available online at www.sciencedirect.com

Journal of Contaminant Hydrology 96 (2008) 113 – 127
www.elsevier.com/locate/jconhyd

Colloid transport in unsaturated porous media: The role of watercontent and ionic strength on particle straining
Saeed Torkzaban a , Scott A. Bradford b,⁎,Martinus Th. van Genuchten b , Sharon L. Walker aaDepartment of Chemical and Environmental Engineering, University of California, Riverside, CA 92521, United Statesb
US Salinity Laboratory, USDA-ARS, 450 W. Big Springs Road, Riverside, CA 92507-4617, United States
Received 14 November 2006; received in revised form 19 October 2007; accepted 24 October 2007
Available online 17 November 2007

Abstract
Packed column and mathematical modeling studies were conducted to explore the influence of water saturation, pore-waterionic strength, and grain size on the transport of latex microspheres (1.1 μm) in porous media. Experiments were carried out underchemically unfavorable conditions for colloid attachment to both solid–water interfaces (SWI) and air–water interfaces (AWI)
using negatively charged and hydrophilic colloids and modifying the solution chemistry with a bicarbonate buffer to pH 10.
Interaction energy calculations and complementary batch experiments were conducted and demonstrated that partitioning of
colloids to the SWI and AWI was insignificant across the range of the ionic strengths considered. The breakthrough curve and final
deposition profile were measured in each experiment indicating colloid retention was highly dependent on the suspension ionicstrength, water content, and sand grain size. In contrast to conventional filtration theory, most colloids were found deposited close
to the column inlet, and hyper-exponential deposition profiles were observed. A mathematical model, accounting for time- anddepth-dependent straining, produced a reasonably good fit for both the breakthrough curves and final deposition profiles.
Experimental and modeling results suggest that straining — the retention of colloids in low velocity regions of porous media suchas grain junctions — was the primary mechanism of colloid retention under both saturated and unsaturated conditions. The extent
of stagnant regions of flow within the pore structure is enhanced with decreasing water content, leading to a greater amount ofretention. Ionic strength also contributes to straining, because the number of colloids that are held in the secondary energy
minimum increases with ionic strength. These weakly associated colloids are prone to be translated to stagnation regions formed at
grain–grain junctions, the solid–water–air triple point, and dead-end pores and then becoming trapped.
Published by Elsevier B.V.
Keywords: Colloid transport; Deposition; Straining; Ionic strength; Hydrodynamics

1. Introduction⁎ Corresponding author. Tel.: +1 951 369 4857; fax: +1 951 342
4963.
E-mail address: sbradford@ussl.ars.usda.gov (S.A. Bradford).
0169-7722/$ - see front matter. Published by Elsevier B.V.
doi:10.1016/j.jconhyd.2007.10.006

Colloid movement through porous media is of greatsignificance in a number of environmental fields including contaminant transport, soil profile development, andsubsurface migration of pathogenic microorganisms.
Pathogenic microorganisms such as bacteria and viruses

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S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127(often referred to biocolloids) pose a high risk to water
resources through land application of raw and treatedwastewater, septic systems, leaking sewage pipes, andanimal manure (Hurst, 1980; Powelson et al., 1993;
Redman et al., 2001). Colloid transport in porous media isalso of concern due to colloid-facilitated transport of awide variety of inorganic and organic contaminants that
adsorb onto these particles and travel significant distances(de Jonge et al., 1998; Ryan et al., 1998; McGechan andLewis, 2002). Hence, comprehensive knowledge of thetransport of colloidal particles in subsurface environments
is essential for predicting biological and chemical contaminant fate. Considerable research has been devoted to
the fate and transport of colloids in saturated porous media(reviews are given by Schijven and Hassanizadeh, 2000;
Harvey and Harms, 2002; de Jonge et al., 2004); however,colloid transport in the unsaturated (vadose) zone, which
often act as a first natural layer against the pollution ofgroundwater, has received little systematic research andthe governing mechanisms are poorly understood.
Mechanisms of colloid retention in unsaturated porous media include adsorption (attachment/detachment
processes) to solid–water interfaces (SWI) (reviews
are given by Ryan and Elimelech, 1996, Schijven and
Hassanizadeh, 2000), air–water interfaces (AWI) (e.g.
Wan and Wilson, 1994a), straining (McDowell-Boyeret al., 1986; Bradford et al., 2002, 2003), and film
straining (Wan and Tokunaga, 1997; Saiers and Lenhart,
2003a). Attachment to the SWI involves colloid
collision with and attachment to grain surfaces, andconsequently depends on the chemical and physicalcharacteristics of the colloids and soil surfaces as well as
the solution chemistry (Ryan and Elimelech, 1996,
Walker et al., 2004). The AWI present within unsaturated porous media is also believed to serve as acollector for colloid particles, reportedly in an irreversible manner, retained by either capillary or electrostaticforces (Wan and Wilson, 1994b; Schafer et al., 1998).
Colloid attachment to the AWI, therefore, depends on
pH, ionic strength, and colloid surface properties(DeNovio et al., 2004; Torkzaban et al., 2006b).
Additionally, Wan and Tokunaga (2002) demonstrated
that only positively charged colloidal particles attachedat the AWI, and Crist et al. (2004, 2005) observed inthree-dimensional porous media that negatively
charged-hydrophilic colloids did not attach to the AWI.
Straining involves the retention of colloids in thesmallest regions of the pore space (McDowell-Boyeret al., 1986; Cushing and Lawler 1998; Bradford et al.,2002, 2003, 2006a) such as those formed near grain-tograin contact points. It should be noted that retention ofcolloids near to grain-to-grain contact points has also

been referred to in the literature as wedging (Herzig
et al., 1970; Johnson et al., 2007). In the smallest regionsof the pore space the water velocity is very low and theselocations can be considered as zones of relative flow
stagnation. Straining may also occur in pore throats thatare too small to allow the passage of multiple colloids(Herzig et al., 1970; Bradford et al., 2002), a processoften referred to as bridging (Ramachandran and Fogler,1999). Criteria for colloid straining in porous media has
traditionally been assumed to be simply a function of theratio of colloid to collector diameters (dp/dg) and thepore size distribution of the medium (Herzig et al., 1970;
McDowell-Boyer et al., 1986; Bradford et al., 2002,
2003). Herzig et al. (1970) computed that when dp/dg
exceeds 0.05, straining significantly contributes to retention of colloids in porous media. Recently, a few
researchers have suggested that the theoretical criteria of
Herzig et al. (1970) underestimates the extent of straining in colloid retention and that straining can be occurring at dp/dg as low as 0.002 (Bradford et al., 2002,
2003; Li et al., 2004).
In unsaturated media, straining has received relatively less attention (Gargiulo et al., 2007). In fact,
straining may be more pronounced in unsaturated versus
saturated porous media because capillary forces constrain water flow within regions having smaller porespaces. Furthermore, unsaturated systems also containsolid–water–air triple points at the intersection of solid–
water and air–water interfaces. Triple points and grain–
grain contact points share many similarities in that theselocations are both low velocity zones. In this work, we
consider retention at the triple point as an additional
form of straining. Moreover, the extent to which saturated and especially unsaturated colloid straining issensitive to changes in the chemical properties of thesystem (i.e. aqueous phase, colloids, and collectors)
remains poorly understood (Bradford et al., 2006a,
2007). In addition to straining, film straining (Wan andTokunaga, 1997) is another potential retention mechanism needing further investigation. Film straining is theremoval of colloids in partially saturated porous media
occurring as a result of the physical restrictions tocolloid transport through water films with thicknesses
smaller than the diameter of the colloids.
Previous studies on unsaturated colloid transport
have mainly focused on the determination of the colloid
concentration in the effluent (e.g. Saiers and Lenhart,
2003a; Torkzaban et al., 2006a,b). Breakthrough concentrations are typically simulated by using a variety ofparameters to best fit the data that consider SWI and/or
AWI adsorption rate coefficients, and/or film straining
coefficients. Few studies have reported the shape of the

S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

colloid deposition profiles for unsaturated conditions.
Bradford et al. (2003) demonstrated in saturated colloidtransport experiments that breakthrough curves can beadequately fit using a variety of models such as an
attachment and detachment model, or an attachment andstraining model. The study showed that consideration ofboth breakthrough curves and deposition profiles inmodel fitting is vital to gain insight on the controlling
deposition mechanisms.
The objective of this work was to explore the effects ofwater content and solution ionic strength on colloidtransport and retention. Highly unfavorable attachment
conditions were employed to ensure a high repulsive
energy barrier against attachment and therefore theretention mechanisms involved were not attachmentby simply chemical interactions, but rather by straining.
To minimize colloid attachment to both the SWI and AWI,
the experiments were conducted using hydrophilic, negatively charged microspheres in a buffered solution
such that the SWI and AWI were negatively charged.
Unfavorable attachment conditions were confirmed toexist through complementary batch experiments and
DLVO calculations. The breakthrough data and final
deposition profile were measured and simulated using the
HYDRUS-1D code that accounts for time and depthdependent deposition processes. Fitted model parameters
were used to gain insight into the various mechanisms
controlling colloid transport in unsaturated systems.
2. Materials and methods
2.1. Tracer, colloid, and sand materials
The background electrolyte solution utilized in thisstudy consisted of deionized water buffered to pH 10(1.67 mM NaHCO3 + 1.67 mM Na2CO3). Sodium nitrate(0.2 mM, Fisher Scientific) was used as a conservative
tracer to characterize the hydrodynamic properties ofthe porous medium. Carboxylate-modified latex (CML)
colloids (Molecular probes, Inc., Eugene, OR) were selected as model colloid particles. These spherical particles
have been employed in previous colloid transport studies
reported in the literature (Wan and Wilson, 1994a,b).
CML was chosen due to the high density of carboxylic
acids on the colloid surface creating a negatively chargedhydrophilic surface. Colloid diameter was 1.1 μm with aparticle density (ρp) of 1.055 g cm− 3 and a particle surface
charge density (ρq) of 0.0175 meq/g. The values of ρp andρq were provided by the manufacturer. The concentrationof colloid suspension (2.5–2.8 × 107 Nc ml− 1; where Nc
denotes number of colloids) was selected to minimize any
permeability reductions of the porous medium.

115

Two different sizes of Ottawa aquifer sand (U.S.
Silica, Ottawa, IL) were used in this study. These sands
are designated hereafter as 3550 and MIX having
median grain sizes (d50) of 360 and 240 μm, respectively. The uniformity index (Ui = d60 / d10 where x % of
the mass was finer than dx) of the 3550 and MIX sands
was measured to be 1.88 and 3.06, respectively. The
capillary pressure–saturation curves for these Ottawa
sands were previously reported by Bradford and Abriola(2001). Ottawa sands typically consist of 99.8% SiO2
(quartz) and trace amounts of metal oxides, are spheroid
in shape, and have rough surfaces. Quartz and iron oxides possess a net negative charge at pH 10 (Tipping,
1981; Redman et al., 2004), and any attractive electrostatic interactions between the CML colloids and theporous medium are expected to be minimized at this pH.
2.2. Experimental set-up
The column experiment was designed to accurately
establish a steady-state and unit hydraulic gradient along
the column in case of unsaturated transport (Fig. 1). A
stainless steel column with internal diameter and length of
5 and 10 cm, respectively, was selected for this study. Ahydrophilic nylon membrane with 10 μm pore size
(SaatiTech, Veniano, Italy), supported by a aluminum
end-plate, was used as a capillary barrier at the bottom of
the column. The nylon membrane had a bubbling pressureof 70 cm-H2O. Results of preliminary experiments (performed without sand) demonstrated that neither the column body nor the nylon membrane retained the colloids.
The column was wet-packed with the water level maintained a few centimeters above the sand surface. After the
addition of sand, the column was vibrated to ensure a
uniform packing and to liberate any trapped air bubbles.
Prior to each experiment, the column was flushed upward
under saturated conditions with about seven pore volumesof the pH 10 electrolyte solution to free the effluent frombackground colloids in the sand. The flow was then reversed and the column was rinsed with an additional twopore volumes before starting the transport experiments.
The solution chemistry conditions were verified by measuring the pH and ionic strength of the influent andeffluent solutions.
A sprinkling apparatus equipped with 7 stainless steel
needles was connected to a high performance liquid chromatography (HPLC) pump (Barnant Company, Barrington, IL) and used to evenly distribute the influent over thesand surface. Capillary pressure head was measured with
two stainless steel miniature tensiometers (Chemiquip
Products Co., West New York, NJ) inserted at 2 and 8 cm
from the upper sand surface. Data from the tensiometers

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S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

Fig. 1. Schematic representation of the experimental set-up.

were collected continuously using a CR10X datalogger(Campbell Scientific Ltd, Lougborough, UK) and monitored with a keyboard display (CR10KD). The averagewater content of the column (under steady-state unit gradient flow conditions) was monitored gravimetricallywith an electronic balance (Sartorius Master Series, LP
Models, Germany) and is listed in Table 1. The lower
boundary condition was controlled using a hanging watercolumn to impose a constant suction.
Unsaturated transport experiments involved draining the saturated column to the desired water saturationlevel by reducing the inflow water rate to the hydraulicconductivity corresponding to that saturation. Simultaneously, the pressure head at the bottom of the column
was gradually reduced until the readings of the tensiometers showed the same values. This resulted in aunit hydraulic head gradient, i.e. constant capillary pressure, which implies a constant saturation level along thecolumn. In some experiments, to eliminate the effect ofvariations in water velocity in our results, a hydraulicgradient was applied in the saturated experiments suchthat the average water velocity was the same as in theunsaturated experiments. Table 1 indicates the parameters of each column experiment.
2.3. Transport experiment protocol
Column transport experiments were systematicallyconducted to investigate the transport and deposition
behavior of the 1.1 μm CML microspheres under sat-urated and unsaturated conditions at three different ionicstrengths (IS = 6, 30, and 60 Mm at a pH of 10). Afterestablishing a specified saturation and water chemistry,transport experiments were carried out in six stages.
These stages are described in greater detail below:
Stage 1: Prior to colloid application, tracer experiments
were carried out to determine the dispersivity
for each saturated condition. A solution
Table 1
Experimental conditions for column experiments in 3550 sand (Li, Mi,
and Hi stand for low, medium, and high ionic strength. Lv, Mv, and Hv
stand for low, medium, and high velocity)
Exp.

Saturation % Ionic
Average Dispersivity Pulse
strength water(cm)
duration(mM)velocity(pore(cm/min)volume)

Li100
Mi100
Hi100Lv

100
100
100

6
30
60

0.6
0.35
0.35

0.08
0.08
0.08

7.12
5.01
4.63

Hi100Mv

100

60

0.56

0.08

5.94

Hi100Hv
Li70
Mi70
Hi70
Li50
Mi50
Hi50
Li40
Mi40
Hi40

100
70
70
70
50
50
50
40
40
40

60
6
30
60
6
30
60
6
30
60

0.87
0.85
0.85
0.85
0.6
0.6
0.6
0.37
0.37
0.37

0.08
0.4
0.4
0.4
0.6
0.6
0.6
0.8
0.8
0.8

5.43
7.08
5.09
5.51
7.12
5.04
5.94
7.05
5.03
4.64

S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

containing 0.2 mM NaNO3 was fed into thecolumn at given water saturation and thebreakthrough curve was obtained by measuring the absorbance of the effluent at 204 nm
using a spectrophotometer (Perkin Elmer
LC95 UV/VIS spectrometer, Irvine, CA).
Stage 2: Following the tracer experiment, the influent
was switched to the background electrolyte
solution in order to flush out the remnant
nitrate. This was verified by measuring theabsorbance of the effluent. This step also
served the purpose of equilibrating the column
with the electrolyte to be used in thesubsequent colloid transport experiment.
Stage 3: A colloid suspension (2.5–2.8 × 107 Nc ml− 1)
was introduced into the column at a constantrate. The colloid suspension was applied for agiven number of pore volumes (pulse duration)
as listed in Table 1.
Stage 4: Colloid-free electrolyte solution was applied tothe column at the same flow rate until theeffluent colloid concentration returned to baseline level. Effluent samples were collected atselected intervals by a fraction collector andanalyzed for colloid concentration using aspectrometer (Perkin Elmer LC95 UV/VIS
spectrometer, Irvine, CA) at 480 nm.
Stage 5: Following completion of the colloid transport
experiments, the spatial distribution of deposited colloids in a sand column was determined(Bradford et al., 2002). The sand was carefully
excavated in 1 cm increments and eachincrement was placed in a 50 mL polypropylene
centrifuge tube containing 30 mL of the background electrolyte solution. The tubes werevery slowly shaken for a few minutes to liberate
reversibly retained colloids. The concentrationof colloids in the supernatant solution wasmeasured using a fluorometer (Turner Quantech
Fluorometer, Dubuque, IA) following anexperimental protocol outlined previously(Bradford et al., 2002). Water and sand werepoured into an aluminum dish and placed in anoven for several hours to volatilize all of theremaining water. The volume of water and massof sand in each tube was determined from massbalance by measuring the weight of the empty
tubes, water and sand tubes, and dry sand.
Stage 6: A colloid mass balance was conducted at the endof the column experiment using effluent concentration data and the deposited colloids in thecolumn. The calculated number of effluent and117

retained colloid particles was normalized by the
total number of particles injected into a column.
2.4. Batch experiments
Batch experiments were conducted by placing 10 g ofsand and 10 ml of a known initial concentration of colloid
suspension into a polypropylene centrifuge tubes with thetemperature kept at approximately 20 °C. Three different
ionic strength solutions (6, 30, 60 mM) buffered at pH 10,
corresponding to the chemical conditions in column
experiments, were used for making colloid suspension.
The suspension and sand were allowed to equilibrate for2 h by gently rotating the tubes end over end (15 rpm) on a
tube rotator (Fisher Scientific, San Diego, CA). The 2-h
equilibration time was chosen to mimic the duration of
the column experiments. A control experiment without
colloids was also run for measuring the background concentration of colloids introduced from the sand. The initialand final concentrations of colloids in the suspension were
determining using the spectrophotometer (Perkin Elmer
LC95 UV/VIS spectrometer, Irvine, CA) after setting thetube to rest for a few minutes. All experiments were performed in duplicate.
2.5. Electrokinetic characterization of colloids
The zeta potential of the colloids was measured using a
ZetaPals instrument (Brookhaven Instruments Cooperation, Holtsville, NY). The measurements were carried out
three times for each condition and the average values were−110, −85, −71 mV for the colloids suspended in 6, 30,
and 60 mM ionic strength solutions, respectively. The
AWI has been reported to be negatively charged over a
very wide range of ionic strength and pH (Li andSomasundaran, 1991; Gracia et al., 1995). According toresults obtained by Li and Somasundaran (1991), the zeta
potential of air bubbles in NaCl solution at pH 10 and asolution ionic strength with a range of 0.01–100 mM
varies from −90 to −50 mV. The zeta potential of quartz
sand surfaces in pH 10 solution has been reported previously to be approximately −70 mV (Elimelech et al.,2000). These values were used in calculations for electrostatic forces presented later in this paper.
3. Colloid transport model for saturated andunsaturated systems
The HYDRUS-1D code (Simunek et al., 2005) is a
finite element model for simulating the one-dimensional
movement of water, heat, and multiple solutes in variably saturated media. The code numerically solves the

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S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

Richards' equation for saturated–unsaturated water flow
and Fickian-based advection–dispersion equations forthe non-linear equilibrium and kinetic reactions between
colloids and the SWI. The code is coupled to a nonlinear least square optimization routine based upon theLevenberg–Marquardt algorithm (Marquardt, 1963) tofit model parameters to breakthrough curve and/or
deposition profile information. Relevant aspects of thecode that were used to simulate the colloid transport data
are described below.
The transport of colloids through the sand columns
was described using the one-dimensional form of theadvection–dispersion equation (ADE) that accounts forcolloid deposition in the column:

depth. When β goes to zero, then depth-dependent
deposition is not considered. Bradford et al. (2003)
reported that the value of β = 0.432 gave a good
description of the spatial distribution of retained colloids
when significant straining occurred; hence this value wasused in the simulations reported in this paper.
Based on the theoretical approach presented above,mechanisms of colloid deposition such as straining, film
straining, and attachment to the SWI and AWI arelumped together in a single exchange term, rd. Below
we present experimental evidence to help identify the
relative importance of each of these deposition mechanisms for our experimental conditions, and to provide
more evidence for our model formulation.

AC
A2 C
AC
¼ kv 2  v
 rd
At
Az
Az

4. Results and discussion

ð1Þ

where C is the number of colloids per unit volume of
the aqueous phase (Nc L− 3), λ is the dispersivity (L), v
is the average pore-water velocity (LT− 1), and rd is themass transfer rate of colloids in aqueous phase to/fromthe deposited phase (Nc L− 3T− 1) given by:qb

ASd¼ rd ¼ hKd ws C  qb Kdet Sd
Atð2Þwhere ρb is the soil bulk density (ML− 3), θ is the volumetric water content (−), Kd is the colloid deposition
coefficient (T− 1), ψs is a dimensionless deposition function for deposited colloids (−), Sd is the concentration ofdeposited colloids in the column (Nc M− 1), and Kdet isthe first-order detachment rate coefficient (T− 1).
A simple and flexible form for ψs is used in the model to account for time and depth-dependent deposition
behavior as (Bradford et al., 2003):
ws ¼




Sd
d50 þ z b
1
d50
Smax

4.1. Tracer experiments
Breakthrough curves for the conservative tracer under both saturated and unsaturated conditions were welldescribed by the classical ADE (Eq. (1)). Fig. 2 shows
an observed and ADE-simulated nitrate breakthroughcurve in 3550 sand at 50% water saturation. Other nitrate breakthrough curves for unsaturated systems gave
similar results. Tables 1 and 2 report the value of dispersivity obtained by fitting the experimental data with
the HYDRUS-1D model. The dispersivity values

ð3Þ

where d50 is the median grain size of the porous medium(L), β is a parameter that accounts for the spatial
distribution of retained colloids (−), Smax is the maximum
concentration of deposited colloids (Nc M− 1), and z is thedown gradient distance from the porous medium inlet (L).
The first term on the right hand side of this equation isused to account for time-dependent deposition in amanner similar to Langmuirian blocking (Adamczyk
et al., 1994). When the value of Smax is large then this term
approaches a value of 1 and time-dependent deposition
behavior becomes irrelevant. The second term on the righthand side of the above equation is used to describe depthdependent deposition behavior; i.e., hyper-exponential
profiles with decreasing deposition rates with increasing

Fig. 2. Measured (symbols) and fitted (lines) breakthrough curves of
the tracer (NaNO3) in an experiment carried out in 3550 sand at 50%
water saturation.

S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127
Table 2
Experimental conditions for column experiments in MIX sand (Li, Mi,
and Hi stand for low, medium, and high ionic strength)
Exp.

Li100
Mi100
Hi100
Li80
Mi80
Hi80
Li60
Mi60

Saturation Ionic Average water Dispersivity
Pulse
strength
velocity(cm)
duration(mM)(cm/min)(pore volume)
100
100
100
80
80
80
60
60

6
30
60
6
30
60
6
30

0.28
0.39
0.56
0.35
0.35
0.35
0.23
0.23

0.1
0.1
0.1
0.22
0.22
0.22
0.5
0.5

3.8
2.7
5.4
3.3
3.0
4.2
3.5
2.8

119

strength. For each water content and sand combination,
increasing the ionic strength resulted in lower peak effluent concentrations, indicating greater retention ofcolloids.
The breakthrough curves shown in Fig. 4 (a–c)
obtained in the experiments conducted with 3550 sandand ionic strength of 60 mM indicate that average water velocity also has a significant effect on the colloid
retention. The mass recovery in the effluent decreased
from 52% to 23% when the average water velocity
decreased from 0.87 to 0.35 cm/min, as shown in
Tables 3 and 4. All of the breakthrough curves forcolloids exhibited an increasing trend: i.e. during theperiod of continued colloid addition, the effluent
concentration increased with time. This suggests theincrease with decreasing water content similar to what
has been reported in the literature (Toride et al., 2003).
Fig. 2 also demonstrates that the tracer exhibits small
amounts of tailing in the declining limb of the breakthrough curve under unsaturated conditions. Similar,
breakthrough tailing behavior has also been reported inliterature (Padilla et al., 1999; Toride et al., 2003), and isbelieved to occur as a result of immobile regions(inaccessible to flow) existing in unsaturated porous
media. Although the physical non-equilibrium model,
which accounts for both mobile and immobile regions,can provide a superior description to the tracer breakthrough curve than the simple advection–dispersion
model (Cherrey et al., 2003), we decided to utilize theADE model to be consistent with subsequent colloidtransport modeling. We do believe, however, that
immobile regions may play an important role on colloidtransport and this will be discussed in greater detail lateron in the paper.
4.2. Colloid transport
Figs. 3–5 present measured and fitted breakthroughcurves for column experiments conducted with varying
water contents and solution ionic strengths in 3550
(Figs. 3a–b and 4a–c) and MIX (Fig. 5a–c) sands,
respectively. In these figures the normalized effluent
concentration is plotted versus the number of pore volumes passed through the column. After approximately 1pore volume, the injected colloids break through thecolumn and are detected in the effluent. The influent was
switched to a colloid-free solution after a given numberof pore volumes listed in Tables 1 and 2. For both sands,
lower water contents tended to result in lower peakeffluent concentrations and greater colloid retention (seeFigs. 3a–b, 4a–c, 5a–c, and Tables 3 and 4). However,this effect was more pronounced with increasing ionicFig. 3. Observed and simulated breakthrough curves of colloids forvarious saturation levels in 3550 sand at an ionic strength of 6 mM (a)and 30 mM (b).

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S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

Figs. 6a–d and 7a–b present the observed andsimulated colloid deposition profiles at various water
saturation levels and IS in 3550 (Fig. 6a–d) and MIX

Fig. 4. Observed and simulated breakthrough curves of colloids forvarious saturation levels in 3550 sand at an ionic strength of 60 mM.
The average water velocity was approximately the same in saturated
and unsaturated conditions.

filling of deposition sites occurred with time. The
apparent tailing behavior of the breakthrough curves
implies a low detachment rate of retained colloids.

Fig. 5. Observed and simulated breakthrough curves of colloids forvarious saturation levels in MIX sand at an ionic strength of 6 mM (a),30 mM (b), and 60 mM (c).

S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127
Table 3Fitted model parameters in 3550 sand and various solution ionicstrengths
Smax⁎
(g­1)

Kd
(min­1)

Kdet(min­1)

ME

MS

MT

R2

Li100
0.03
Mi100
0.65
Hi100Hv 1.8
Hi100Mv 3.6
Hi100Lv
5.5
Li70
0.07
Mi70
0.74
Hi70
2.5
Li50
0.1
Mi50
1.3
Hi50
8.4
Li40
0.16
Mi40
1.8
Hi40
12

0.01
0.019
0.1
0.16
0.26
0.015
0.084
0.17
0.02
0.1
0.39
0.024
0.13
0.6

0.004
0.00240.001
0.00080.00050.003
0.004
0.00080.00240.003
0.000630.002
0.00080.0002

98
87.6
53
32
23
97
78
54
93
66
22
87
38
1.5

N.m a
11.7
52
55
67
N.m
20
44
N.m
22
75
N.m
61
86

N98
99.3
105
87
90
N97
98
98
N93
88
97
N87
99
87.5

98
99
97
97
98
97
96
97
94
96
97
97
96
95

Exp.

Also included in this table are the effluent (ME), sand (MS), and the total(MT) mass percentage recovered for the experimental systems and thecoefficient of linear regression. The parameter Smax⁎ =Smax/Nic; where
Nic in the number of colloids in a unit volume of influent suspension.
aN.m: Not measured.

(Fig. 7a–b) sands, respectively. The data are presented
here as normalized concentration (number of colloids
recovered in the sand, Nc, divided by the total number ofcolloids injected into the column, Nct) per gram of dry
sand and are plotted as a function of distance from thecolumn inlet. The data indicate that the highest retention
occurred near to the column inlet and that the profile
shape was hyper-exponential with depth.
Consistent with the breakthrough curves, Tables 3 and4 indicates that the percent recovery of colloids in thesands enhanced with decreasing water content and increasing ionic strength. The total percent recovery for colloids
in the effluent and sands ranged from 87–105% (Tables 3
and 4). This signifies that most of retained colloids in thecolumn were recovered — either by elution or simply
resuspension of the sand after the column experiments.

121

more pronounced in higher ionic strength solutions. The
values of Kdet in Tables 3 and 4 were typically several
orders of magnitude lower than Kd. It can also be observed in Figs. 6a–d and 7a–b that this model predicted
the deposition profile behavior reasonably well.
4.4. Batch experiments and DLVO calculations
Batch experiments were conducted to determine thepotential for colloid attachment to the sand without the
influence of pore structure. These experiments were conducted under a range of selected experimental conditions(20 °C, pH = 10, ionic strength = 6, 30, and 60 mM), andwere consistent with unfavorable conditions for attachment. The difference between the initial and final concentrations of colloids in solution was less than 1%. Thissuggests that the presence of any chemical heterogeneity
on the quartz sands had negligible effect on irreversible
colloid attachment.
To better understand the chemical interactions between
colloids and the SWI the total interaction energy wascalculated using the classic Derjaguin–Landau–Verwey–
Overbeek (DVLO) theory (Derjaguin, 1954). In this case,the total interaction energy consists of the sum of
attractive van der Waals (Gregory, 1981) and repulsive
electrostatic (Hogg et al., 1966) interactions, and wasapproximated as a sphere-plate interaction. Zeta potential
values were used in the place of surface potential values inthe DLVO calculations, and the Hamaker constant for the
carboxylate-modified latex (CML) colloids–water–sandsystem was set equal to 4.04 × 10− 21 (Bergendahl andGrasso, 1999). As noted earlier, the measured zeta
potential of the colloids becomes less negative withincreasing ionic strength which is due to compression of
the electrostatic double layer. The same behavior is likely
for both the AWI and SWI; however for purposes ofTable 4Fitted model parameters in MIX sand and various solution ionic strengths

4.3. Application of HYDRUS-1D model

Exp.

Smax⁎
(g­1)

Kd
(min­1)

Kdet(min­1)

ME

MS

MT

R2

To quantitatively compare the experiments, breakthrough and deposition data were simulated by fittingwith the solutions of Eqs. (1) and (2). Tables 3 and 4
summarize the fitted parameters and R2 values for allcolumn experiments. Application of the transport anddeposition model produced a good fit to the breakthrough data with R2 values close to one as seen in
Tables 3 and 4 for all of the experiments conducted. For
both sand sizes, the values of Kd and Smax increased
with ionic strength. The same behavior for Kd and Smax
was observed for decreasing water content but it was

Li100
Mi100
Hi100
Li80
Mi80
Hi80
Li60
Mi60

0.075
0.78
5
0.08
1.5
11
0.09
2.7

0.024
0.042
0.29
0.027
0.1
0.4
0.035
0.26

0.003
0.002
0.00060.003
0.00120.0004
0.002
0.001

92
77.6
25
91
49
5
86
9

N.m a
19.2
63
N.m
55
82
N.m
94

N92
96.8
88
N91
104
87
N86
103

92
97
93
94
98
97
98
96

Also included in this table are the effluent (ME), sand (MS), and the total(MT) mass percentage recovered for the experimental systems and thecoefficient of linear regression. The parameter Smax⁎ =Smax/Nic; where
Nic in the number of colloids in a unit volume of influent suspension.
aN.m: Not measured.

122

S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

Fig. 6. Observed and simulated deposition profiles of colloids for various saturation levels in 3550 sand at an ionic strength of 30 mM (a) and 60 mM(b–d). The average water velocity was the same in saturated and unsaturated conditions in experiments conducted at an ionic strength of 60 mM.

DLVO calculations, we assumed these values to beconstant over the range of ionic strengths. Fig. 8 presents
the total interaction energy between the colloids andquartz surface upon close approach over the range ofsolution chemistry conditions tested in transport experiments. These calculations indicate the presence of asignificant energy barrier to attachment in the primaryenergy minimum and a shallow secondary energy
minimum at greater distance from the SWI. The depthof the secondary energy minimum increases with ionicstrength ranging from 0.3 kT at 6 mM to 2.9 kT at 60 mM,
with corresponding separation distances of 46 to 10 nm,
respectively. Note that k is the Boltzmann constant and T
is the temperature in degrees Kelvin. These DLVO
calculations corroborate with the batch experiment finding that there is a negligible amount of colloid adsorption
to sand particles.
Similar DLVO calculations were also made to predict
the interaction energy between the CML colloids andthe AWI. As noted earlier, the zeta potential of thecolloids and the AWI is negative resulting in a repulsive
electrostatic interaction between the colloids and AWI.
In contrast with the SWI, the value of the Hamaker
constant for the AWI-CML colloids–water system isnegative (− 1.2 × 10− 20 J; e.g. see Israelachvili, 1992)
leading to a repulsive van der Waals interaction for thesecolloids as they approach the AWI. Hence, colloid
attachment to the AWI is predicted to be even lessfavorable for the AWI than for the SWI.
4.5. Implications for colloid transport and retention
Experimental evidence in this study has demonstrated that attachment to the SWI is not the dominantmechanism responsible for colloid retention. The firstpiece of indirect evidence is the batch experiments
which found no significant colloid attachment to thesand. Additionally, the experimental protocol for

S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

123barrier against colloid attachment. Finally, the colloid
deposition profiles resulting from the column experiments were not consistent with first-order attachment–
detachment model predictions. Specifically, the value ofβ (Eq. (3)) was greater than zero, indicating depthdependent deposition rather than first-order attachment.
Non-exponential deposition profiles under saturated
conditions have been attributed to charge variability ofthe porous medium (Johnson and Elimelech, 1995),
heterogeneity in colloid surface charge characteristics(Bolster et al., 1999; Li et al., 2004), and deposition ofcolloids in a secondary energy minimum (Redman et al.,
2004; Tufenkji and Elimelech, 2005b). These factors
may be involved; however, these mechanisms cannot
fully explain the experimental data presented in thispaper. The experiments were conducted in a solution at a
pH 10, which should minimize any effect of charge
heterogeneity on the sand surface because the isoelectric points of most metal oxides fall below this pH(Elimelech et al., 2000). The results of our batch
experiments do not support the existence of any significant heterogeneity on the grain or colloid surfaces.
Furthermore, the colloids may be held in secondary
minima; however, this cannot explain the observed
depth- and grain size-dependent deposition. Therefore,
another retention mechanism must also be involved.
Retention of colloids under unsaturated conditions
has also been attributed to partitioning at the AWI and/or
film straining (e.g. Wan and Wilson 1994a; Wan andTokunaga 1997; Lenhart and Saiers, 2002; Saiers andLenhart, 2003a). However, attachment to the AWI is notbelieved to play a significant role in the reported unsaturated experiments, as both the AWI and colloids

Fig. 7. Observed and simulated deposition profiles of colloids forvarious saturation levels in MIX sand at an ionic strength of 30 mM (a)and 60 mM (b).

determining the deposition profiles was based upon the
rapid release of colloids into solutions, and the highrecoveries were not consistent with the low detachment
rates that were observed in the column experiments. If
the colloids were irreversibly attached to the SWI, theyshould have remained on the grain surface even aftersuspending the sand in the same solution that was used
for the transport experiments. The next piece ofevidence is the fact that colloid retention occurred in
the column, even under conditions when DLVO
calculations indicate the presence of a substantial energy

Fig. 8. Calculated DLVO interaction energies for 1.1 μm CML colloids
as a function of separation distance and ionic strength (indicated next
to each curve). Interaction energies were calculated using the zeta
potentials in the place of surface potentials. The Hamaker constant forthe colloid–water–sand media was assumed to be 4.04 × 10− 21 J
(Bergendahl and Grasso, 1999).

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S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

were negatively charged even in the highest ionicstrength solution (see Table 2) and the van der Waals
interaction was repulsive. It has been well documented
that hydrophilic-negatively charged colloids are unlikely to attach to the negatively charged AWI (e.g. Wan
and Tokunaga 2002; Crist et al., 2004, 2005; Torkzaban
et al., 2006a, 2006b). Torkzaban et al. (2006a)
investigated viral transport under a range of water saturation levels at pH 9 and reported no retention of viruses in the unsaturated columns. Crist et al. (2004,
2005) visually demonstrated that hydrophilic latex colloids did not adsorb on the AWI using a real-time porescale microscopic method.
It is also unlikely that film straining plays a majorrole in the reported colloid retention as the l.1 μm latex
colloids are too large to be bound within a thin film.
These thin water films have calculated thicknesses
around 50 nm during steady-state water flow over anorder of magnitude thinner than the diameter of thecolloids used in this study (Zevi et al., 2005). Moreover,film straining is theoretically independent of solution
ionic strength and flow velocity (Wan and Tokunaga,
1997). In contrast, notably more colloid retention isobserved in higher ionic strength solutions and for lower
water velocities.
Straining of colloids provides a plausible explanationand mechanism for the observed colloid deposition behavior. Strained colloids become trapped in the smallest
regions of the pore space where the flow velocity is
reduced. These nearly immobile regions (Patzek andSilin, 2001; Patzek and Kristensen, 2001) include thesmall pore spaces formed at grain-to-grain contacts,
dead-end pores, and the three-phase contact line of thesolid–water–air interface (in case of unsaturated conditions). Fluorescent microscopy and X-ray microtomography studies have demonstrated that colloids
accumulate in the narrow region of the pore spaces
near the contacts of irregularly shaped sand grains underunfavorable attachment conditions (Bradford et al.,2005, 2006a; Xu et al., 2006; Li et al., 2006; Yoon et al.,2006). In these studies, pore-space constrictions apparently served as locations for colloid retention bystraining, whereas few colloids appeared to be immobilized far from the grain-to-grain contacts. Colloid
retention in the pore network is further supported by
Hoek and Agarwal (2006) who reported that DLVO
forces act on colloids up to 5 times more in small porespaces (surface roughness) than with a single flat surface. Straining, as the mechanism of colloid retention, isalso supported by mass balance calculations and the factthat once the sand is resuspended in the solution and thepore structure eliminated, the colloids return to solution.

Straining has recently been demonstrated to be a strong
function of DLVO and hydrodynamic forces (Bradford
et al., 2006a; Bradford et al., 2007). Colloids that are
weakly associated with the SWI via the secondary energy
minima experience significant hydrodynamic forces (e.g.
fluid drag, lift forces) due to fluid flow. The shear force
acting on the colloid surface held in the secondary energy
minimum is different than that acting on the colloid
surface in the bulk fluid. Consequently, at close range to
the SWI the colloids experience a combination of forces(hydrodynamic forces, electrical double-layer repulsion,and London-van der Waals) that creates a torque andhence rotation on the surface. (Cushing and Lawler 1998;
Bergendahl and Grasso 2000). It has been proposed thatweakly associated colloids with the SWI via thesecondary energy minimum can be translated and/or
funneled by these fluid drag forces to low velocity regionsof the pore structure or “straining sites” (Bradford et al.,2007). Indeed, recent experimental evidence by Kuznar
and Elimelech (2007) demonstrates that colloids captured
in the secondary energy minimum can be translated along
the collector surface via hydrodynamic forces and beretained in low velocity regions. Based on this argument,
more colloids will be retained in a secondary energy
minimum as the ionic strength is increased and thesecolloids will subsequently be funneled to straining sites.
The coupled effects of DLVO and hydrodynamic
forces on straining also can explain the observed decrease in colloid retention with increasing fluid velocity.
In this case, enhanced hydrodynamic forces may overcome the electrostatic and van der Waals interactions
and detach colloids from the grain surface, and thereby
minimize the amount of straining. It is also likely thatthe extent of relatively stagnation regions decreases as
the water velocity increases (Patzek and Silin, 2001;
Patzek and Kristensen, 2001). This is consistent with
our observations and modeling results presented by
Cushing and Lawler (1998). In contrast with the column
experiments, there is no pore structure in the batch
experiments. Therefore, the hydrodynamic shear forces
as the result of rotation prevented colloid attachment tothe sand grains in the batch experiments.
It was anticipated that the magnitude of straining
would be enhanced with decreasing sand size and water
saturation level due to greater amount of low velocity
regions. Both of these expected trends were verified byour experimental observations. The extent of retentionof colloids increased with ionic strength and decreasing soil grain size for all of the various saturationlevels tested. This is especially true for the higher
ionic strength conditions (Fig. 5b–c) where very little
breakthrough of colloids occurred. Comparison of the

S. Torkzaban et al. / Journal of Contaminant Hydrology 96 (2008) 113–127

breakthrough curves for all of the ionic strength conditions reveals a decrease in peak effluent concentrations with water content. All these results provide
substantial direct and indirect evidence that straining is
an important removal mechanism for the CML colloids
in the Ottawa sands investigated.
The comparison of experimental and modeled results
also suggests that straining is the underlying mechanism
in colloid deposition in both the saturated and unsaturated systems tested. The concentration of retained
colloids enumerated after the column experiments wasfound to exhibit a hyper-exponential spatial distribution
through the length of the column. This indicates thedeposition coefficient was depth-dependent, a trend thathas previously been associated with straining (e.g.,Bradford et al., 2002, 2003, 2006b).
5. Conclusions
Experimental and theoretical studies were conducted todetermine the role of solution chemistry and water content
on colloid retention under unfavorable attachment conditions. To better understand the underlying mechanism on
colloid retention, the experimental conditions wereselected to minimize the potential for colloid attachment(solution pH of 10, quartz sands, and highly negatively
charged colloids that were hydrophilic). DLVO calculations, mass balance information, and batch experiments
confirmed our assumption that attachment to the SWI and
AWI was not the dominant mechanism in colloid
retention. All the observations discussed above provide
convincing evidence that straining was the primarymechanism of colloid retention in our column experiments. The straining rate in a given porous medium isapparently a complicated mechanism, coupled with suchparameters as pore size distribution, hydrodynamics,
solution chemistry and water content. Specific findings
are highlighted below.
• Straining increases in magnitude with increasingionic strength due to an increased force (secondary
energy minimum) and number of colloids that are
funneled to and retained in small pores formed
adjacent to grain–grain junctions.
• Straining increases in magnitude with decreasingwater content due to an increase in the extent of
stagnant regions of flow within the pore medium.
• Increasing the flow rate of a system tends to decrease
the amount of straining of colloids as a result of
the increased fluid drag force that acts on weaklyattached colloids on the SWI and also decreased flow
stagnation regions.

125• The shape of the colloid deposition profile is highly
sensitive to the physical (grain size, water content,
and flow rate) and chemical (solution IS and pH)
properties of a system due to the interrelation of theseparameters on colloid straining.
Additional research is required to better understandand quantify the coupling of physical and chemical
processes that influence colloid straining in saturated
and unsaturated porous media. This information isbelieved to be essential for predicting colloid transportand fate in many natural environments.
Acknowledgments
We would like to acknowledge the technical assistance and support provided by Hugo Galdamez. This
research was supported in part by the grants from the
EPA (IAG # DW-12-92189901-0) and the USDACSREES (NRI #:2006-02541).
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