Bacteria Transport and DeposiƟon under
Unsaturated Flow CondiƟons: The Role of Water
Content and Bacteria Surface Hydrophobicity

O

R

G. Gargiulo, S. A. Bradford,* J. Simunek, P. Ustohal, H. Vereecken, and E. Klumpp

Column experiments were conducted to inves gate the transport and deposi on behavior of representa ve hydrophobic and hydrophilic bacteria strains in sand at diﬀerent water satura ons. These strains are similar in surface charge,
shape, and size, and diﬀer primarily in their surface hydrophobicity and tendency to form aggregates. The amount ofbacteria that were retained in the sand increased with decreasing water satura on, especially for the more hydrophobicstrain that formed larger cell aggregates. Most of the cells were retained close to the column inlet, and the rate of deposi on rapidly decreased with depth. The experimental data were analyzed using a mathema cal model that accounted
for deposi on on two kine c sites. Considera on of depth-dependent deposi on in the model formula on significantly
improved the descrip on of the data, and the amount of cell reten on was typically dominated by this site. The depthdependent deposi on coeﬃcient tended to increase with decreasing water content, especially for the hydrophobic
bacteria. Straining is believed to account for these observa ons because it increases in magnitude with increasing celland aggregate size and when a greater frac on of the water flows through a larger number of small pore spaces withdecreasing water content. Cell reten on on the other kine c deposi on site was well described using a conven onal
model for a achment and detachment. Consistent with interac on energy calcula ons for bacteria a achment, however, low amounts of cell reten on occurred on this site. A empts to separately determine the amounts of a achment
to solid–water and air–water interfaces were confounded by the influence of straining.
A: DLVO, Derjaguin–Landau–Verwey–Overbeek; EC, electrical conductivity; MATH, microbial adhesion to hydrocarbon; PBS,
phosphate buﬀer saline; TOC, total organic carbon.

Aof the transport and fate of bacteria in subsurface environments is needed for many practicalscenarios. An understanding of bacteria migration, for example, isused to assess the risk that pathogenic microorganisms pose to water
resources (Ginn et al., 2002), to develop eﬃcient water treatment
methods (Tufenkji et al., 2002; Ray et al., 2002; Weiss et al., 2005),
and to design bioremediation strategies for hazardous waste sites(Mishra et al., 2001; Vidali, 2001). Mobile colloids, such as bacteria,
can also facilitate the transport of a wide variety of inorganic andorganic contaminants that can adsorb onto these high surface area
particles (Kim et al., 2003; Šimůnek et al., 2006).
Considerable research has been devoted to the fate and transport of microbes and other colloids in porous media (see reviewsin Schijven and Hassanizadeh, 2000; Harvey and Harms, 2002;
G. Gargiulo, P. Ustohal, H. Vereecken, and E. Klumpp, Agrosphere(ICG-IV), Ins tute of Chemistry and Dynamics of the Geosphere (ICG),
Forschungszentrum Jülich GmbH D-52425, Jülich, Germany; S.A. Bradford, USDA-ARS, US Salinity Lab., 450 W. Big Springs Rd., Riverside, CA
92507-4617; J. Simunek, Dep. of Environmental Sciences, Univ. of California, Riverside, CA 92521. Received 3 Apr. 2007. *Corresponding author(sbradford@ussl.ars.usda.gov).
Vadose Zone J. 7:406–419
doi:10.2136/vzj2007.0068© Soil Science Society of America
677 S. Segoe Rd. Madison, WI 53711 USA.
All rights reserved. No part of this periodical may be reproduced ortransmi ed in any form or by any means, electronic or mechanical,
including photocopying, recording, or any informa on storage andretrieval system, without permission in wri ng from the publisher.

www.vadosezonejournal.org · Vol. 7, No. 2, May 2008406

Jin and Flury, 2002; Ginn et al., 2002; de Jonge et al., 2004).
Microbe deposition in unsaturated porous media has typically
been assumed to be dominated by attachment to the solid–water
and/or air–water interfaces. Attachment involves mass transportof colloids to a particular interface and deposition via chemicalinteractions (Elimelech and O’Melia, 1990). Hence, attachment
depends on the microbe’s aﬃnity for and accessibility to thisinterface, as well as the magnitude of the area.
Previous colloid transport studies conducted under unsaturated conditions have highlighted the role of moisture content andcolloid hydrophobicity on the transport behavior (e.g., Powelson
et al., 1990; Wan et al., 1994; Schaefer et al., 1998; Jewett etal., 1999; Chu et al., 2001; Sirivithayapakorn and Keller, 2003;
Keller and Sirivithayapakorn, 2004; Auset et al., 2005; Crist et al.,2005; Chen and Flury, 2005). Enhanced bacteria retention has
been reported for decreasing water saturation (Wan et al., 1994;
Schaefer et al., 1998; Jewett et al., 1999) and has been attributed
to attachment at the air–water interface, which increases in magnitude with decreasing water saturation. Bacteria hydrophobicity
has also been observed to play an important role in deposition in
unsaturated systems. Wan et al. (1994) and Schaefer et al. (1998)
reported that for comparable experimental conditions, eﬄuent
concentrations decreased for a hydrophobic bacteria strain compared with hydrophilic bacteria. This enhanced retention of thehydrophobic bacteria has been attributed to greater attachment at
the air–water interface that was controlled by long-range hydrophobic interactions.
Recent research ﬁndings, however, do not always support
the concept of bacteria attachment to the air–water interface.

For example, Wan and Tokunaga (2002) demonstrated in bubble
column experiments that only positively charged particles
attached to the negatively charged air–water interface. Column
transport experiments conducted under carefully controlled conditions of solid and/or aqueous phase chemistry have indicatedthat enhanced retention of colloids in unsaturated systems is
unlikely to be due to attachment at the air–water interface (Chuet al., 2001; Chen and Flury, 2005).
Models of attachment to the solid–water and air–water interfaces have traditionally assumed a constant ﬁrst-order deposition
term, which predicts an exponential spatial distribution of retained
colloids with distance (e.g., Yao et al., 1971; Logan et al., 1995;
Tufenkji and Elimelech, 2004a). Under unfavorable attachment
conditions (when repulsive electrostatic interactions exist between
the colloids and a porous medium), however, retained colloids insaturated porous media frequently do not exhibit an exponential
distribution with depth, and the deposition rate has been found to
be depth dependent (Albinger et al., 1994; Baygents et al., 1998;
Simoni et al., 1998; Bolster et al., 2000; DeFlaun et al., 1997;
Zhang et al., 2001; Redman et al., 2001; Bradford et al., 2002,
2006b; Li et al., 2004; Bradford and Bettahar, 2005; Tong et al.,2005a,b). A variety of chemical and physical explanations havebeen proposed in the literature to account for these observations(Tan et al., 1994; Liu et al., 1995; Johnson and Elimelech, 1995;
Kretzschmar et al., 1997; Cushing and Lawler, 1998; Bolster etal., 1999; Redman et al., 2001, 2004; Bradford et al., 2002, 2003,
2004, 2005; Tufenkji et al. 2003, 2004; Li et al. 2004, 2005; Hahn
et al., 2004; Tufenkji and Elimelech, 2004b, 2005a,b; Bradford
and Bettahar, 2005).
Colloid retention in porous media may occur by otherprocesses than attachment on a single solid–water or air–waterinterface, which provides one plausible explanation for nonexponential deposition proﬁles (Bradford et al., 2002). In saturated
systems, retention of colloids at two or more bounding solid–
water interfaces has been referred to as straining (Hill, 1957;
Cushing and Lawler, 1998). When multiple colloids collide andare retained in a pore constriction, this process has also beenreferred to as straining (Herzig et al., 1970). Other related colloid retention mechanisms may occur in unsaturated systems.
Film straining refers to retention of colloids in thin water ﬁlms
that are smaller than the colloid diameter (Wan and Tokunaga,
1997), and colloids may also be retained at the solid–water–air
triple point (Crist et al., 2004, 2005; Chen and Flury, 2005) inmuch the same way as straining at grain-to-grain contact points.
Straining, ﬁlm straining, and retention at the triple point sharemany similarities in that they all involve colloid retention at multiple interfaces and in low-velocity regions of the porous media.
In this work, we use a general deﬁnition of straining as colloid
retention in the smallest regions of the pore space to encompass
all of these retention processes (McDowell-Boyer et al., 1986;
Bradford and Torkzaban, 2008). It should be mentioned that
small pore spaces such as those formed at grain–grain and solid–
air–water contact points provide optimum locations for colloids
that are weakly associated with the solid phase to be retained
because of reduced ﬂuid drag and size limitations (Bradford and
Torkzaban, 2008).
Straining processes have only recently begun to receive
research attention, and many questions have yet to be resolved.
Straining processes, for example, have traditionally been assumed
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008

to be purely physical phenomena (Herzig et al., 1970; McDowellBoyer et al., 1986) and therefore only determined by geometry
considerations. Recent experimental evidence, however, indicatesa strong coupling of straining processes on solution chemistry
and hydrodynamics (Bradford et al., 2006a, 2007). The potential
inﬂuence of colloid hydrophobicity on straining behavior has not
yet been studied. Attractive hydrophobic forces between colloids,
however, may result in the formation of aggregates that can subsequently be strained (Crist et al., 2005). Temporal changes in the
air–water interfacial area have also been reported to produce colloid aggregates (Sirivithayapakorn and Keller, 2003). Furthermore,
the average size of water-ﬁlled pores and the thickness of waterﬁlms decrease with decreasing water saturation. Hence, underunsaturated conditions a greater fraction of the mobile colloids
will be transported through regions of the pore space where straining processes may occur. Straining is therefore expected to increase
with decreasing water saturation (Gargiulo et al., 2007).
Previous research has provided little data on bacteria retention with depth under unsaturated conditions and for diﬀerent
surface hydrophobicity of the bacteria. Unsaturated colloidtransport studies reported in the literature also have typicallynot considered straining as a deposition mechanism. The objective of this research thus was to study the unsaturated transportand deposition behavior of representative hydrophilic and hydrophobic bacteria strains. For each experiment, the breakthroughcurves and deposition proﬁles were measured. The experimental
data was simulated using a two-site kinetic deposition model that
accounts for time- and depth-dependent deposition processes.
Fitted model parameters were used to help deduce mechanisms
controlling unsaturated bacteria transport, as well as diﬀerences
due to surface hydrophobicity.

Materials and Methods
Bacteria

Representative hydrophilic (Deinococcus radiodurans) andhydrophobic (Rhodococcus rhodochrous) bacterial strains in thestationary growth phase were used in the unsaturated transport
experiments. Deinococcus radiodurans (DSMZ 20539) is a Grampositive, nonmotile, nonspore-forming, spherical bacterium(1.0–1.5 μm diam.). It belongs to the family of Deinococcaceae,
which includes widespread soil organisms with an extraordinary
ability to survive in dry, nutrient-poor environments. This bacteria
strain is known to tolerate DNA-damaging agents like ionizing
radiation (Mattimore and Battista, 1996). Rhodococcus rhodochrous(DSMZ 11097) is a Gram-positive spherical bacterium (1 μm
diam.). This strain was isolated from soil contaminated with alkenes by Kästner (1989). Rhodococci are aerobic, Gram-positive
actinomycetes that exhibit a diverse range of metabolic activities.
Rhodococci have the ability to degrade hydrocarbon chains and avariety of organic compounds, including xenobiotic compounds
like polychlorinated biphenyls and benzothiophene. Both bacteria
strains were grown on agar plates consisting of ATCC medium
220, CASO agar, peptone from casein (15.0 g), peptone fromsoy meal (5.0 g), NaCl (5.0 g), agar (15.0 g), and distilled water(1 L). For column experiments, both bacterial strains were cultivated at 30°C in a nutrient broth that was agitated at 13.6 rads−1 using a shaker. The growth media for D. radiodurans consisted of casein peptone, tryptic digest (10.0 g), yeast extract (5.0407g), glucose (5.0 g), NaCl (5.0 g), and distilled water (1 L). The
media for R. rhodochrous consisted of mineral medium, Na2HPO4(2.44 g), KH2PO4 (1.52 g), (NH4)2SO4 (0.50 g), MgSO4 × 7
H2O (0.20 g), CaCl2 × 2 H2O (0.05 g), trace element solution(10 mL), glucose (5.0 g), and distilled water (1 L). The bacteria
cells were harvested from the media in the late stationary phaseby gentle centrifugation (10 min, 7100 times gravity, 25°C) andresuspended in phosphate buﬀer saline (PBS) 10−4 M, pH = 7.
In this phase, the substrate had been consumed, the cell culture
stopped growing, and the cells had reached a resting mode. Sinceno substrate was available inside the sterile sand packing, the bacteria suspension was considered to have constant properties withrespect to the cell number, size, and surface properties during theexperiment.
Fluorescent dyes and epiﬂuorescent microscopy were used tovisualize the bacteria cells before and after the column transport
experiments and to determine the morphology of the bacteria
strains. The microscope consisted of a PC-supported ECLIPSE E
1000 (Nikon, Melville, NY) with a motorized and PC–controlled
three-axis cross table. The images were captured with a CCD
camera (DXC-9100 P, Sony, Köln, Germany) and a Matrox
Corona Framegrabber (Dorval, Quebec, Canada). The cross-table,
microscope, and image acquisition were controlled by LUCIA
32 4.11 software (Nikon, Germany). Our protocol was basedon that presented by Klauth et al. (2004). In brief, an aliquotof the sample was sonicated on ice for 1 min before incubation
with the dye (Sybr green). The sample was pipetted into a reactor(Poschen et al., 2002) containing 4 mL of PBS (pH 7). The liquidsample was ﬁltered through an Anodisc ﬁlter (Whatman, Kent,
UK, 0.2 μm, 25-mm diam.) by applying a vacuum of 13,000 Pa,
and the retained particles were washed twice with 4 mL of PBS
buﬀer (pH 7). After washing, the ﬁlter was coated with 1.5 mL of
25 μM Sybr green solution in PBS buﬀer (pH 7) and incubatedfor 15 min. Two washing steps were subsequently performed as
described above. The ﬁlter was mounted into a drop of immersion
oil on a microscope slide after drying, and a drop of immersion oil was put on the surface. A cover slip was used, and an
additional drop of immersion oil was put on the cover slip. The
sample was viewed under blue excitation light (Nikon B-2A, excitation 450–490 nm, dichroic mirror 505 nm, longpass 520 nm)
at 600-fold (in some cases, 450- or 1000-fold) magniﬁcation.
The hydrophobicity of D. radiodurans and R. rhodochrous wasquantiﬁed using the microbial adhesion to hydrocarbon (MATH)
approach (Rosenberg and Doyle, 1980, 1990). The test is basedon the determination of the relative equilibrium-partitioning
coeﬃcient between an aqueous (polar) and a hydrocarbon (nonpolar) phase (similar to the octanol-water partition coeﬃcient for
dissolved chemicals). The test was performed under the following
conditions. The microbial cultures were successively harvested at
diﬀerent growth stages by centrifugation (7100 times gravity, 10
min. and 25°C) and resuspended in a 10−1 M NaCl solution. A
glass test tube (10 mm diam.) was ﬁlled with 3 mL of the bacteria
suspension, and the optical density of the bacteria solution wasmeasured at 600 nm in a detector (Spectrophotometer DU800,
Beckman Coulter, Fullerton, CA). Next, 300 μL of n-hexadecane
was added to the suspension, and the glass tube was stirred for
2 min (Vortex-Genie 2, Bohemia, NY). When the phases in theglass tube were clearly separated, a sample of the aqueous phase
was carefully taken out of the tube with a sterile glass capillarywww.vadosezonejournal.org · Vol. 7, No. , May 2008

and the sample’s optical density at 600 nm was determined again.
The relative hydrophobicity Hr was then calculated from⎛ od ⎞[1]
H r = ⎜⎜1− f ⎟⎟⎟×100%⎜⎝
od i ⎠⎟
where odi denotes the optical density of the original suspension
and odf is the optical density of equilibrated aqueous phase afterpartitioning. This analysis was repeated three times per sample.
Electrophoretic mobilities of the two bacteria strains were
measured at 25°C using a suspension of 7 × 108 cells mL−1 (10−4
M PBS at pH = 7) using a Lazer Zee Meter (Model 501, Pen
Kem, Bedford Hills, NY) equipped with a video system. The zeta
potential was then calculated from the measured electrophoretic
mobility using the Smoluchowski equation.
Sand

Sterile fused silica sand (Teco-Sil, C-E Minerals Greenville,TN) was used as the porous medium in the column experiments.
The sand was treated with 33% peroxide to avoid any source oforganic material. The grain-size distribution of this sand was determined by sieve analysis. The median grain size and the coeﬃcientof uniformity of this sand were determined to be 567 μm and 1.87,
respectively. The van Genuchten (1980) water retention curve andhydraulic conductivity function parameters were determined frommultistep outﬂow data and inverse modeling (e.g., Hopmans etal., 2002). According to this approach, the porosity was 0.428, thesaturated hydraulic conductivity was 0.576 cm min−1, α (reciprocal of the air entry pressure) was 0.0234 cm−1, n (related to theslope of the retention curve at the inﬂection point) was 12.13, andl (exponent on the tortuosity portion of the relative permeability
model) was 3.617. The average pore radius of the water-ﬁlled sandwas determined from the water retention curve using Laplace’s
equation of capillarity to be 34.7, 33.8, and 30.8 μm at water
saturations of 100, 80, and 40%, respectively.
Column Experiments

Figure 1 presents a schematic of the experimental setupthat was used to produce steady-state, unit gradient (i.e., identical matrix potentials at the top and bottom of the column)
unsaturated ﬂow conditions with the selected sand and bacteria(harvested in the stationary growth phase). The experimental
column (8.0 cm diam.; 22.5 cm in length) was constructed from
Plexiglas and consisted of four ﬁlled sections (5 cm in length)and one empty section (2.5 cm in length) that were clamped
together. The bottom was formed by a porous stainless steel plate
covered with a membrane (polyester fabric, mesh size 15 μm).
The hydrophilic membrane was used to maintain capillary contact
with the water inside the column. Before the experiments, thepolyester fabric was tested to make sure that the bacteria were
not retained on the membrane and that the air entry pressure
was not exceeded.
The column was ﬁlled with dry sand by continuous free fallingthrough a tube equipped with two homogenizing screens. The tube
was slowly elevated during the ﬁlling procedure to keep a constantdistance of 10 cm from the rising sand surface. The column was
equipped with tensiometers (PMP 4070 pressure transducers, GE,
Munich, Germany) near the top, in the middle, and at the bottom of
the column. The tensiometers were inserted into the free gap between
the sand surface and the ﬁlling tube and were embedded by the408

falling sand. Because the tube had the same diameter as the column,
the sand was evenly distributed over the entire cross-section of thecolumn and resulted in compact and homogeneous packing. The
porosity of the packing was determined gravimetrically (CP12001S
digital balance, Sartorius, Goettingen, Germany).
At the top of the column, a sprinkling plate equipped with80 stainless steel needles was used to distribute the inﬂuent evenly
over the sand surface. The water and the solution were supplied
to the sprinkling plate using a piston pump (Ismatec Reglo CPF,
Ismatec Laboratoriumstechnik, Wertheim-Mondfeld, Germany;see Fig. 1). During unsaturated conditions, the air phase in thecolumn was maintained at atmospheric pressure by means of
two aeration openings. The suction at the bottom of the column
was adjusted to achieve unit gradient conditions by changing
the elevation of the drip point on the hanging water column.
Steady-state water ﬂow conditions were kept constant for theremainder of the transport experiment. The hydraulic propertiesof the homogeneous sand were assumed to be spatially invariant, and the measured capillary pressure was used as an indicatorof the local water content. The total column water content wascontinuously monitored gravimetrically using a digital balance(CP12001S, Sartorius). The constant ﬂow rate was measured
independently using a ﬂow meter (SF-591, softﬂow.de GmbH,
Gross Machnow, Germany) and a digital balance, and it was ﬁxed
to a value between 165 and 170 mL h−1 for each experiment (aDarcy velocity of 0.055 to 0.056 cm min−1).
The column bottom was connected with PVC tubes (2mm i.d.) to a conductivity probe, UV-Vis spectrophotometer,and ﬂuorescence detector (F1050, Merck–Hitachi, Darmstadt,
Germany), as illustrated in Fig. 1. Both the bacteria and the tracer
outﬂow concentrations were monitored on-line.
Diﬀerent saturation procedures were used to generate either
fully or partially saturated conditions in the column. For full water
saturation (100%), the column was completely evacuated using
a vacuum pump and subsequently ﬂushed from the top withdegassed buﬀer solution. For partial water saturation, the column
containing dry sand was slowly ﬁlled at a constant ﬂow rate supplied through the bottom. The latter procedure resulted in a water
saturation (approx. 80%) containing residual entrapped air bubbles.
Water saturation of 40% was obtained by gradually reducing theinﬂow rate at the top while at the same time as increasing the suction pressure at the bottom until unit gradient conditions wereachieved. The water saturation level and the uniformity in thecolumn were veriﬁed with the electronic balance readings and thetensiometer data at three locations. The sand in the column wasthen equilibrated by ﬂushing it with several pore volumes of PBS(pH = 7, 10−4 M). Note that PBS may potentially modify surface
charge characteristics when positive sites are present, such as on
metal oxide surfaces. The PBS concentration used in the column
experiments, however, was extremely low (10−4 M), and the sandwas rigorously cleaned, so we expect this level of PBS to have aminimal impact on the bacteria transport and retention behavior.
The transport of both a conservative tracer and the bacteriacell solution was investigated by applying a continuous injection of 3.2 pore volumes to the column. Unlike the conservative
tracer, the cell concentrations could not be adjusted to be identical for all the experiments but were approximately 4 to 5 ×
107 cells mL−1. The bacteria concentration in the outﬂow wasmonitored on-line every 20 s during the experiment using the
UV-Vis spectrophotometer (in the range between 350 and 750nm) and the ﬂuorescent detector (excitation 360 nm, emission
520 nm) (Hitachi–Merck f-1050) system discussed above and aﬂow-through vial. Bacteria concentrations were determined from
instrument response and calibration curves that were determinedover relevant experimental conditions.
The conservative tracer experiment was conducted using the
PBS solution as the resident and elution background solution,with demineralized water as the conservative tracer. The electricalconductivity (EC) of the column eﬄuent was measured using
a conductivity probe connected with a thermally compensatedconductometer. The measured diﬀerence in EC between the PBS
solution (high EC) and demineralized water (low EC) was used
to quantify the transport of the demineralized water pulse.
After completion of the transport experiment, the column
was rapidly frozen to avoid any water movement. To determine thebacteria retention proﬁle, the column was unclamped and a piston
was used to remove the frozen sand from the four sections. The
sand from each section was partitioned into two portions (?160 gof sand each) using a sharp knife. After the ice melted, each sample
was thoroughly mixed to achieve a homogeneous concentration
and was analyzed for total organic carbon (TOC) content. About
0.5 g of wet sand from each portion was used in solid-state TOC
analysis (RC-412 Multiphase Determinator, Leco, St. Joseph, MI).
The sand had been treated with a 33% hydrogen peroxide solution
before conducting the experiments to oxidize any possible organiccarbon contamination that would interfere with the TOC signal.
The amount of water in the sand (diﬀerence in wet and oven dried

F . 1. Schema c of the column experiment setup.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008409

sample) was subtracted from the total mass. The carbon concentration per gram of sand was related to the bacteria number pergram of sand using a linear calibration curve established between
TOC response and step-dilutions of a bacteria solution containing
known cell concentrations. The percentage of bacteria retained in
the sand was calculated from the sum of the bacteria number foundin each sand slice compared with the total number of bacteria
injected (determined with a Coulter counter).

ψ t = 1−

[4]

in which smax1 is the maximum solid phase concentration [Ncm−1] of retained bacteria cells on site 1. Under unsaturated conditions, attachment to the solid phase and the air–water interface
are lumped in the ka term of Eq. [3].
As mentioned above, measured colloid deposition proﬁles are
frequently not exponential with depth under unfavorable attachment conditions. A variety of physical and chemical explanations
have been proposed in the literature to account for observed nonexponential deposition proﬁles. Unfortunately, it is frequently
not possible to separate all the possible causes for this depthdependent deposition behavior. For simplicity, the second kinetic
site (site 2) lumps all depth-dependent mass transfer processes
from the aqueous to the solid phase as

Theory and Model
The HYDRUS-1D code (Šimůnek et al., 2005) is a ﬁnite
element model for simulating the one-dimensional movementof water, heat, and multiple solutes in variably saturated media.
The code numerically solves Richards’ equation for saturated–unsaturated water ﬂow and Fickian-based advection–dispersion
equations for solute transport in the liquid phase. The transport
equations also include provisions for nonlinear and/or nonequilibrium reactions between the solid and liquid phases. The code
may be used to analyze water and solute movement in unsaturated, partially saturated, or fully saturated porous media. The
governing ﬂow and transport equations are numerically solved
using the Galerkin ﬁnite element scheme. Integration in time isachieved using implicit (backward and Crank–Nicholson) ﬁnite
diﬀerence schemes. The code allows us to ﬁt model parameters tothe breakthrough curve and the retention proﬁle simultaneously
using a nonlinear least square optimization routine based on theLevenberg–Marquardt algorithm (Marquardt, 1963).
In this study, the bacteria transport was modeled using a
modiﬁed form of the advection–dispersion equation that includes
two kinetic deposition sites (e.g., Schijven and Simunek, 2002;
Bradford et al., 2003). This approach divides the retained bacteria
into two fractions (s1 + s2) and assumes diﬀerent rates or processes
occurring for each deposition site. The total bacteria mass balance
equation is deﬁned as

∂ s2
[5]
= θψ x k2c∂twhere k2 [T−1] is the deposition coeﬃcient on site 2, and ψx isthe dimensionless colloid retention function that accounts for
depth-dependent deposition asρb⎛ d + x − x 0 ⎞⎟−βψ x = ⎜⎜ c
[6]
⎟⎟
⎜⎝
dc
⎠⎟
where dc is the median diameter of the sand grains [L], x0 is thecoordinate [L] of the location where the depth-dependent deposition process starts (in this case, the surface of the soil proﬁle),and β is an empirical factor controlling the shape of the spatial
distribution. Bradford et al. (2003) found that a value of β =0.432 provided an optimum description of experiments in whichsigniﬁcant depth-dependent deposition occurred; we therefore ﬁx
β to this value in simulations discussed herein. Release of colloids
from site 2 was not needed in the analysis of the data discussed
below (detachment was found to play only a minor role), but isan available option in the HYDRUS-1D code.
The eﬄuent and deposition data presented below was simulated using the HYDRUS-1D computer code (Šimůnek et al.,2005) as described by Eq. [2–6]. In these simulations, the meanpore water velocity and dispersivity were obtained by ﬁtting
the solution of the advection dispersion equation for the tracer
breakthrough curve. The code allowed us to ﬁt simultaneously
the parameters ka, kd, k2, and smax1 while considering both the
breakthrough curve and the retention proﬁle in the parameter
optimization. To minimize the potential for nonunique parameter ﬁts, we used available information to limit the number ofparameters that were optimized in these simulations. Below subsequently refer to 1 site (s2 = 0) model ﬁts based on Eq. [2] and[3] with ψt = 1 and kd = 0 (i.e., without blocking and detachment) as the attachment model and with ψt ≤ 1 and kd > 0 (i.e.,with blocking of favorable deposition sites and detachment) as
the Langmuirian model. Model ﬁts based on Eq. [2–6] will bereferred to as the 2 site model.

∂θ c
∂s
∂s
∂ ⎜⎛
∂ c ⎞⎟ ∂ qc
+ ρb 1 + ρb 2 =
[2]
⎟−
⎜ θD
∂t
∂t
∂t
∂ x ⎝ ∂ x ⎠⎟ ∂ x
where θ is the volumetric water content, ρb is the soil bulk density[M L−3], t is the time [T], q is the ﬂow rate [L T−1], x is thespatial coordinate [L], D is the dispersion coeﬃcient [L2 T−1], c
is the bacteria concentration in the aqueous phase [Nc L−3, where
Nc is the number of bacteria cells], and s1 [Nc m−1] and s2 [Ncm−1] are the solid phase concentrations associated with deposition sites 1 and 2, respectively.
The ﬁrst kinetic site (site 1) employs the conventional attachment and detachment model to describe mass transfer between
the aqueous and solid phase as∂ s1= θψ t ka c − kd ρ b s1
[3]∂t
where ka is the ﬁrst-order attachment coeﬃcient [T−1], kd is theﬁrst-order detachment coeﬃcient [T−1], and ψt is a dimensionless colloid retention function that accounts for time-dependent
deposition. To simulate reductions in the time-dependent
deposition coeﬃcient due to the blocking or ﬁlling of favorable
deposition sites, ψt is sometimes assumed to decrease with increasing colloid mass retention. A Langmuirian dynamics (Adamczyk
et al., 1994) equation has been proposed for ψt to describe thisphenomenon asρbwww.vadosezonejournal.org · Vol. 7, No. , May 2008

s1
s max1Results and Discussion
Bacteria Hydrophobicity and Morphology

The MATH test measures the hydrophobicity of bacteria as
the percentage reduction of cells in the aqueous solution due to410partitioning at the hydrocarbon–water interface. The percentage hydrophobicity for the two bacteria strains was determinedat various stages of the bacteria growth curve. For R. rhodochrous,
the minimum value was 55% and the maximum was about 90%.
In contrast, the percentage hydrophobicity was much lower for
D. radiodurans and varied between 0 and 8%. The measured zeta
potential for R. rhodochrous and D. radiodurans was not statisticallydiﬀerent, with values of −47 ± 7 and −38 ± 5 mV, respectively.
Epiﬂuorescent microscopy was a useful technique to determine the shape and morphology of the bacteria during diﬀerent
stages of the growth curve. Figure 2A and 2B present photographsof log phase D. radiodurans and R. rhodochrous, respectively,
when suspended in 10−4 M PBS. The cell diameter of both D.
radiodurans and R. rhodochrous is approximately 1 μm, but thephotographs indicate that these cells may also form diﬀerentsized aggregates during the logarithmic growth phase. Deinococcus
radiodurans tend to form pairs and tetra-coccus–shaped aggregates of about 2 to 4 μm in diameter, whereas R. rhodochrous
exhibited variably sized three-dimensional aggregates that reached
the size of 10 to 15 μm. Since the zeta potential for these twobacterial strains was similar, diﬀerences in the size distributionof these bacteria and cell aggregates likely occurred as a result of
diﬀerent factors. The bacteria surface is covered with polymers
that can change with the growth phase and the availability ofnutrients (Sanin et al., 2003). The bacteria surface macromolecular composition plays an important role in the cell surfacehydrophobicity, adhesive properties, and in the formation of

aggregates (Sanin et al., 2003; Gargiulo et al., 2007). Colloid
stability and aggregation are also reported to be sensitive to thesurface hydrophobicity (Crist et al., 2005; Breiner et al., 2006);
that is, hydrophobic colloids are less stable than hydrophilic
colloids. van Oss (1994) has proposed a mechanistic model tocalculate hydrophobic interactions that is based on the Lewis
acid-base free energy of adhesion. Unfortunately, disagreement
about the origins of hydrophobic interactions still prevails (Tsaoet al., 1993, Yaminsky and Ninham, 1993; Rabinovich and Yoon,
1994; van Oss, 1994; Yoon and Ravishankar, 1996), and quantitative theory has not been generally accepted.
For the transport experiments discussed below, the bacteria
were harvested in the late stationary phase. Bacteria in the latestationary phase (also observed with the epiﬂuorescent microscope) showed decreased aggregation behavior compared with thelog phase bacteria shown in Fig. 2. Decreased hydrophobicity forbacteria in the stationary growth phase has also been observed
by other researchers (van Loosdrecht et al., 1987; Fontes et al.,
1991; Caccavo, 1999; Sanin et al., 2003). In the late stationary
phase, D. radiodurans occurred primarily as single cells, whereas
R. rhodochrous still exhibited large aggregates.

F . 3. (A) Measured and fi

ed breakthrough curves and (B) retenon profiles for Deinococcus radiodurans at 100% satura on.
Fi ed curves were obtained using the a achment model, the Langmuirian model, and the 2 site model. In Fig. 3A, 127 min is equal
to 1 pore volume. C/C0 = rela ve eﬄuent concentra on, where C0
is the influent concentra on of bacteria; Nt, number of bacteria
recovered in the sand; Ni, number in a unit volume of the input
bacterial suspension.

F . 2. Photograph of log phase (A) Deinococcus radiodurans and (B)Rhodococcus rhodochrous when suspended in 10-4 M phosphatebuﬀer saline. The photographs were taken using an epifluorescent
microscope.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008411

Transport Experiments

Each transport experiment was replicated twice. In general,
replicate experiments exhibited consistent transport and retention
behavior for given conditions (Table 1). The total mass balance forthe bacteria in the transport experiments was very good, ranging
from 88 to 104%. Hence, mass balance information and replicate data suggests a high level of conﬁdence in the experimental
methodologies to determine eﬄuent and deposition data.
The mean arrival time of the bacteria breakthrough typicallycoincided with the conservative tracer (data not shown). The timethat corresponds to 1 pore volume (dependent on the saturation,
porosity, and water ﬂow rate) is provided in the captions for Fig.
3 to 8. No appreciable retardation between the bacteria and thetracer breakthrough curves was observed. This observation wasconsistent for both bacteria and the diﬀerent saturations. The
bacteria transport, however, was clearly nonconservative because
diﬀerent amounts of bacteria were retained in the sand at diﬀerent water contents.
Table 1 indicates that higher eﬄuent concentrations occurred
for saturated than for unsaturated systems for both bacteria strains.
A reduction in the moisture content produced a decrease in the peakeﬄuent concentration and a decrease in the total cell recovery in
the eﬄuent. For D. radiodurans the average percentage of bacteria
recovered in the eﬄuent was 93, 82, and 43.5% at water saturations

Figures 3A, 4A, 5A and 6A, 7A, 8A present observed andsimulated eﬄuent concentration curves for stationary phase D.
radiodurans and R. rhodochrous, respectively, at diﬀerent water
saturations (100% in Fig. 3A and 6A, 80% in Fig. 4A and 7A,
and 40% in Fig. 5A and 8A). Here the relative eﬄuent concentration, C/C0, where C0 is the inﬂuent concentration of bacteria,
is plotted as a function of time. The corresponding observed
and simulated ﬁnal spatial distribution of retained bacteria after
completion of the transport experiment is given in Fig. 3B, 4B,
and 5B and 6B, 7B, and 8B. In this case, the data are presented
as normalized concentration (number of bacteria recovered in
the sand, Nt, divided by the number in a unit volume of the
input bacterial suspension, Ni) per gram of dry sand and areplotted as a function of the distance from the column inlet.
Table 1 gives the percentage of bacteria recovered in the eﬄuent
and deposited in the sand for these experiments. Simulations
presented in Fig. 3 to 8 used the attachment, Langmuirian,and 2 site models discussed earlier. Table 2 provides a summaryof the ﬁtted attachment and Langmuirian model parametersand statistical information on the goodness-of-ﬁt (95% conﬁdence intervals on ﬁtted parameters; and the coeﬃcient oflinear regression, R2). Table 3 provides similar information forthe 2 site model.

F . 5. (A) Measured and fi ed breakthrough curves and (B) reten-

F . 4. (A) Measured and fi ed breakthrough curves and (B) reten-on profiles for Deinococcus radiodurans at 40% satura on. Fi ed
curves were obtained using the a achment model, the Langmuirian model, and the 2 site model. In Fig. 5A, 55 min is equal to1 pore volume. C/C0 = rela ve eﬄuent concentra on, where C0
is the influent concentra on of bacteria; Nt, number of bacteria
recovered in the sand; Ni, number in a unit volume of the input
bacterial suspension.

on profiles for Deinococcus radiodurans at 80% satura on. Fi ed
curves were obtained using the a achment model, the Langmuirian model, and the 2 site model. In Fig. 4A, 101 min is equal
to 1 pore volume. C/C0 = rela ve eﬄuent concentra on, where C0
is the influent concentra on of bacteria; Nt, number of bacteria
recovered in the sand; Ni, number in a unit volume of the input
bacterial suspension.
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412

F . 6. (A) Measured and fi ed breakthrough curves and (B) reten-F . 7. (A) Measured and fi ed breakthrough curves and (B) reten-on profiles for Rhodococcus rhodochrous at 100% satura on.
Fi ed curves were obtained using the a achment model, the Langmuirian model, and the 2 site model. In Fig. 6A, 134 min is equal
to 1 pore volume. C/C0 = rela ve eﬄuent concentra on, where C0
is the influent concentra on of bacteria; Nt, number of bacteria
recovered in the sand; Ni, number in a unit volume of the input
bacterial suspension.

on profiles for Rhodococcus rhodochrous at 80% satura on. Fi ed
curves were obtained using the a achment model, the Langmuirian model, and the 2 site model. In Fig. 7A, 152 min is equal
to 1 pore volume. C/C0 = rela ve eﬄuent concentra on, where C0
is the influent concentra on of bacteria; Nt, number of bacteria
recovered in the sand; Ni, number in a unit volume of the input
bacterial suspension.

of 100, 80, and 40%, respectively. Similarly, the average percentage
of R. rhodochrous in the eﬄuent was 82.5, 61, and 32.5% at water
saturations of 100, 80, and 40%, respectively. These ﬁndings are inaccordance with previously reported unsaturated bacteria transport
studies (Schaefer et al., 1998; Auset et al., 2005).
The breakthrough curves at lower water saturations weremore asymmetric, showing increasing eﬄuent concentrations as
the injection of bacteria proceeded. This observation suggeststhat the time dependency of the deposition process increased
with decreasing water saturation. Time-dependent deposition has
typically been ascribed to blocking of favorable attachment sites(Johnson and Elimelech, 1995; Rijnaarts et al., 1995; Schaefer
et al., 1998; Bolster et al., 2001). The air–water interfacial area
increases with decreasing water content (e.g., Bradford and Leij,
1997), and thus, blocking phenomena on the air–water interface
should not increase with decreasing saturation. Blocking of favorable attachment sites on the solid–water interface may provide
a plausible explanation of this behavior only if the accessible
solid surface area to the bacteria decreases with decreasing water
saturation. Alternatively, Bradford et al. (2005) and Bradford
and Bettahar (2006) have suggested that ﬁlling of straining sites
provides another explanation for this observation. This hypothesis is consistent with the experimental observations reported in
Gargiulo et al. (2007).

Comparisons of Fig. 3, 4, 5 with Fig. 6, 7, 8 reveal diﬀerences in the transport behavior of hydrophilic (D. radiodurans)
and hydrophobic (R. rhodochrous) bacteria strains. At a given
water saturation, the hydrophilic bacteria always showed higher
eﬄuent concentrations than the hydrophobic bacteria (Table 1).
Diﬀerences in surface charge of the bacteria cannot explain thisenhanced deposition behavior because the zeta potentials of R.
rhodochrous and D. radiodurans were not statistically diﬀerent(–47 ± 7 mV compared with –38 ± 5). Hence, diﬀerences in thedeposition behavior are probably due to hydrophobic interactions,which enhanced the aggregation of R. rhodochrous (Fig. 2a and2b). Note that there is not yet a consensus in the literature on theorigins of hydrophobic interactions (Tsao et al., 1993; Yaminsky
and Ninham, 1993; Rabinovich and Yoon, 1994; van Oss, 1994;
Yoon and Ravishankar, 1996).
Bacteria retention inside the column was strongly inﬂuenced by the packing’s water saturation. Table 1 indicates that a
reduction of the water saturation tended to produce an increasein the bacteria retention. For a given water saturation, greater
amounts of deposition were also observed for the more hydrophobic strain (R. rhodochrous) than for the hydrophilic strain(D. radiodurans) (Table 1).
The shape of the cell retention proﬁle was not consistent withthe ﬁrst-order attachment model ﬁt that is shown in Fig. 3B towww.vadosezonejournal.org · Vol. 7, No. 2, May 2008

413

2005a), and Johnson et al. (2005) in saturated column studies thatused various colloids and microorganisms. These authors attributed nonexponential deposition proﬁles to surface heterogeneityof colloids and/or porous media, and attachment in the secondary energy minima of the Derjaguin–Landau–Verwey–Overbeek(DLVO) potential energy proﬁle. Conversely, Bradford et al. (2002,
2003) attributed deviations from attachment model predictions tostraining of colloids in the smallest regions of the pore space.
Additional simulations were conducted to better quantify
mechanisms of bacteria deposition using the 2 site model. Similar
to Bradford et al. (2003), we assumed in this analysis that depthdependent deposition processes (site 2) occur primarily near thecolumn inlet and that conventional attachment (site 1 with ψt =1) dominates in the region of the deposition proﬁle that exhibits
less concentration change with distance; in this case, for depths
greater than ?6 cm from the inlet. Figures 3 through 8 and Tables
2 and 3 indicate that the 2 site model provided a signiﬁcantly
better description of experimental data than either the attachment
or the Langmuirian models, especially the deposition proﬁles.
This improvement was not due to diﬀerences in the number ofﬁtting parameters, as both the 2 site and the Langmuirian models
had three parameters that were optimized.
Table 4 provides the corresponding mass balance information for deposition on sites 1 and 2 that were determined in
HYDRUS. The depth-dependent deposition (site 2) accounts
for 71 to 99% and 51 to 97% of the total deposition for D.
radiodurans and R. rhodochrous, respectively. The total amountof the bacteria deposited in site 2 also dramatically increased
with decreasing water saturation. This was especially true for thehydrophobic bacteria R. rhodochrous that forms larger aggregatesand had as much as 97% retained in site 2 at a water saturationof 40%. These ﬁndings are consistent with trends in site 2 model
parameters with saturation and bacteria hydrophobicity (Table3). The values of k2 for both D. radiodurans and R. rhodochrous
increased with decreasing water saturation. At a given saturation,
the value of k2 for the hydrophobic R. rhodochrous was always
higher than that for the hydrophilic D. radiodurans.
We believe that straining of cells and/or aggregates can
explain the observed trends discussed above for k2. Straining of
colloids has been reported to occur when the ratio of the colloid to the median grain diameter is greater than 0.003 to 0.005(Bradford et al., 2003; Bradford and Bettahar, 2006; Bradford etal., 2006c), with increasing amounts of deposition occurring forlarger values of this ratio. This ﬁnding has also been conﬁrmed inpore-scale micromodel studies using latex microspheres (Bradford
et al., 2005) and bacteria (Bradford et al., 2006a,b). On the basis

F . 8. (A) Measured and fi ed breakthrough curves and (B) reten-on profiles for Rhodococcus rhodochrous at 40% satura on. Fi ed
curves were obtained using the a achment model, the Langmuirian model, and the 2 site model. In Fig. 8A, 62 min is equal to1 pore volume. C/C0 = rela ve eﬄuent concentra on, where C0
is the influent concentra on of bacteria; Nt, number of bacteria
recovered in the sand; Ni, number in a unit volume of the input
bacterial suspension.

8B for all saturations and for both bacteria strains (the proﬁles
are not exponential). Compared with the attachment model ﬁts,
the observed deposition proﬁles typically exhibited greater retention in the section adjacent to the column inlet, especially for thedrier conditions and for the strain with higher hydrophobicity(see Table 1). Consequently, the attachment model ﬁt also overestimated the amount of bacteria retention near the column outlet.
Consideration of blocking and detachment in the Langmuirian
model ﬁt to the data provided a poorer characterization of thedeposition proﬁle than the attachment model but a slightly better
description of the breakthrough curves (Table 2). The coeﬃcientof linear regression for the deposition proﬁles is quite poor using
the attachment and Langmuirian models (Table 2). Hence, theparameter values for these models have limited physical signiﬁcance and are not further discussed.
The failure of the attachment and Langmuirian models indescribing colloid deposition has been reported in other experimental studies. Jewett et al. (1999) measured the deposition
proﬁle of Pseudomonas ﬂuorescens in unsaturated systems. Theirresults indicated that the bacterial deposition rate decreased withdepth and was not consistent with attachment model predictions. Deviation from the attachment model predictions was also
reported by Tufenkji et al. (2003), Tufenkji and Elimelech (2004b,
www.vadosezonejournal.org · Vol. 7, No. , May 2008

1. Percentage of bacteria in the ou low and retained in thecolumn for two replicates (1 and 2).

T

Replicate

1
2
1
2
1
2

Rhodococcus
Deinococcus
rhodochrous
radiodurans
Ou low
Retained
Ou low
Retained———————————— % ————————————
100
86
8 (3)†
95
6 (4)†
100
79
12
91
4
80
63
33 (12)†88
14 (7)†
80
59
35
76
16
40
36
65 (31)†47
53 (23)†
40
29
75
40
48

Satura on† Retained in the top 0 to 5 cm of the column.
414

T
2. Fi ed parameters of the first-order a achment and Langmuirian
models for Deinococcus radiodurans and Rhodococcus rhodochrous.
Parameter†ka (min −1)
R2
R2 (BTC)§
R2 (RP)¶

Satura on
100%
80%
40%
Value
95% CI‡
Value
95% CI
Value
95% CIFirst-order a achment model (D. radiodurans)
6.90e-04 ± 5.09e+00 2.54e-03 ± 6.51e+00 1.85e-02 ± 1.40e+01
0.992
0.974
0.298
0.994
0.985
0.315
0.633
0.673
0.599
Langmuirian blocking model (D. radiodurans)
9.94e-04 ± 3.67e-04 3.87e-03 ± 6.97e-04 4.36e-02 ± 1.68e-02
2.00e-04 ± 4.13e-04 1.72e-04 ± 2.08e-04 4.29e-03 ± 2.08e-03

ka(min −1)
kd (min −1)
smax1 (Nt/Ni)/g sand 1.71e-01 ± 1.80e-01 3.06e-01 ± 1.11e-01 3.56e-01
0.993
0.980
0.518
R2
0.995
0.992
0.643
R2 (BTC)
0.600
0.627
0.430
R2 (RP)First-order a achment model (R. rhodochrous)ka (min −1)
1.31e-03 ± 4.99e+01 3.05e-03 ± 1.10e+01 2.20e-02
0.991
0.950
0.826
R2
0.993
0.958
0.909
R2 (BTC)
0.485
0.421
0.734
R2 (RP)
Langmuirian blocking model (R. rhodochrous)
1.73e-03 ± 3.58e-04 3.08e-03 ± 6.09e-04 2.68e-02
ka (min −1)
kd (min −1)
1.53e-04 ± 1.88e-04 2.96e-05 ± 1.63e-04 1.00e-06#
smax1 (Nt/Ni)/g sand 3.62e+01 ± 2.01e-01 1.00e+03# ± 1.33e+06 6.48e-01
0.993
0.950
0.830
R2
0.995
0.957
0.969
R2 (BTC)
R2 (RP)
0.461
0.419
0.627

± 1.54e-01± 7.98e-00± 4.70e-03± 2.42e-04± 3.27e-01† ka, first-order a achment coeﬃcient; kd, first-order detachment coeﬃcient; smax1, maximum solid phase concentra on of retained bacteria cells; Nt, number of bacteria
recovered in the sand; Ni, number in a unit volume of the input bacterial suspension.
‡ CI, confidence interval.
§ BTC, breakthrough curve.
¶ RP, reten on profile.
# Upper or lower constraint.

3. Fi ed parameters of the two site depth-dependent deposi on modelfor Deinococcus radiodurans and Rhodococcus rhodochrous.

T

Parameter†ka (min −1)
kd (min −1)
k2 (min −1)βR2R2 (BTC)§
R2 (RP)¶

Satura on
100%
80%
Value
Value
95% CI
95% CI‡
Deinococcus radiodurans
5.11e-05 ± 3.17e-04 3.46e-03 ± 1.70e-03
2.41e-03 ± 3.90e-02 2.81e-02 ± 1.62e-02
0.0172± 9.33e-04± 0.0023
0.0051
0.432
0.432
0.996
0.994
0.998
0.994
0.954
0.980
Rhodococcus rhodochrous
1.88e-03 ± 6.43e-04 1.55e-03 ± 1.25e-04
3.38e-02 ± 1.38e-02 6.36e-05 ± 3.15e-04± 0.0088
0.00892 ± 0.00044 0.011
0.432
0.432
0.955
0.998
0.958
0.998
0.771
0.869

40%
Value

95% CI9.77e-02
7.70e-02
0.078
0.432
0.928
0.931
0.896

± 4.27e-02± 3.55e-02± 0.0087

1.58e-02# ± 6.47e-03
ka (min −1)
4.00e-02 ± 1.99e-03
kd (min −1)
0.144± 0.0060
k2 (min −1)
0.432
β
0.977
R2
0.987
R2 (BTC)
0.960
R2 (RP)† ka, first-order a achment coeﬃcient; kd, first-order detachment coeﬃcient; β,empirical factor controlling the shape of the spa al distribu on.
‡CI, confidence interval.
§ BTC, breakthrough curve.
¶ RP, reten on profile.
# Upper or lower constraint.
www.vadosezonejournal.org · Vol. 7, No. 2, May 2008415

of the cell size and aggregation behavior presented in Fig.
2, the ratio of the cell aggregate size to median sand size is
expected to range from 0.002 to 0.007 for D. radiodurans
and from 0.002 to 0.026 for R. rhodochrous. Hence,straining is anticipated to occur for both bacteria strainsin this sand, but greater amounts of straining are expected
for the more hydrophobic bacteria (R. rhodochrous) that
produced larger cell aggregates (see Fig. 2). The retentionof aggregates by straining is also in accordance with thepore-scale observations of Sirivithayapakorn and Keller(2003) and Crist et al. (2004).
The observed dependency of k2 on water saturation
can also be explained by straining. Figure 9 presents anillustration of a triangular-shaped capillary tube undersaturated and unsaturated conditions. Potential straining
sites are indicated in this ﬁgure where multiple interfaces
intersect (at the air–water–solid triple point and at vertices of the triangular capillary tube). For a given water ﬂow
rate through the capillary tube, a greater fraction of thewater ﬂow will occur near straining sites under unsaturated than under saturated conditions. Furthermore, thenumber of straining sites will increase under unsaturated
conditions due to the presence of more air–water–solid
triple points. Both of these factors are expected to contribute to greater amounts of straining (higher values ofk2) with decreasing water saturation.
The relative water ﬂux to straining sites as a functionof the water saturation can be estimated from measured
capillary pressure-saturation curve information using theapproach outlined by Bradford et al. (2006a). In brief, ahypothetical fraction of the pore space where straining
occurs (γ) is assumed or estimated for a particular porous
medium and colloid-size distribution. Measured capillary pressure-saturation data is then used in a pore-size
distribution model (Burdine, 1953) to estimate a water
relative permeability for the fraction of the pore spacethat is deﬁned by γ. The water ﬂux to this region is subsequently calculated using Darcy’s law in conjunction withthis relative permeability information. For the sand usedin our study, Fig. 10 presents an illustrative plot of therelative water ﬂux to straining sites as a function of water
saturation for various hypothetical values of γ. The relative
water ﬂux to straining sites increases dramatically when
the saturation decreases or γ increases. For our particularsand and bacteria, the value of γ will be appropriately
equal to the residual water saturation (e.g., <10%).
It unlikely that surface heterogeneity of the bacteria
and sand can account for the large amounts of bacteria
retention in site 2 that increased with decreasing water
saturation, for the following reasons. First, DLVO calculations following the approach outlined by Bradford
et al. (2006a) indicate highly unfavorable conditions for
attachment to the solid–water interface (primary or secondary minimum of the interaction energy proﬁle) for theselected solution and solid chemistries, cell aggregate sizes,
and the measured ranges in cell zeta potential. Second,
DLVO calculations presented by Crist et al. (2005) also
indicate a low potential for attachment of the bacteria andcell aggregates to the air–water interface (due to repulsive

4. Mass balance of applied and deposited (sites 1 and 2) bacteria. (Deposi on calculated at me equal to the pulse dura on
and one pore volume).
T

Satura on
%
100
80
40
100
80
40

Hence, below, we only discuss general trends in site 1 parameters.
Mass balance information for sites 1 and 2 that was calculated in
HYDRUS is also discussed and is presented in Table 4.
For D. radiodurans, the value of ka increased with decreasing water saturation, suggesting greater attachment. Consistent
with these ﬁndings, the information in Table 4 indicates that agreater percentage of D. radiodurans cells was retained on site 1
with decreasing water saturation (at water saturations of 100, 80,
and 40%, the retained mass on site 1 was 0.01, 1.14, and 15.7%,
respectively). The value of kd for D. radiodurans also increased
with decreasing water saturation and was greater than or of asimilar magnitude as ka. These observations indicate that attachment was approaching linear equilibrium sorption conditions(van Genuchten et al., 1974).
Conversely, values of ka and kd for R. rhodochrous at diﬀerent
water saturations did not follow a systematic trend, and mass balance information for site 1 (Table 4) indicates that cell retention
actually decreased with decreasing water saturation. This result
is somewhat misleading; it is really a consequence of strainingof aggregates of this bacterium. Equation [3] indicates that theamount of attachment is proportional to the aqueous phase concentration of the cells. When deposition on site 2 increases, theaqueous concentration of the cells is decreased, and the rate of
attachment on site 1 will therefore also decrease.
Under saturated conditions, the value of ka for D. radiodurans
was lower than that for R. rhodochrous. This result is consistent
with the higher hydrophobicity showed by R. rhodochrous compared with D. radiodurans and suggests that R. rhodochrous has
a higher sticking coeﬃcient (assuming that the single collector contact eﬃciency is the same for both strains). Cell surfacehydrophobicity has been reported to directly inﬂuence bacteria
adhesion behavior (Rijnaarts et al., 1995; van Loosdrecht et al.,1987). A similar conclusion about bacteria adhesion and hydrophobicity was reported by Unc and Goss (2003), who foundslower attachment and detachment rates for hydrophilic compared with hydrophobic strains under saturated conditions.

Total mass
Mass Site 1 Mass Site 2 Mass Site 1 Mass Site 2
injected———— cells cm −2 —————— % ——
Deinococcus radiodurans
4.56E+09
4.56E+07
3.99E+08 0.01 ± 5.6 8.74 ± 6.01
8.41E+08
9.58E+06
1.68E+08 1.14 ± 0.39 20.4 ± 0.93
1.69E+08
2.65E+07
6.71E+07 15.7 ± 7.9 39.7 ± 1.21
Rhodococcus rhodochrous
1.07E+09
3.85E+06
1.54E+08 0.36 ± 0.13 14.4 ± 0.65
2.89E+08
5.03E+07
5.32E+07 17.4 ± 8.6 18.4 ± 10.3
4.30E+08
9.72E+06
2.89E+08 2.26 ± 1.16 67.4 ± 0.88

van der Waals and electrostatic interactions). Third, attachmentof D. radiodurans on the air–water interface is unlikely to occur
by hydrophobic interactions because this bacterium had a lowhydrophobicity (MATH was 0–8%). Hence, the large amountsof D. radiodurans retention that increased with decreasing water
saturation cannot be explained by attachment to the air–waterinterface (Table 1).
Table 4 indicates that the total attachment (site 1) to solid–
water and air–water interfaces only accounted for 0.7 to 16.7%of the injected bacteria cells into a column. These low percentages
are likely to be more physically realistic for attachment than theamounts of retention on site 2 given the ﬁndings of the DLVO
calculations discussed in the proceeding paragraph. The ﬁtted
attachment coeﬃcient ka in Table 3 is a lumped parameter thatcharacterizes both the attachment to the solid surface and to theair–water interface. Due to the confounding inﬂuence of straining
in site 2 and the relatively low amounts of bacteria retention insite 1, it may not be possible to mechanistically separate the inﬂuence of attachment to the solid–water and air–water interfaces.

Conclusions
The aim of this work was to study the transport and deposition behavior of representative hydrophilic and hydrophobic

F . 10. A plot of the rela ve water flux to straining sites (qws/qw;

F . 9. Illustra on of a triangular-shaped capillary tube under saturated

where qws and qw are the Darcy water veloci es to straining sites
and the porous medium at a given water satura on, respec vely)
for various hypothe cal frac ons of the pore space where straining
occurs (γ) and the indicated water satura ons (Sw).

and unsaturated condi ons. Poten al straining sites are indicated inthis figure where mul ple interfaces intersect (at the air–water–solid
triple point and the ver ces of the triangular capillary tube).
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bacteria strains under unsaturated conditions. Two bacteria
strains, Deinococcus radiodurans and Rhodococcus rhodochrous,that were used in the transport experiments strongly diﬀered inhydrophobicity but are similar in size (1 μm), surface charge, andshape (coccoid). Although both strains were observed to form
aggregates in solution, the hydrophobic R. rhodochrous tended
to form larger aggregates (as large as 10–15 μm).
For both bacteria strains, a decrease in water content led
to decreasing eﬄuent concentrations and increased retention of
the bacteria. This eﬀect was more pronounced for the hydrophobic strain and with drier conditions. The proﬁles of retained
cells were not exponential with depth. Most of the bacteria were
deposited in the ﬁrst centimeters below the column inlet and the
proﬁle monotonically decreased with increasing depth.
Three models were used to characterize the bacteria transportand retention data: a ﬁrst-order attachment model, a Langmuirian(attachment, detachment, and blocking) model, and a 2 site
(attachment, detachment, and depth-dependent deposition)model. In contrast to attachment or Langmuirian models, the 2site model accurately simulated the experimental breakthroughcurves and deposition data for all the saturations and for bothbacteria strains. The vast majority of the deposited cells wereretained in site 2 that considered depth–dependent deposition.
Analysis of the transport and retention data and ﬁtted model
parameters suggests that straining was the dominant mechanismof cell retention on site 2. Speciﬁcally, straining is expected toincrease with increasing hydrophobicity of the bacteria becauseof the tendency of these bacteria to form larger aggregates thanthe hydrophilic bacteria. Furthermore, straining is expected toincrease with decreasing water saturation because a greater fraction of the water ﬂows through a larger number of small porespaces (near grain to grain contacts and air-water-solid triple
points). Conversely, DLVO calculations suggest that attachment
to the solid–water and air–water interfaces cannot likely accountfor the observed magnitudes of depth-dependent deposition onsite 2 but rather was consistent with relatively low amounts ofattachment on site 1. It was not possible to mechanistically separate the inﬂuence of attachment to the solid–water and air–waterinterfaces due to the confounding inﬂuence of straining.

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