Published February 7, 2014

Journal of Environmental Quality

Reviews and Analyses

Modeling Microorganism Transport and Survival in the Subsurface
Scott A. Bradford,* Yusong Wang, Hyunjung Kim, Saeed Torkzaban, and Jiri Šimůnek

An understanding and ability to predict the trans-

An understanding of microbial transport and survival in thesubsurface is needed for public health, environmental applications,and industrial processes. Much research has therefore been directed
to quantify mechanisms influencing microbial fate, and the results
demonstrate a complex coupling among many physical, chemical,
and biological factors. Mathematical models can be used to help
understand and predict the complexities of microbial transportand survival in the subsurface under given assumptions andconditions. This review highlights existing model formulations
that can be used for this purpose. In particular, we discuss models
based on the advection–dispersion equation, with terms for kinetic
retention to solid–water and/or air–water interfaces; blocking andripening; release that is dependent on the resident time, diffusion,and transients in solution chemistry, water velocity, and water
saturation; and microbial decay (first-order and Weibull) and growth(logistic and Monod) that is dependent on temperature, nutrient
concentration, and/or microbial concentration. We highlight a tworegion model to account for microbe migration in the vicinity of asolid phase and use it to simulate the coupled transport and survivalof Escherichia coli species under a variety of environmentally relevant
scenarios. This review identifies challenges and limitations ofmodels to describe and predict microbial transport and survival. In
particular, many model parameters have to be optimized to simulate
a diversity of observed transport, retention, and survival behavior
at the laboratory scale. Improved theory and models are needed to
predict the fate of microorganisms in natural subsurface systems thatare highly dynamic and heterogeneous.

port and fate of microorganisms (viruses, bacteria, andprotozoa) in the subsurface is needed for a wide variety of applications including bioremediation and bioaugmentation (Mishra et al., 2001; Vidali, 2001), microbially enhanced
oil recovery (Banat, 1995), water treatment (Stuyfzand, 1989;
Tufenkji et al., 2002; Ray et al., 2002; Schijven et al., 2003; Weisset al., 2005), and assessing and mitigating the risk of pathogen
contamination (Schijven and Hassanizadeh, 2000; Foppen
and Schijven, 2006; Tufenkji, 2007). Considerable amounts ofresearch have therefore been directed to this topic (see reviews
by Herzig et al., 1970; McDowell-Boyer et al., 1986; McCarthy
and Zachara, 1989; Ryan and Elimelech, 1996; Khilar and
Fogler, 1998; Schijven and Hassanizadeh, 2000; Ginn et al.,
2002; Harvey and Harms, 2002; Jin and Flury, 2002; DeNovio
et al., 2004; Rockhold et al., 2004; Unc and Goss, 2004; Foppen
and Schijven, 2006; Kanti Sen and Khilar, 2006; Bradford and
Torkzaban, 2008; Pang, 2009; Bradford et al., 2013a).
The transport and survival of microorganisms are wellknown to depend on the processes of advection, dispersion,diffusion, size exclusion, retention and release from the solid–
water (SWI) and/or air–water (AWI) interfaces, growth, death,
and/or inactivation, as well as initial conditions and sources.
Many of these processes are highly coupled to a wide varietyof physicochemical, biological, and hydrodynamic factors. For
example, microorganism retention and release on the SWI
and AWI are highly sensitive to the microorganism size andsurface properties; the porous medium size, pore structure, andsurface properties; the solution chemistry; the water velocity
and saturation; and the input concentration (Ginn et al., 2002;
Harvey and Harms, 2002; Foppen and Schijven, 2006; Tufenkji
et al., 2006; Bradford et al., 2013a). In addition, a wide variety
of abiotic (temperature, metal oxides, salinity, water content,
organic sources, nutrients, and electron donors and acceptors)
and biotic (microbial community, quorum sensing, andbiofilms) factors are known to influence microorganism growth,
death, and inactivation (Schijven and Hassanizadeh, 2002;
Harvey and Ryan, 2004; Berry and Miller, 2005; Torkzaban et

Copyright © American Society of Agronomy, Crop Science Society of America,and Soil Science Society of America. 5585 Guilford Rd., Madison, WI 53711 USA.
All rights reserved. No part of this periodical may be reproduced or transmitted
in any form or by any means, electronic or mechanical, including photocopying,recording, or any information storage and retrieval system, without permission inwriting from the publisher.

S.A. Bradford, U.S. Salinity Lab., Riverside, CA 92507; Y. Wang and J. Šimůnek, Dep.
of Environmental Sciences, Univ. of California, Riverside, CA 92521; H. Kim, Dep.
of Mineral Resources and Energy Engineering, Chonbuk National Univ., 664-14
Duckjin, Jeonju, Jeonbuk 561-756, Republic of Korea; and S. Torkzaban, CSIROLand and Water, Glen Osmond, SA 5064, Australia. Assigned to Associate Editor
Carl Bolster.

J. Environ. Qual. 43:421–440 (2014)
doi:10.2134/jeq2013.05.0212
Received 30 May 2013.
*Corresponding author (Scott.Bradford@ars.usda.gov).

Abbreviations: AWI, air–water interface; IS, ionic strength; PV, pore volumes; SWI,
soil–water interface.

421

al., 2006a; Foppen and Schijven, 2006; Cook and Bolster, 2007).
Furthermore, microbial population heterogeneity is known to
influence both transport and survival (Binnerup et al., 1993;
DeFlaun et al., 1997; Bolster et al., 2000; Fuller et al., 2000;
Morohashi et al., 2007; Oliver, 2010; Foppen et al., 2010).
A dramatic increase in the number and sophisticationof mathematical models for microbial transport and/or
survival has occurred in the last several decades to reflect the
research community’s evolving understanding (e.g., Sim andChrysikopoulos, 1996; Ginn, 2002; Murphy and Ginn, 2000;
Rathfelder et al., 2000; Schijven and Šimůnek, 2002; Lenhart
and Saiers, 2003; Saiers and Lenhart, 2003; Bradford et al.,2003, 2011a, 2012; Tufenkji et al., 2003; Scheibe and Wood,
2003; Chrysikopoulos and Vogler, 2004; Gabriel et al., 2005;
Tufenkji and Elimelech, 2005b; Grolimund and Borkovec,
2006; Šimůnek et al., 2006; Cortis et al., 2006; Bradford andToride, 2007; Mostafa and Van Geel, 2007; Šimůnek and van
Genuchten, 2008; Wang et al., 2008; Cheng and Saiers, 2009;
Chatterjee and Gupta, 2009; Tosco et al., 2009; Wang andFord, 2009; Yukalov et al., 2009; Molin and Cvetkovic, 2010;
Shapiro and Bedrikovetsky, 2010; Tosco and Sethi, 2010; Yuan
and Shapiro, 2010, 2011; Russell et al., 2012; Zhang et al., 2012;
Hosseini and Tosco, 2013; Landkamer et al., 2013). Thesemodels are based on different assumptions to conceptualize
water flow and microbial transport, retention, release, andsurvival within a mathematical framework. There is presently noconsensus on the best model formulation, and no single model is
expected to accurately simulate all scenarios. Most models do notconsider the full physical, chemical, and biological complexities
of dynamic natural systems because of uncertainty in processdescriptions, difficulty in parameter estimation, incompletecharacterization of heterogeneity, and the strong coupling withhydrodynamic and physicochemical factors. In addition, models
and research studies have mainly examined transport andsurvival processes separately due to their individual complexity,
even though both processes are known to strongly influence
microbial fate. Consequently, mathematical models are notalways accurate predictors of reality but are only as good as their
input parameters and modeling assumptions.
This review is divided into two main sections: (i) the
conventional model; and (ii) alternative models. We outline
the standard approach to simulate microbial transport, whichshares many similarities with solute transport models, in theconventional model section. The alternative models section
highlights existing model formulations to account for many
microbial transport and survival processes that are neglected in
the conventional model. In addition, we show the ability andchallenges of one promising alternative to the conventionalmodel (the two-region model) to simulate microbial transport,
retention, release, and survival. In both sections, we identify
gaps in knowledge and note model limitations. The information
presented in this review is intended to be illustrative and is not
exhaustive.

Conventional Model
Microbes are transported in the subsurface environment
with water as a result of advection, diffusion, and mechanicaldispersion. Models for microorganism transport and fate are422

commonly based on some form of the advection–dispersion
equation, with terms for retention and release from the SWI
and AWI (Harvey and Garabedian, 1991; Hornberger et al.,
1992; Corapcioglu and Choi, 1996). Water flow is typicallydescribed using either Richards’ equation (Richards, 1931) for
the vadose zone or the Bousinesque equation for groundwater.
An expression for microbe transport in the aqueous phase that
includes exchange to the SWI and AWI can be given in onedimensional form as¶q w C¶æ¶C ÷ö ¶qw C= ççq w D
- Esw - Eaw + Bw
÷ç
¶t
¶z è
¶z ÷ø
¶z

[1]

where z [L] is the distance in the direction of flow, t [T] is time,
C [N L−3, where N is number] is the microbe concentration in
the aqueous phase, qw [L3 L−3] is the volumetric water content, D[L2 T−1] is the hydrodynamic dispersion coefficient for microbes,
qw [L T−1] is the Darcy water velocity, Bw [N L−3 T−1] is thesurvival of the microbes in the water phase, and Esw [N L−3 T−1]
and Eaw [N L−3 T−1] are the exchange terms from/to the aqueous
phase to/from the SWI and AWI, respectively. The first andsecond terms on the right-hand side of Eq. [1] account for thedispersive and advective fluxes of the microbes, respectively.
First-order kinetic expressions are frequently used to accountfor microbial retention and release. The solid-phase mass balance
equation for microbes is commonly given as
rb¶S= Esw + Bs = q w ksw C -r b krs S + Bs¶t[2]

where S [N M−1] is the solid-phase microbe concentration,
rb [M L−3] is the bulk density, ksw [T−1] is the retention rate
coefficient to the SWI, krs [T−1] is the release rate coefficientfrom the SWI, and Bs [N L−3 T−1] is the survival of microbes on
the solid phase. The first and second terms on the right-hand sideof Eq. [2] account for microbe retention and release, respectively.
Each of these model parameters are discussed in detail below.
Filtration theory (Yao et al., 1971) attempts to predict ksw as
ksw =3(1-q w )
2 d50

ahv

[3]

where v [L T−1] is the average pore water velocity, d50 [L] is
the median grain diameter, h (dimensionless) is the single
collector contact efficiency, and a (dimensionless) is the sticking
efficiency. Mass transfer of microbes to the SWI is quantified
by h. Correlation equations to predict h as a function of systemvariables (water velocity, microbe size and density, and collectorsize) have been developed from pore-scale simulations of colloidtransport in simplified grain geometries under water-saturated
conditions (e.g., Rajagopalan and Tien, 1976; Tufenkji andElimelech, 2004; Nelson and Ginn, 2005; Ma et al., 2009).
Favorable attachment conditions occur in the absence of anenergy barrier when a = 1 (Eq. [3]). Conversely, unfavorable
attachment conditions occur in the presence of an energy barrier
to attachment. In this case, only a fraction of the microbes thatare transported to the SWI will be retained and a < 1. Several
theoretical approaches have been developed to estimate a fromthe fraction of the solid surface area that is chemically favorable
for deposition (Elimelech et al., 2000; Abudalo et al., 2005) or
Journal of Environmental Quality

the probability of diffusing microbes to be retained in a primaryor secondary energy minimum (Spielman and Friedlander, 1974;
Simoni et al., 1998; Shen et al., 2007). The kinetic energy model(also known as the Maxwell model) predicts that a rapidly
increases with the depth of the secondary minimum (Simoni
et al., 1998; Hahn and O’Melia, 2004; Shen et al., 2007), suchthat larger microbes will have much higher values of a thansmaller microbes. Conversely, the energy barrier to the primary
minimum increases with microbe size, and therefore the valueof a that is associated with the primary minimum also decreases(Shen et al., 2007).
The value of a is well known to be sensitive to the solution
chemistry (Tufenkji and Elimelech, 2005a; Shen et al., 2007)
and the surface properties of the SWI and microbe (Kim et al.,2009a, 2010a, 2010b; Bolster et al., 2009, 2010; Foppen et al.,2010). Additional research also suggests that a will depend on
the system hydrodynamics ( Johnson et al., 2007; Torkzaban
et al., 2007; Shen et al., 2010) and the input concentration(Bradford et al., 2009a). Innovative approaches are needed to
predict the effects of all these factors on a. Due to all of thesecomplexities, the value of a is frequently viewed as an empiricalparameter that is obtained by fitting to measured transport data
(Tufenkji and Elimelech, 2005a).
Figure 1 presents an illustrative example of the sensitivityof E. coli transport to the species type and physicochemical
conditions. Breakthrough curves for E. coli D21g and E. coli
O157:H7 are shown in Fig. 1a and 1b, respectively, when thesolution ionic strength (IS) ranged from 1 to 100 mmol L−1
KCl. The breakthrough curves are presented as aqueous-phasenormalized concentrations (C/Co, where Co is the influent
concentration) as a function of the pore volumes (PV). The E.
coli D21g and O157:H7 data have previously been reported by
Torkzaban et al. (2008) and Kim et al. (2009a), respectively.
Pronounced differences in the transport behavior of E. coli
D21g and O157:H7 occurred with increases in solution IS. In
particular, increasing the IS produced an increase in retention
for D21g, whereas the opposite trend occurred for O157:H7.
This behavior is primarily due to differences in the surface
properties of the two E. coli strains, as well as physicochemical
conditions. Standard interaction energy calculations (Derjaguin
and Landau, 1941; Verwey and Overbeek, 1948) predict anincrease in the depth of the secondary minimum with an increasein IS that will enhance cell retention. Escherichia coli D21g has

minimal amounts of extracellular polysaccharide on its surface(Walker et al., 2004), and it behaves in a manner consistent withthis interpretation. Conversely, the amount of and conformationof the surface macromolecules on E. coli O157:H7 is much
more complex (Kim et al., 2009b), and this produces pH- andIS-dependent electrosteric repulsion that decreases cell retention
with increasing IS (Kim et al., 2009a). Other differences inFig. 1 occurred as a result of the physicochemical conditions.
For example, the E. coli D21g experiments were conducted in
205-mm ultrapure quartz sand at a Darcy water velocity of 0.66 cm
min−1 and solution pH of 5.8. Conversely, the E. coli O157:H7
experiments were conducted in 275-mm ultrapure quartz sandat a Darcy water velocity of 0.1 cm min−1 and a solution pH of
9.2. Consequently, the results in Fig. 1 demonstrate that E. colitransport will be sensitive to the strain type and physicochemical
properties, and that the surface macromolecules may have alarge impact on retention under different solution chemistry
conditions.
Under steady-state flow and solution chemistry conditions,krs has been reported to be a function of the diffusion coefficient,
the adhesive interaction, and the boundary layer thickness (Ryanand Gschwend, 1994; Ryan and Elimelech, 1996). The strengthof the hydrodynamic forces will also influence microbe release(Bergendahl and Grasso, 1998, 1999; Lenhart and Saiers,
2003; Torkzaban et al., 2007; Tosco et al., 2009). The value ofkrs has therefore been commonly viewed as an empirical fitting
parameter, and additional research is warranted to predict thisparameter.
Microbe retention and release under unsaturated conditions
may also occur on the AWI in addition to the SWI. The valueof Esw will again be described in a manner similar to Eq. [2].
Under unsaturated conditions, however, the value of ksw is notconsistent with the assumptions used to develop filtration theory(Eq. [3]). The mass balance equation for microbes at the AWI
may be described similar to Eq. [2] as (Šimůnek et al., 2006)¶Aaw G= Eaw + Ba = q w kaw C - Aaw kra G + Ba¶t[4]

where kaw [T−1] is the microbe retention coefficient on the AWI,
kra [T−1] is the release coefficient from the AWI, Aaw [L2 L−3] isthe air–water interfacial area per unit volume, G [N L−2] is the
microbe concentration retained on the AWI, and Ba [N L−3T−1]
is the survival of the microbes on the AWI.

Fig. 1. Observed breakthrough curves for (a) E. coli D21g and (b) E. coli O157:H7 as a function of solution ionic strength (IS) (range 1–100 mmol kg−1
KCl). The E. coli D21g and O157:H7 data and experimental details were previously reported by Torkzaban et al. (2008) and Kim et al. (2009a).
www.agronomy.org • www.crops.org • www.soils.org423

No comprehensive theory is presently available to predict
kaw and kra. In general, hydrodynamic forces are expected to be
more important for microbe retention on the AWI than the SWI
due to differences in the boundary conditions. In particular, the
SWI is typically considered to be a no-slip boundary condition(the water velocity is zero at the SWI), whereas the AWI iscommonly assumed to be a partial-slip (non-zero water velocity
at the AWI) or perfect-slip (the water velocity is unaffectedby the AWI) boundary condition (Bird et al., 2002; Zheng etal., 2012). Adhesive interactions on the AWI are controlled
by hydrophobic, electrostatic, and capillary forces. It should
be noted that the van der Waals interaction with the AWI isrepulsive and the AWI is negatively charged at pH values foundin most natural environments (Bradford and Torkzaban, 2008).
Microbe retention tends to increase with a decrease in watercontent under given hydrodynamic and solution chemistry
conditions due to: (i) sorption onto the AWI for positively
charged or hydrophobic microbes (Wan and Wilson, 1994a,
1994b; Schäfer et al., 1998; Cherrey et al., 2003; Saiers andLenhart, 2003; Torkzaban et al., 2006a, 2006b; Kim et al.,2008); (ii) physical restrictions imposed by thin water films(film straining) (Wan and Tokunaga, 1997; Veerapaneni etal., 2000); (iii) retention at the air–water–solid contact line
(Crist et al., 2004, 2005; Chen and Flury, 2005; Zevi et al.,2005, 2009, 2012; Lazouskaya et al., 2006; Lazouskaya and Jin,
2008); (iv) immobilization in dead-end pores (Gao et al., 2006);(v) enhanced deposition onto the SWI due to a reduction in
the diffusive length in partially filled pores (Torkzaban et al.,2006b); and (vi) a greater fraction of water flow in small porespaces (Gargiulo et al., 2008).
The survival of microorganisms in the subsurface reflects the
net rate of death or inactivation (referred to as decay) and growth.
The relative importance of decay and growth can vary dramaticallywith the microorganism type. For example, pathogenic viruses
and protozoa are obligate parasites that do not replicate outside
their hosts, whereas pathogenic bacteria are capable of growth in
the environment. The rates of microorganism growth and decay
in the water, solid, and air phases are usually modeled using firstorder kinetics as (Crane and Moore, 1986; Himathongkham etal., 1999; Pachepsky et al., 2006; Lang and Smith, 2007; Charles
et al., 2008)

Bw = q w (L w -C w )C[5]

Bs = r b (Ls -Cs ) S[6]

Ba = Aaw (La -Ca )G[7]

where X [T−1] is a decay coefficient, L [T−1] is the microbe
growth coefficient, and the subscripts w, s, and a denote thewater, solid, and air phases, respectively. The net survival rate
(L − X) may be determined in microcosm or batch experiments
or by inverse fitting to available transport data. It is usually
not feasible to separately determine rates for X and L in thewater, solid, and air phases in these experiments. In addition,
independent determination of microbial survival is hampered byirreversible microbial retention on the solid phase that produces
mass balance errors (Bradford et al., 2006b). Incomplete massbalance information may be incorrectly attributed to decay.
424

Identical rates for X and L are commonly assumed for all phases;
however, some research has indicated that rates of decay arehigher or lower on the solid than in the water phase (Schijven
and Hassanizadeh, 2000; Harvey and Ryan, 2004; Asadishad etal., 2011).
Solute transport models have historically served as thestarting point for the conventional microbial transport model.
Many model assumptions that are valid for solutes may beviolated for microorganisms. For example, Eq. [1] assumes thattransport occurs at the average pore water velocity and that allof the pore space is accessible, dispersion is a Fickian process,and water flow is unaffected by the presence of microbes. The
above model also assumes that microbe retention, release,
growth, and decay are first-order processes, primarily based onmathematical convenience (e.g., linear transport equations canbe solved analytically) and ease of analyses (e.g., determinationof rate coefficients from log–linear plots). In reality, theseprocesses can be highly nonlinear. Consequently, considerable
deviations have been observed between the transport and fate of
microbes and conventional model simulations. In an attempt toaccount for some of these discrepancies, a variety of alternativemodel formulations have been developed. Several representativemodeling classes are highlighted below.

Alternative Models
Advection and Dispersion
Sedimentation
Most microbes are neutrally buoyant. In some cases, however,the density of cultured microorganisms can be greater than water(Wan et al., 1995; Harvey et al., 1996). In this case, the transport
velocity of microbes may be influenced by sedimentation. To
account for sedimentation, qw in Eq. [1] has been replaced withqw + qwvs (Wan et al., 1995; Murphy and Ginn, 2000), where vs[L T−1] is the component of the sedimentation velocity in the
direction of qw. The value of vs may be determined from Stokes’
law after correcting for the influence of the soil grains (Wan etal., 1995).

Size and/or Anion Exclusion
The conventional transport model assumes that microbes
sample the full distribution of water velocities and are therefore
transported at the same average pore-water velocity as solutes.
Size and/or anion exclusion may limit microbes to larger portionsof the pore space, which produces a higher average transport
velocity than for solutes. Size exclusion occurs when microbes
are physically excluded from some of the pore space (velocity
distribution) by virtue of their size (Ryan and Elimelech, 1996).
Anion exclusion may occur as a result of repulsive interactions
between negatively charged ions and/or microbes and interfaces(SWI or AWI) that limit their approach to the interface andchannel them to pore-throat centerlines (Krupp et al., 1972; Bolt
and de Haan, 1979).
Several methods have been reported in the literature toaccount for the influence of size and/or anion exclusion on
microbe transport (Ginn, 2002; Bradford et al., 2003; Scheibeand Wood, 2003). The models of Ginn (2002) and Scheibe andWood (2003) are based on the truncation of the distribution of
local dispersive displacements in a random-walk particle model.
Journal of Environmental Quality

The pore-water velocity and apparent dispersion in Eq. [1] werepredicted to increase and decrease, respectively, as a result of
exclusion (Scheibe and Wood, 2003). Bradford et al. (2003)
related the microbe size to an excluded pore size that was usedin existing hydraulic property models to predict the effects
of exclusion on qw and qw (Eq. [1]). Earlier breakthrough waspredicted for greater amounts of exclusion (e.g., larger microbes
and finer soil textures) and for more graded soils.

Chemotaxic Migration
Chemotaxic migration of motile microbes may occur in
response to an increasing concentration gradient of a chemoattractant (e.g., nutrients) or a decreasing concentration gradientof a chemo-repellant (Ford and Harvey, 2007). Chemotaxis
requires energy to follow the chemical gradient through acomplex network of pores and pore throats. Consequently,
chemotaxis has been reported to be closely linked to growth
processes and may be an important transport mechanism in lownutrient environments (Murphy and Ginn, 2000). Chemotaxic
migration may be simulated using Eq. [1] after modifying qw andD (Ford and Harvey, 2007; Wang et al., 2008; Wang and Ford,2009). In particular, the value of qw is replaced with qw + qwvc,
where vc [L T−1] is the component of the chemotaxic velocity inthe direction of qw. The value of vc may be determined as (Chenet al., 1998)
é
ù
Kc
¶a ú
1ê
vc = ê c o[8]ú3 ê ( K c + a)2 ¶z úëûwhere co [L2 T−1] is the chemotactic sensitivity coefficient, Kc[M L−3] is the chemotactic binding constant, and a [M L−3] isthe chemo-attractant concentration. The diffusion coefficientfor motile bacteria has been reported to be up to three ordersof magnitude greater than nonmotile bacteria (Camesano andLogan, 1998). However, dispersion may dominate D undertypical groundwater velocities (Ford and Harvey, 2007).

Physical Nonequilibrium
The conventional transport model assumes uniform flow
and Fickian dispersion. Many laboratory and field experiments
have demonstrated more complex flow and transport behavior
because of spatial variations in soil texture and structure (e.g.,fractured rock; cracks in clayey soils; macropores in agriculturalsoils from earthworms, animals, and/or decaying roots; orinter- and intraaggregate pore space) (Evans and Owens, 1972;
Beven and Germann, 1982; Dean and Foran, 1992; Guber et al.,2005; Cey and Rudolph, 2009; Cey et al., 2009; Garbrecht etal., 2009; Jarvis, 2007; McGechan and Lewis, 2002; Pang et al.,2008; Passmore et al., 2010; Fox et al., 2012; Wang et al., 2013).
For example, breakthrough curves for solutes and microbes
in soils frequently exhibit early arrival and concentration
tailing or multiple peaks (e.g., Wang et al., 2013). Transportmodels of varying complexity have been developed to simulate
nonequilibrium flow and transport processes (Dhawan et al.,
1993; McGechan and Vinten, 2003, 2004; Gharasoo et al., 2012;
Guzman and Fox, 2011; Martins et al., 2013). Detailed reviews
on nonequilibrium flow and transport models are available in
the literature ( Jarvis, 2007; Šimůnek and van Genuchten, 2008;
Köhne et al., 2009) and are only briefly outlined below.
www.agronomy.org • www.crops.org • www.soils.org

Physical nonequilibrium models include the mobile–immobile water model (e.g., van Genuchten and Wierenga,1976), the dual-porosity model (Philip, 1968; Šimůnek etal., 2003), and the dual-permeability model (Gerke and van
Genuchten, 1993a, 1993b; Šimůnek and van Genuchten, 2008).
The mobile–immobile model assumes uniform water flow (theRichards equation) and solves separate transport equations formobile and immobile water fractions with diffusive exchange
between the domains. The dual-porosity model is similar to
the mobile–immobile model but allows for exchange between
the domains due to both advection and diffusion. The dualpermeability model considers separate water flow and transport
equations for fracture (fast) and matrix (slow) domains and allows
for exchange by advection and diffusion. The dual-permeability
model has been further extended to include immobile water anddiffusive exchange within the matrix domain (Pot et al., 2005;
Köhne et al., 2006).
Alternatively, non-Fickian models for dispersion have beendeveloped to account for physical nonequilibrium processes.
Examples of these types of models include the fractional
advection–dispersion equation (e.g., Benson et al., 2000) andthe continuous-time random walk approach (Cortis et al.,2006; Shapiro, 2007; Yuan and Shapiro, 2010). The non-Fickiantransport behavior of the continuous-time random walk approach
can be simply approximated by including a temporal dispersion
term (e.g., the second partial derivative of concentration withrespect to time multiplied by a temporal dispersion coefficient)in Eq. [1] (Shapiro, 2007; Yuan and Shapiro, 2010).

Microbial Retention
Retention profiles for microbes and other colloids frequently
exhibit a shape that is not exponential with depth as predicted
by Eq. [2]. Rather, retention profiles have been observed to be
hyperexponential (Albinger et al., 1994; DeFlaun et al., 1997;
Baygents et al., 1998; Simoni et al., 1998; Bolster et al., 2000;
Redman et al., 2001; Zhang et al., 2001; Bradford et al., 2003; Liet al., 2004), nonmonotonic (Tong et al., 2005; Bradford et al.,2006a), or uniform (Xu et al., 2006; Bradford et al., 2009a) with
distance. Furthermore, breakthrough curves for microorganisms
are sometimes retarded (Bales et al., 1991; Powelson et al., 1993)
or exhibit a decreasing (blocking) or increasing (ripening) rate ofretention with time (Deshpande and Shonnard, 1999; Bradford
et al., 2006a; Tufenkji, 2007; Kim et al., 2010a). Consequently,
a variety of alternative models for microbial retention have beendeveloped.

Blocking
Equation [2] assumes that ksw is a constant with time. Under
unfavorable attachment conditions, only a small fraction of
the SWI may contribute to retention (Bradford et al., 2009a).
Consequently, ksw may decrease with time as available retention
sites become filled—a process known as blocking. In this case, Eq.
[2] is rewritten as
rb¶S= Esw + Bs = q w ysw ksw C -r b krs S + Bs¶t

[9]where ysw is a dimensionless function. A similar modification
can be made to Eq. [4] to account for blocking on the AWI. The
Langmuirian dynamics (Adamczyk et al., 1994) and random425

sequential adsorption (RSA) ( Johnson and Elimelech, 1995)
models have been developed to account for blocking phenomena.
The Langmuir model assumes that ysw is a linear function of S
that is given as

y sw = 1-

S
Smax

[10]

where Smax [N M−1] is the maximum retained solid-phasemicrobe concentration. Conversely, the RSA model assumes that
ysw is a nonlinear function of S. Breakthrough concentrations
will increase with time and retention profiles will change fromexponential to uniform in shape as Smax fills. If the value of ksw is
sufficiently large, retarded breakthrough curves may also occur
when using Eq. [9] and [10] (Harmand et al., 1996; Torkzaban
et al., 2010a, 2012). This filling process will be highly sensitive tothe input pulse duration and concentration, solution chemistry,
and flow velocity when values of Smax are small (Bradford et al.,2009a).
The value of Smax is commonly viewed as an empirical fitting
parameter, but it may also be estimated from the fraction of
the surface area (Sf ) that contributes to retention. The value ofSf can be determined from a balance of applied hydrodynamic
and resisting adhesive torques over a porous medium surface(Bradford et al., 2011b; Bradford and Torkzaban, 2012). Resultsfrom such calculations indicate that Smax will be sensitive to
microbe deformation, the microbe size and surface charge, thesolution chemistry, the amount of chemical heterogeneity, theflow velocity, the amount and size of the roughness, and the grain
size and number of grain–grain contact points (Bradford et al.,2013b). In addition, competitive retention of other colloids (e.g.,organic matter and clays) and solutes (e.g., phosphate ions andsurfactants) may reduce or increase Sf in particular locations(Liang et al., 2013). The value of aSf has been used to correct afor the influence of hydrodynamics (Shen et al., 2010; Bradford
et al., 2012) or to correct Sf for the effect of diffusion (Bradford
et al., 2013b).

Ripening
Microbes may experience an increase in the rate of retention
with time as a result of attractive interactions between microbes
in the aqueous phase and those retained on the solid phase that
produces decreasing effluent concentrations with time following
breakthrough (Chiang and Tien, 1985a, 1985b; Tien, 1989;
Deshpande and Shonnard, 1999; Tufenkji, 2007). This process
is known as ripening, and it can theoretically be described using
a functional form of ysw that increases with the retained microbemass. For example, Hosseini and Tosco (2013) accounted forripening using the following empirical expression:

ysw = 1 + AS b

426

Multiple Retention Rates
Different rates and strengths of microbial interaction with
the SWI are possible for a variety of reasons. For example,
strong primary minimum interactions may rapidly occur as aresult of nanoscale physical (e.g., roughness) and/or chemical(e.g., mineral defects, isomorphic substitution, protonation–
deprotonation of hydroxyl groups, and adsorption of different
ions, organics, and clay particles) heterogeneity on the SWI and/or microbial suspension that locally reduces or eliminates theenergy barrier (Duffadar and Davis, 2007, 2008; Bendersky andDavis, 2011) or because a fraction of the microbial population
may possess sufficient kinetic energy to diffuse over the energy
barrier to the primary minimum (Shen et al., 2007). Conversely,
relatively slower and weaker interactions of microbes with the
SWI may occur in a secondary minimum depending on thechemical and hydrodynamic conditions (Torkzaban et al., 2007,2008; Kuznar and Elimelech, 2007). Two modeling approaches
that have been developed to describe different rates and types of
microbial retention are briefly discussed below.

[11]

where A [Mb N−b] and b (dimensionless) are fitting parameters.
Alternatively, ripening may also be modeled by adding a separate
term to Eq. [9] as (Bradford et al., 2005b; Bradford and Bettahar,
2006)
¶S
rb
= Esw + Bs¶t
= q w ysw ksw C +q w C r b Skint -r b krs S + Bs

where kint [L3 T–1 N–1] is the microbe interaction rate coefficient.
Enhanced retention as a result of ripening is simulated using
the second term on the right-hand side of Eq. [12]. Similar
to aggregation models (a review was given by Elimelech et al.,1995), this approach assumes that ripening is second orderwith respect to concentration and therefore proportional to thefrequency of collisions between microbes in the aqueous phase(qwC) and immobilized microbes on the collector surface (rbS).
Figure 2 presents observed and simulated breakthrough curves
for pathogenic E. coli O157:H7 in 275-mm ultrapure quartz sandwhen the Darcy water velocity was 0.1 cm min−1, the IS = 0.01
mmol L−1 KCl, and the solution pH = 5.8. Other experimental
details were provided by Kim et al. (2010a). In this case, ripening
behavior was observed for the E. coli O157:H7 transport, andEq. [1] and [12] were used to simulate the observed behavior.
Transport parameters were obtained by inverse optimization to
the data. Note that the model provides an excellent descriptionof the observed breakthrough data that exhibits ripening andsignificant concentration tailing (coefficient of linear correlation>0.96).

[12]

Fig. 2. Observed and simulated breakthrough curves for pathogenic
E. coli O157:H7 in 275-mm ultrapure quartz sand when the Darcy
water velocity was 0.1 cm min−1, the solution ionic strength was 0.01
mmol L−1 KCl, and the solution pH was 5.8. Other experimental details
were provided by Kim et al. (2010a). The conventional model was
modified to simulate the observed ripening behavior using Eq. [12].
Journal of Environmental Quality

Retention models have considered two kinetic sites that are
similar to Eq. [9] (Schijven and Hassanizadeh, 2000; Schijvenand Šimůnek, 2002; Bradford et al., 2003; Gargiulo et al.,2007a). Both retention sites may be reversible (Schijven andŠimůnek, 2002), or one site may be irreversible and the secondsite reversible (Bradford et al., 2003). A faster rate is typicallyassumed for the irreversible site to be consistent with straining or
primary minimum interactions, whereas a slower rate is used torepresent attachment in a secondary minimum on the reversible
site. One- and two-site kinetic models are mathematicallyequivalent when only a single value of krs is considered; however,differences in the simulated breakthrough curves and retention
profiles occur when separate krs and/or ysw terms are consideredon each kinetic site.
Population heterogeneity (size or charge) of a microbial
suspension can be simulated explicitly using multispecies
transport models. In this case, separate transport equations(Eq. [1]) may be used for discrete or continuous distributionsof microbial subpopulations (Baygents et al., 1998; Bolster
et al., 1999; Tufenkji et al., 2003; Tufenkji and Elimelech,
2005b; Bradford et al., 2006a; Bradford and Toride, 2007;
Chatterjee and Gupta, 2009; Shapiro and Bedrikovetsky, 2010;
Landkamer et al., 2013). This approach increases the flexibilityof the simulation output (allowing for hyperexponential,
nonmonotonic, and uniform retention profiles) but requires
knowledge of the population heterogeneity, exchange rates
between the subpopulations, and retention coefficients foreach subpopulation. Independent determination of all of theseparameters is a daunting task. Consequently, most deterministic
multispecies models consider only two discrete subpopulations(Bolster et al., 1999; Tufenkji and Elimelech, 2005b; Bradford etal., 2006a; Chatterjee and Gupta, 2009; Landkamer et al., 2013).
In contrast, probabilistic modeling approaches use continuous
single or joint probability density functions to generate input
parameters that are iteratively used in a deterministic model (e.g.,
Tufenkji et al., 2003; Bradford and Toride, 2007). The model
outputs can subsequently be analyzed statistically to determinemean values and confidence intervals.

Physical and Chemical Nonequilibrium Models
A growing body of experimental and theoretical evidence
indicates that microbe retention is a combined chemical andphysical nonequilibrium process. Many physical nonequilibrium
processes can occur in homogeneous porous media. For
example, pore-scale simulations of the flow field at grain–
grain contacts, at large-scale roughness locations, and near the
air–water–solid (AWS) triple point clearly show eddy zones
that are hydrodynamically isolated from the bulk fluid flow
(Taneda, 1979; Sheng and Zhou, 1992; Torkzaban et al., 2008;
Cardenas, 2008; Li et al., 2010a, 2010b). Microbes that are
weakly associated with the SWI and/or AWI can be funneledby hydrodynamic forces to locations where they can become
immobilized (Torkzaban et al., 2007, 2008; Kuznar andElimelech, 2007; Lazouskaya and Jin, 2008; Zevi et al., 2012).
Enhanced microbe retention has been observed to occur where
the hydrodynamic force is weaker (grain–grain contacts, surface
roughness, and the AWS triple point) or the adhesive force isstronger (chemical heterogeneity) (Crist et al., 2004, 2005;
Bradford et al., 2005a, 2006a; Gao et al., 2006; Li et al., 2006a,
www.agronomy.org • www.crops.org • www.soils.org

2006b; Yoon et al., 2006; Xu et al., 2006; Choi et al., 2007;
Gaillard et al., 2007; Lazouskaya and Jin, 2008; Tong et al., 2008;
Zevi et al., 2005, 2009, 2012; Zhang et al., 2010).
Two-region models have been used to simulate different ratesof microbial transport that occur in the bulk aqueous phase(Region 1) and in low-velocity regions (Region 2) adjacent to
the SWI in homogeneous porous media (Bradford et al., 2009b,
2011a, 2012; Yuan and Shapiro, 2011). Rigorous derivation of
the two-region model by volume averaging still has not appearedin the literature. Nevertheless, the two-region transport model
is mathematically equivalent to the well-established dualpermeability transport model, and these names have been usedinterchangeably in the literature. The microbial mass balance
equations for Regions 1 (bulk fluid) and 2 (adjacent to the solid
phase) are given for saturated conditions (no AWI) as¶ (q w1C1 )¶t¶ (q w2C2 )¶t¶J1-q w1a i k12C1¶z+q w2 (1-a i ) k21C2 + Bw1

[13]

¶J 2
+q w1a i k12C1¶z-q w2 (1-a i ) k21C2 - Esw + Bw2

[14]

=-

=-

where subscripts 1 and 2 denote the respective regions, J [N L−2
T−1] is the microbe flux (sum of the advective and dispersive
fluxes), k12 [T−1] is the mass transfer coefficient for microbes
from Regions 1 to 2, k21 [T−1] is the mass transfer coefficientfor microbes from Regions 2 to 1, and ai (dimensionless) is aninteraction efficiency. The value of Esw is given in the two-region
model in a similar manner to Eq. [9] asrb¶S= Esw + Bs = q w2 ysw ksw C2 -r b krs S + Bs
¶t

[15]

where the parameter ksw = v2/duf (Bradford et al., 2011a), wherev2 [L T−1] is the pore-water velocity in Region 2 and duf [L] is theaverage distance that the microbes travel in Region 2 before theyfind a retention location.
Bradford et al. (2011a) demonstrated that hyperexponential,
exponential, nonmonotonic, and uniform retention profiles
occurred when using the two-region model depending on thehydrodynamic, solution chemistry, and input concentration
conditions. Various combinations of irreversible (solid phase)and reversible (Region 2) retention are achieved depending on
the values of ai, k21, and ksw. Favorable attachment conditions(irreversible retention) occur when ai = 1 and ksw is high(immobilization is instantaneous). Unfavorable, irreversible
retention is achieved in the model when ai < 1 and ksw is high;e.g., results are analogous to conventional filtration theory whenai = a and ysw = 1. Unfavorable, completely reversible retention
occurs when ai < 1 and ksw = 0. In this case, microbes in Region
2 move slowly over the solid surface (reversibly retained on thesolid) and the term k21 is multiplied by (1 − ai) to account for
the influence of the strength of the adhesive interaction on therelease of mobile microbes in Region 2. The two-region model istherefore ideally suited to handle a blurred distinction between
favorable and unfavorable conditions, which frequently occurs
427

in natural porous media. In addition, earlier breakthroughbehavior (similar to size exclusion) sometimes occurred for larger
microbes.
Figure 3 presents observed and simulated breakthrough curves(Fig. 3a) and final retention profiles (Fig. 3b) for pathogenic
E. coli O157:H7 in various quartz sands (d50 = 710, 360, 240,
and 150 mm) when the Darcy water velocity was approximately
0.1 cm min−1. Figure 4 presents similar information in 150-mm
quartz sand when the Darcy water velocity was 0.017, 0.102, and
0.177 cm min−1. The experimental data were previously describedin detail by Bradford et al. (2006a). In brief, the solution IS
was 1 mmol L−1 NaBr, the solution pH was buffered to 6.7,
and the porosity was about 0.35. The simulation results wereobtained using the two-region model (Eq. [13–15]), and theretention profiles were plotted in terms of the total normalized
concentration [CT = (qw1C1 + qw2C2 + rbS)/Co] as a function ofdimensionless distance (z divided by the column length). The
parameter k12 was determined using filtration theory (Eq. [3]with a = 1 and h determined with the correlation equation of
Tufenkji and Elimelech [2004]). In contrast to the traditional
dual-permeability model, only one flow equation needs to besolved to determine the total water content and flow rate inhomogeneous porous media. The hydrodynamic parameters(water contents and velocities for both regions) were obtained
from this information and scaling relations developed frompore-scale water flow simulations in sphere packs (Bradford etal., 2011b). The parameters that depend on adhesive interactions
were obtained by inverse optimization to the transport data forthe 150-mm sand when the Darcy water velocity was 0.1 cm min−1

as ai = 0.05, Sf = 0.007, k21 = 0, and ksw = 0.01 min−1 and assumed
to be constants for the other sand sizes and Darcy velocities.
Consequently, the simulated transport behaviors in Fig. 3
when d50 = 710, 360, and 240 mm are independent predictions.
Similarly, predictions are shown in Fig. 4 for Darcy velocities of
0.017 and 0.177 cm min−1.
The two-region model correctly predicted the trend of
decreasing cell retention with increasing grain size (Fig. 3) andincreasing water velocity (Fig. 4). Some deviation in the observed
and simulated retention profiles occurred because of experimental
mass balance errors that occurred due to irreversible cell retention.
However, the model was able to describe the general trends of thenonmonotonic retention profiles for different grain sizes andvelocities, which cannot be simulated using the conventional
approach (Eq. [1] and [2]). Collectively, Fig. 3 and 4 demonstratethat the two-region model is a promising approach to accountfor observed differences in microbe transport and retention
for different grain sizes and velocities. Additional theory andinnovative approaches are needed to predict the parameters of
the two-region model. In particular, prediction of the adhesive
parameters (ai, Sf, k21, and ksw) for different chemical conditions
and the hydrodynamic parameters for different soil types (grain
size distributions, nonspherical shape, and roughness) and watercontents remains a challenge.

Microbial Release
Residence Time
The strength of colloid and microbial adhesion to the SWI
has been reported to increase with contact time (Kolakowski

Fig. 3. Observed (top) and simulated (bottom) breakthrough curves (left) and final retention profiles (right) for pathogenic E. coli O157:H7 invarious quartz sands (median grain size d50 = 710, 360, 240, and 150 mm). The experimental data were previously described in detail by Bradford
et al. (2006a). The simulated results were obtained using the two-region model (Eq. [13–15]) with values of interaction efficiency ai = 0.05, thefraction of the surface area that contributes to retention Sf = 0.007, mass transfer coefficient for microbes from Region 2 to 1 k21 = 0, and theretention rate coefficient to the solid–water interface ksw = 0.01 min−1 fitted to 150-mm data and other parameters predicted.
428

Journal of Environmental Quality

Fig. 4. Observed (top) and simulated (bottom) breakthrough curves (left) and final retention profiles (right) for pathogenic E. coli O157:H7 in
150-mm quartz sand under various Darcy water velocities (q = 0.017, 0.102, and 0.177 cm min−1). The simulated results were obtained using thetwo-region model (Eq. [13–15]) with values of interaction efficiency ai = 0.05, the fraction of the surface area that contributes to retention Sf =0.007, mass transfer coefficient for microbes from Region 2 to 1 k21 = 0, and the retention rate coefficient to the solid–water interface ksw = 0.01
min−1 fitted to q = 0.102 cm min−1 data and other parameters predicted. No additional parameter optimization was undertaken.

and Matijevic, 1979; Dabroś and Van De Ven, 1982; Weiss et al.,
1998; Xu and Logan, 2006; Kumar et al., 2013). This has been
attributed to plastic deformation that increases the contact area
(Weiss et al., 1998; Kumar et al., 2013), water exclusion, protein
rearrangement and conformation, and bond formation (Ginn etal., 2002; Xu and Logan, 2006), and cell-surface changes such as
the production of extracellular polymeric substances (Williams
and Fletcher, 1996; Jucker et al., 1997). Consequently, the release
rate of microbes from the SWI may decrease with residence time
( Johnson et al., 1995; Ginn, 2000a), and this effect probably
contributes to the observed hysteresis in colloid and microberelease with transients in solution IS (Torkzaban et al., 2010b;
Bradford and Kim, 2012; Bradford et al., 2012).
Ginn (2000ab) presented a modeling framework to simulate
microbial release that is dependent on the residence time. Thistransport model is written for saturated conditions as¶q w C ¶q w vwwC¶æ¶C ÷ö ¶qw C+= ççq w D
÷ç
¶t
¶w
¶z è
¶z ÷ø
¶z
-q w y sw ksw C +r b krs (w) S + Bw

[16]

information is currently available on the proper functional
form for krs(w). Dabroś and Van De Ven (1982), Meinders etal. (1992), and Johnson et al. (1995) proposed that krs(w) is aconstant when w < w* and drops to a lower value when w ≥ w*,
where w* [T] is a critical value of w. This is implemented in theresidence time model as follows. When the cumulative residence
time on a surface controls the microbe release rate, there is a
1:1 correspondence between w and the total time the microbe
has spent on the SWI. In this case, the value of vww = 0 and vsw= 1 (Ginn, 2000b). Conversely, a contiguous residence time
description is needed when microbes do not retain any structural
memory of changes induced on the SWI, in which case vsw = 1
and Eq. [16] is replaced with a form that has no w coordinate andthat assigns detaching microbial fraction at w = 0 (Ginn, 2000b):¶q w C ¶q w vwwC
+
=
¶t
¶w
¶ æç
¶C ö÷ ¶qw C-q w y sw ksw C÷ççq w D
¶z è
¶z ÷ø
¶z
+d (w) ò

¥

0

rb

¶v S
¶S
+r b sw = q w ysw ksw C -r b krs (w)S + Bs
¶t
¶w

[17]

where w [T] is the residence time, vww (dimensionless) is the rateof displacement of aqueous-phase microbes in the resident time
dimension, and vsw (dimensionless) is the rate of displacementof solid-phase microbes in the resident time dimension. Little
www.agronomy.org • www.crops.org • www.soils.org[18]

r b krs (w)S (w)dw + Bw

Aqueous Chemistry
Microorganism release is known to be sensitive to temporalchanges in solution chemistry (Lenhart and Saiers, 2003;
Grolimund and Borkovec, 2006; Tosco et al., 2009; Bradford
et al., 2012) and flow rate (Bergendahl and Grasso, 1998,
1999, 2000). The conventional release term in Eq. [9] is unable429

to account for such observations because only a fraction of
the deposited particles are released with a change in solution
chemistry. Several models for microbe transport, retention, andrelease during transient solution chemistry conditions have beenpresented in the literature (Lenhart and Saiers, 2003; Grolimundand Borkovec, 2006; Tosco et al., 2009; Bradford et al., 2012).
In general, microbe transport equations are coupled to thegeochemistry by making relevant microbe retention parameters(e.g., a and Smax) functions of solute concentrations (e.g., ionicstrength and/or adsorbed divalent cations). The transport
equations for geochemistry and microbes are subsequently solved
and microbe transport parameters are updated at each time step.
Bradford et al. (2012) outlined such an approach for transient
IS conditions. In this case, the solid-phase mass balance equation
is given as
rb¶S= Esw + Bs¶t
= q w ysw ksw C[19]-r b krs (S - f c Si ) H o (S - f c Si ) + Bs

where Si [N M−1] is the value of S before a change in chemicalcomposition, fc (dimensionless) is the fraction of retained
microbes that are not released with a change in chemicalcomposition, and Ho(S − fcSi) is the Heaviside function that isequal to 1 when S > fcSi and 0 when S ≤ fcSi. The value of fc isgiven as

fc =

Seq

S
Sf
= max =
Sif Simax
Si[20]

where Sif (dimensionless) is the value of Sf before the change inchemistry, Simax [N M−1] is the value of Smax before the change inchemistry, and Seq [N M−1] is the equilibrium value of S at the endof the chemical perturbation. When these equations are written
in terms of Sf, the amount of microbes that is released is directly
related to changes in the balance of the applied hydrodynamic
and resisting adhesive torques. Consequently, this approach
applies to both transient solution chemistry and hydrodynamic
conditions. As mentioned above, a wide variety of factors are
known to influence Sf.
Figure 5 presents the observed and simulated breakthroughand release curves for E. coli D21g under transient IS conditions.
The experimental data and simulation were previously presented
by Bradford et al. (2012). In brief, the transport experiment
was conducted in 360-mm Ottawa sand at a Darcy watervelocity of around 0.1 cm min−1. A pulse of E. coli D21g was
flushed through the column in 106 mmol L−1 NaCl solution at
pH = 10, and then the IS of the cell-free eluting solution was
decreased in steps of 106, 56, 31, 6, and 0 mmol L−1 NaCl. The
simulation result was obtained using the two-region model (Eq.
[13], [14], and [15]), with release modeled using the second
term on the right-hand side of Eq. [19]. The determination of
the two-region model parameters was already outlined above.
The parameters ai and Sf were functions of the simulated IS(1:1 electrolyte) that were determined from experimental
results, and other model parameters were either predicted or
obtained from a sensitivity analysis (Bradford et al., 2012).
Results demonstrated that cell release was especially sensitive to430

Fig. 5. Observed and simulated breakthrough and release curves
for E. coli D21g under transient ionic strength (IS) conditions. The
experimental data and simulation were previously presented by
Bradford et al. (2012). A pulse of E. coli D21g was flushed through thecolumn in 106 mmol L−1 NaCl solution at pH = 10, and then the IS of
the cell-free eluting solution was decreased in steps of 106, 56, 31, 6,
and 0 mmol L−1 NaCl. The simulation result was obtained using thetwo-region model with release modeled using the second term on
the right-hand side of Eq. [19].

low solution IS. There is currently a need to develop predictive
procedures to determine the effects of solution chemistry,
aging time, and nanoscale heterogeneity on ai and Sf. This isespecially true for microorganisms that exhibit electrosteric
repulsion (Fig. 1b).

Water Saturation
Transients in water content commonly occur in thevadose zone as a result of infiltration and drainage events,
evapotranspiration, and fluctuations in the water table height
and/or surface water levels (waves, tides, and river stage). Several
mathematical models have been developed to simulate thesubstantial amounts of colloid and microbe release that have been
observed with changes in water saturation (Saiers and Lenhart,
2003; Cheng and Saiers, 2009; Zhang et al., 2012; Russell et al.,2012). Saiers and Lenhart (2003) simulated colloid release usinga kinetic expression that included a dependence on the porewater velocity. Zhang et al. (2012) simulated virus interactions
at the AWI using a linear equilibrium partition coefficient andretardation factor. Cheng and Saiers (2009) and Russell et al.
(2012) used a kinetic expression that was a function of temporalchanges in water content (¶qw/¶t) to represent the propagationof the AWI at a particular location. Release was turned on bya distribution of snap-on/snap-off pressure heads in the modelof Cheng and Saiers (2009), whereas positive values of ¶qw/¶t(imbibition) turned on release in the model of Russell et al.
(2012). Equation [9] may be rewritten to include the releasemodel of Russell et al. (2012) as

rb¶S= Esw + Bs¶t
= q w y sw ksw C -r b krs S-r b krt S[21]

æ ¶q ö
¶q w
H o çç w ÷÷÷ + Bsçè ¶t ø
¶twhere krt (dimensionless) is the release rate coefficient associatedwith transients in water content and Ho(¶qw/¶t) is the Heavisidefunction that is equal to 1 when ¶qw/¶t > 0 (imbibition) and
Journal of Environmental Quality

0 when ¶qw/¶t £ 0 (drainage). Additional experimental andmodeling research is needed to directly relate microbial releaseduring transient saturation conditions with changes in the AWI
area and the adhesive force.

where m [T−n] and n (dimensionless) are empirical parameters.
Additional inactivation models are discussed in the literature(Oliver et al., 2006, 2010).

Microbial Survival

Expressions from Monod (1942), Tessier (1942), Contois(1959), or Andrews (1968) are commonly used to simulate
microbial growth These models relate specific growth rates with
substrate concentrations using saturation kinetics. For example,
the Monod model relates the microbial population growthrate to the concentration of a limiting nutrient (Ng [M L−3]) as(Monod, 1942)

Survival is an extremely complex process that depends on awide variety of abiotic and biotic factors that may not always
be independent, including: nutrient levels, degree of water
saturation, temperature, pH, dissolved and particulate organicC, ionic strength/salinity, redox conditions, presence or absenceof biofilms, environmental microbial diversity and ecology,
physicochemical characteristics of the solid phase, and nature of
the rhizosphere (Schijven and Hassanizadeh, 2002; Harvey and
Ryan, 2004; Berry and Miller, 2005; Foppen and Schijven, 2006;
Cook and Bolster, 2007; Bradford et al., 2013a). Consequently,
mechanistic modeling of microorganism survival using simple
first-order expressions (Eq. [5–7]) is frequently inadequate todescribe the observed behavior (Petterson et al., 2001; Johnand Rose, 2005; Charles et al., 2008; de Roda Husman et al.,2009). Potential models to quantify the effects of temperature,
population heterogeneity, nutrients, and competition on thesurvival parameters Xw and Lw (Eq. [5]) are discussed below.
Similar expressions may be developed for the solid and air phases.

Decay
Temperature is widely recognized to be one of the mostcritical factors in determining microorganism decay, and its
effect may be described using the Arrhenius equation (Stumm
et al., 1981):

é Ea (Tk -Tr ) ùúX w (Tk ) = X r exp êê
ú
RT
T
k
r
ëê
ûú

[22]

where Tk is temperature (K), R (8.3144621 J mol−1 K−1) is theuniversal gas constant, Ea ( J mol−1) is the activation energy, andXr [T−1] is the reference decay rate at a reference temperature (Tr,K). Equation [22] requires knowledge of the temperature at agiven location and time. Heat movement can be modeled using
numerical or analytical solutions of an advection–dispersiontype equation (e.g., Šimůnek et al., 2008).
A number of studies have indicated the presence of
microbial subpopulations that are more or less persistent underenvironmental conditions (Besnard et al., 2002; Kussell et al.,2005; Proctor et al., 2006; Cook and Bolster, 2007; Morohashi
et al., 2007; Oliver, 2010; Rotem et al., 2010). Intrapopulation
variability is evident in the ability of some bacteria to form robust
spores (Morohashi et al., 2007) or to enter a pseudo-dormant
viable but nonculturable state (Kussell et al., 2005; Proctor et al.,2006; Oliver, 2010). The effects of population heterogeneity on
decay have been modeled using time-dependent, pseudo-firstorder rate coefficients (Sim and Chrysikopoulos, 1996; Pelegand Cole, 1998; Chrysikopoulos and Vogler, 2004; Molin andCvetkovic, 2010). For example, the Weibull model (e.g., Pelegand Cole, 1998) describes the time dependency of the decaycoefficient as
X w (t ) = mnt n-1
www.agronomy.org • www.crops.org • www.soils.org[23]

GrowthLw =Lmax N g
K N + Ng[24]

where Lmax [T−1] is the maximum specific growth rate when
Ng >> KN, and KN [M L−3] is the value of Ng when Lw/Lmax =0.5. Monod expressions may be further modified to accountfor the utilization of electron donors, electron acceptors,
multiple substrates, yield coefficients, and inhibition
functions (Bailey and Ollis, 1977; Rathfelder et al., 2000;
Mohamed et al., 2007).
Microbial survival in microcosm experiments has frequently
been simulated using the logistic model (Semenov et al., 2009)and its variants (Verhulst, 1838; Gabriel et al., 2005; Yukalov
et al., 2009). The logistic model considers the effects of both
growth and competition on microbial survival:

æ
C ö÷
÷
L w (C ) = Lo ççç1çè Cmax ÷÷ø[25]

where Lo [T−1] is the growth rate in the absence of competition
and Cmax [N L−3] is the maximum microbe concentrationthat is associated with the upper limit of population growth.
The logistic model predicts that microbe concentrations will
increase when C < Cmax reaches a plateau at C = Cmax and will
decrease when C > Cmax. Theoretically, the value of Cmax is
expected to change with the biogeochemical conditions, andthe logistic model has been extended for this purpose (Yukalov
et al., 2009). The logistic model has been reported to provide asuperior description of pathogen survival in manure-amended
soils than linear, exponential, or Weibull survival models(Semenov et al., 2009).

Coupled Transport and Survival
Most models and research studies have separately examinedtransport and survival processes due to their individualcomplexity. In reality, transport and survival processes for
microbes may be highly coupled. This is especially true forbacteria that can undergo growth and/or decay. For example,
dynamic nutrient fronts can promote the division of retained“mother” cells and induce the transport of “daughter” cells,
a process referred to as cell-division-mediated transport(Reynolds et al., 1989; Sharma et al., 1993; Murphy and Ginn,
2000). Changes in the metabolic activity of cells with age andnutrient availability may also produce differences in cell surface
properties that promote release or enhance retention (Sanin etal., 2003; Gargiulo et al., 2007b). Models can be useful tools
to better understand the complex coupling between microbial431

transport and survival processes, which otherwise might beexperimentally intractable. For example, Murphy and Ginn
(2000) simulated the transport and dynamic partitioningof a consortium of anaerobic bacteria in response to a pulseof growth substrate. Gargiulo et al. (2007b) simulated thetransport and deposition of metabolically active and stationaryphase Deinococcus radiodurans in unsaturated sand. Below we
present several illustrative examples of simulated microbial
transport and survival at the column scale.
Figure 6 presents simulated breakthrough curves (Fig. 6a)and retention profiles (Fig. 6b, 6c, and 6d) for E. coli O157:H7
in 150-mm sand when considering Weibull decay (Eq. [23]).
Figure 6a also shows the sinusoidal temperature fluctuations at
the soil surface that were used to simulate the soil temperature
distribution with an analytic solution ( Jury et al., 1991). The
two-region model (Eq. [13–15]) was used in these simulations,using transport and retention parameters that were given in
Fig. 3. Three conditions were considered: (i) no death; (ii)
Weibull decay (Eq. [23]); and (iii) Weibull decay (Eq. [23])that used Eq. [22] to account for a temperature dependency onm. The same Weibull model parameters (m = 1.67 ´ 10−8 min−n
and n = 2.02419) were used for Regions 1 and 2 of the aqueous
phase and the solid phase. The retention profiles in Fig. 6b, 6c,
and 6d are shown after 1.0, 3.9, and 5.8 PV of eluting solution.
The effects of decay on breakthrough curves were rather
minimal for these small scale and short duration simulations.
In contrast, consideration of decay had a large impact on theamount and shape of the retention profile, especially at larger
PV, and temperature fluctuations further accentuated theseeffects. These hypothetical results demonstrate that decay will
have a controlling influence on transport behavior at larger
temporal scales and that neglecting these effects will lead toinaccurate model output and conclusions. However, the relative
importance of decay to transport and retention will depend on
the magnitudes of the model parameters. Consequently, model
simulations that consider transport, retention, and decay areuseful tools to understand these factors and to make informed
decisions.
Figure 7 presents simulated breakthrough curves (Fig. 7a)and retention profiles (Fig. 7c and 7d) for E. coli O157:H7 in
150-mm sand when considering logistic growth and/or death(Eq. [25]). The two-region model (Eq. [13–15]) was again usedin these simulations, using transport and retention parametersthat were given for Fig. 3. The logistic growth and/or deathmodel (Eq. [25]) was used in terms of CT; e.g., Eq. [25] wasrewritten as LT(CT ) = Lo(1 – CT/CTmax), where the subscript
T is used to denote variables associated with CT. Three valuesof CTmax were considered, namely: (i) CTmax = 1; (ii) CTmax =0.1; and (iii) CTmax that was determined by the transport ofa hypothetical nutrient and/or substrate shown in Fig. 7b.
The value of Lo was set equal to 0.012 min−1 in all cases. The
retention profiles in Fig. 7c and 7d are shown after 1.0, 3.9, and
5.8 PV of eluting solution. The simulation results demonstrate
a strong coupling between transport and retention behavior
and the value of CTmax. Very complex breakthrough curves andtailing behavior were obtained when considering the logistic
model. In particular, periods of growth (CT < CTmax) and death(CT > CTmax) occurred depending on the relative values of CT

Fig. 6. Simulated (a) breakthrough curves and (b,c,d) retention profiles for E. coli O157:H7 in 150-mm sand when considering: (b) no death; (c)Weibull survival (Eq. [23]); and (d) Weibull survival that used Eq. [22] to account for a temperature dependency of the empirical parameter m. Figure
6a also shows the sinusoidal temperature fluctuations at the soil surface. The two-region model was used in these simulations, using interaction
efficiency ai = 0.05, the fraction of the surface area that contributes to retention Sf = 0.007, mass transfer coefficient for microbes from Region 2 to
1 k21 = 0, and the retention rate coefficient to the solid–water interface ksw = 0.01 min−1.
432

Journal of Environmental Quality

Fig. 7. Simulated (a) breakthrough curves and (c,d) retention profiles for E. coli O157:H7 in 150-mm sand when considering no growth or death,logistic survival (Eq. [25]) with maximum total concentration CTmax = 1; logistic survival with CTmax = 0.1, and logistic survival with CTmax determinedby the transport of a hypothetical nutrient and/or substrate shown in (b). The two-region model was again used in these simulations using
interaction efficiency ai = 0.05, the fraction of the surface area that contributes to retention Sf = 0.007, mass transfer coefficient for microbes from
Region 2 to 1 k21 = 0, and the retention rate coefficient to the solid–water interface ksw = 0.01 min−1.

and CTmax. The results shown in Fig. 7 demonstrate the potential
for strongly nonlinear dynamic effects on the transport andfate of microorganisms that is dependent on biological factors(competition) and growth conditions (CTmax).
There is presently a need to study and predict microbial
transport and survival throughout a range of environmentally
relevant conditions at the laboratory scale. An understanding
and ability to simulate these effects at the field scale is evenmore complex due to the spatial and temporal variability ofconditions and parameters in the heterogeneous environmentsof the soil surface, the root zone, the vadose zone, and aquifers.
Consequently, deterministic modeling of microbial transportand survival through the collective transport pathways will be
exceedingly difficult.

Clogging
A reduction in soil porosity and permeability frequently
occurs in porous media due to the retention and release ofcolloids and microorganisms, and/or biological growth (reviews
have been given by Herzig et al., 1970; McDowell-Boyer et al.,
1986; Baveye et al., 1998; Khilar and Fogler, 1998; Pérez-Paricio
and Carrera, 1999; Mays and Hunt, 2005). As discussed above,these clogging processes will strongly depend on a wide varietyof physical, chemical, and biological properties that influenceretention, release, and growth. In turn, microbial retention,
release, and survival are expected to change in a nonlinear
manner as clogging progresses (Ives, 1970). Below we provide abrief overview of clogging models.
www.agronomy.org • www.crops.org • www.soils.org

A large number of empirical and theoretical models for
clogging have appeared in the literature (Ives and Pienvichitr,
1965; O’Melia and Ali, 1978; Taylor et al., 1990; Kildsgaard
and Engesgaard, 2002; Thullner et al., 2002a, 2002b, 2004;
Mostafa and Van Geel, 2007; Wissmeier and Barry, 2009;
Tosco and Sethi, 2010). Empirical clogging models haveestablished correlations between the time evolution of pressurebuildup (permeability decline) and key soil and water quality
properties. Most of these correlations have been developedfor infiltration rates at the soil surface and are site specific.
A detailed list of empirical clogging models was provided by
Pérez-Paricio and Carrera (1999). The soil permeability has
also been inversely related to some function of S, denoted asf(S). Various forms for f(S) have also appeared in the literature(Herzig et al., 1970; McDowell-Boyer et al., 1986; Mays andHunt, 2005). A large class of these models can be approximatedwhen f(S) is a polynomial function (McDowell-Boyer et al.,1986). Theoretical clogging models are more sophisticatedthan empirical correlations but are based on a number ofassumptions, and they require additional information onmodel parameters. These clogging models have been developed
based on the Kozeny–Carman equation (Ives and Pienvichitr,
1965; Taylor et al., 1990; Tosco and Sethi, 2010), pore
network models (Kildsgaard and Engesgaard, 2002; Thullner
et al., 2002a, 2002b, 2004), and pore-size distribution models(Mostafa and Van Geel, 2007; Soleimani et al., 2009; Wissmeierand Barry, 2009).

433

Kozeny–Carman type models relate changes in the soil
porosity and specific surface area with S to the saturated hydraulicconductivity as (e.g., Baveye et al., 1998)
é e(S ) ù 3 é A ùú ê so ú
K s (S ) = K so êêúú êeëê o ûú ëê As ( S ) ûú

2

[26]

where Ks [L T−1] is the saturated hydraulic conductivity,
Kso [L T−1] is the initial saturated hydraulic conductivity, e(dimensionless) is the porosity, eo (dimensionless) is the initialporosity, As [L2 M−1] is the specific surface area of the soil, andAso [L2 M−1] is the initial specific surface area of the soil. Valuesof e(S) and As(S) in Eq. [26] may be determined as (e.g., Tosco
and Sethi, 2010)

e(S ) = eo -

rb
S
rm

As (S ) = Aso + f A Am

[27]

rb
S
rm

[28]

where rm [M L−3] is the bulk density of the retained microbes,
Am [L2 M−1] is the specific surface area of the microbes, and fA(dimensionless) is the fraction of Am that contributes to theincrease in the surface area of the soil.
Clogging models based on the Kozeny–Carman equation
implicitly assume that microorganisms uniformly coat thegrain surfaces with a constant thickness at a particular location.
Experimental evidence indicates that this assumption may
not be valid in many instances (Baveye et al., 1998). Pore-size
distribution models may potentially overcome some of theselimitations by allowing for different microbial distributions in
the pore space under saturated or unsaturated conditions. For
example, Mostafa and Van Geel (2007) related S to a microbial
saturation [Sm = (rb/eorm)S] and then used this value in existing
pore-size distribution models (Burdine, 1953; Mualem, 1976;
Parker and Lenhard, 1987) to determine the water relative
permeability for various microbial distributions.

Conclusions
We have reviewed existing model formulations to simulate
microbial transport and survival in the subsurface. The
conventional model is based on the solution of the advection–
dispersion equation, with first-order kinetic terms for survivaland exchange with the SWI and AWI. This model is frequently
used to describe microbial transport experiments in which only
the breakthrough curve was measured. The limitations of thismodel may not be apparent under such circumstances because
the full mass balance (e.g., the soil) was not quantified. Whenexperiments have been designed to achieve mass balance, thenthe conventional model has frequently proven to be inadequate,
even when the model parameters were obtained by inverse
optimization.
Alternative model formulations were highlighted to describe
the observed kinetic retention on the SWI and AWI; blocking
and ripening; release that is dependent on the resident time,
diffusion, and transients in solution chemistry, water velocity,
and water saturation; and microbial decay and growth that isdependent on temperature, nutrient concentration, and/or the434

microbial concentration. In particular, we demonstrated that the
two-region model can be modified with appropriate terms for
microbial retention, release, and survival to describe a wide varietyof observed behavior. Nevertheless, parameter optimization was
frequently required to obtain a meaningful description of theexperimental data, and independent predictions at the column
scale are still not feasible. Consequently, model calibration
under site-specific conditions is highly recommended before
making predictions. In such cases, simulation results are usefulin predicting outcomes under given assumptions, testing
hypotheses, identifying conditions of vulnerability, developmentof treatment strategies, and for informing management decisions.
Models are especially useful for understanding the potential
effects of complex interactions that occur during microbial
transport and survival that are experimentally intractable.
There is still a critical need to improve our understanding
and description of many fundamental microbial transport,
retention, and survival processes and especially inindependently determining model parameters for dynamic
natural environments. In saturated systems, the retention andrelease parameters are known to be strong functions of thesystem hydrodynamics (qw, d50, and colloid size), the microbialconcentration, and the chemistry of the aqueous phase, the solid
phase, and the microbe. Few methods currently exist to predictthe dependency of retention parameters on these factors. In
addition, under unsaturated conditions, the rates of microbial
mass transfer and retention on the SWI and AWI have not yet
been quantified, and temporal changes in water saturation willfurther complicate microbial retention and release. Accurate
determination of survival parameters is hampered by massbalance errors that may arise from irreversible microbial
retention. Furthermore, microbial decay and growth are strongly
coupled to a wide variety of biotic and abiotic factors that areimperfectly characterized.

Acknowledgments
We would like to thank Scott Yates, Lifang Luo, and A. Mark Ibekwe
for helpful discussion concerning microbial survival, and Timothy Ginn
and Carl Bolster for constructive review comments that greatly improved
this manuscript. This research was supported by the Agricultural andIndustrial Byproducts project (NP 214) of the USDA-ARS.

References
Abudalo, R.A., Y.G. Bogatsu, J.N. Ryan, R.W. Harvey, D.W. Metge, and M.
Elimelech. 2005. Effect of ferric oxyhydroxide grain coatings on thetransport of bacteriophage PRD1 and Cryptosporidium parvum oocysts
in saturated porous media. Environ. Sci. Technol. 39:6412–6419.
doi:10.1021/es050159h
Adamczyk, Z., B. Siwek, M. Zembala, and P. Belouschek. 1994. Kinetics of
localized adsorption of colloid particles. Adv. Colloid Interface Sci.
48:151–280. doi:10.1016/0001-8686(94)80008-1
Albinger, O., B.K. Biesemeyer, R.G. Arnold, and B.E. Logan. 1994. Effectof bacterial heterogeneity on adhesion to uniform collectors by
monoclonal populations. FEMS Microbiol. Lett. 124:321–326.
doi:10.1111/j.1574-6968.1994.tb07303.x
Andrews, J.F. 1968. Mathematical model for the continuous culture of
microorganisms utilizing inhibitory substrates. Biotechnol. Bioeng.
10:707–723. doi:10.1002/bit.260100602
Asadishad, B., G. Subhasis, and N. Tufenkji. 2011. Method for the direct
observation and quantification of survival of bacteria attached tonegatively or positively charged surfaces in an aqueous medium. Environ.
Sci. Technol. 45:8345–8351. doi:10.1021/es201496q
Bailey, J.E., and D.F. Ollis. 1977. Biochemical engineering fundamentals.
McGraw-Hill, New York.
Journal of Environmental Quality

Bales, R.C., S.R. Hinkle, T.W. Kroeger, K. Stocking, and C.P. Gerba. 1991.
Bacteriophage adsorption during transport through porous media:
Chemical perturbations and reversibility. Environ. Sci. Technol. 25:2088–
2095. doi:10.1021/es00024a016
Banat, I.M. 1995. Biosurfactant production and possible uses in microbial
enhanced oil recovery and oil pollution remediation: A review. Bioresour.
Technol. 51:1–12. doi:10.1016/0960-8524(94)00101-6
Baveye, P., P. Vandevivere, B.L. Hoyle, P.C. DeLeo, and D.S. de Lozada. 1998.
Environmental impact and mechanisms of the biological clogging ofsaturated soils and aquifer materials. Crit. Rev. Environ. Sci. Technol.
28:123–191. doi:10.1080/10643389891254197
Baygents, J.C., J.R. Glynn, O. Albinger, B.K. Biesemeyer, K.L. Ogden, and R.G.
Arnold. 1998. Variation of surface charge density in monoclonal bacterial
populations: Implications for transport through porous media. Environ.
Sci. Technol. 32:1596–1603. doi:10.1021/es9707116
Bendersky, M., and J.M. Davis. 2011. DLVO interaction of colloidal particles
with topographically and chemically heterogeneous surfaces. J. Colloid
Interface Sci. 353:87–97. doi:10.1016/j.jcis.2010.09.058
Benson, D.A., S.W. Wheatcraft, and M.M. Meerschaert. 2000. Application ofa fractional advection–dispersion equation. Water Resour. Res. 36:1403–
1412. doi:10.1029/2000WR900031
Bergendahl, J., and D. Grasso. 1998. Colloid generation during batch leaching
tests: Mechanics of disaggregation. Colloids Surf. A 135:193–205.
doi:10.1016/S0927-7757(97)00248-3
Bergendahl, J., and D. Grasso. 1999. Prediction of colloid detachment in a model
porous media: Thermodynamics. AIChE J. 45:475–484. doi:10.1002/
aic.690450305
Bergendahl, J., and D. Grasso. 2000. Prediction of colloid detachment in amodel porous media: Hydrodynamics. Chem. Eng. Sci. 55:1523–1532.
doi:10.1016/S0009-2509(99)00422-4
Berry, E.D., and D.N. Miller. 2005. Cattle feedlot soil moisture and manurecontent: II. Impact on Escherichia coli O157. J. Environ. Qual. 34:656–
663. doi:10.2134/jeq2005.0656
Besnard, V., M. Federighi, E. Declerq, F. Jugiau, and J.-M. Cappelier. 2002.
Environmental and physico-chemical factors induce VBNC state in Listeria
monocytogenes. Vet. Res. 33:359–370. doi:10.1051/vetres:2002022
Beven, K., and P. Germann. 1982. Macropores and water flow in soils. Water
Resour. Res. 18:1311–1325. doi:10.1029/WR018i005p01311
Binnerup, S.J., D.F. Jensen, H. Thordal-Christensen, and J. Sørensen. 1993.
Detection of viable, but non-culturable Pseudomonas fluorescens DF57
in soil using a microcolony epifluorescence technique. FEMS Microbiol.
Ecol. 12:97–105. doi:10.1111/j.1574-6941.1993.tb00021.x
Bird, R.B., W.E. Stewart, and E.N. Lightfoot. 2002. Transport phenomena. 2nd
ed. John Wiley & Sons, New York.
Bolster, C.H., K.L. Cook, I.M. Marcus, B.Z. Haznedaroglu, and S.L. Walker.
2010. Correlating transport behavior with cell properties for eight
porcine Escherichia coli isolates. Environ. Sci. Technol. 44:5008–5014.
doi:10.1021/es1010253
Bolster, C. H., B. Z. Haznedaroglu, and S.L. Walker. 2009. Diversity in cellproperties and transport behavior among 12 different environmental
isolates. J. Environ. Qual. 38:465–472. doi:10.2134/jeq2008.0137
Bolster, C.H., A.L. Mills, G.M. Hornberger, and J.S. Herman. 1999. Spatial
distribution of deposited bacteria following miscible displacement
experiments in intact cores. Water Resour. Res. 35:1797–1807.
doi:10.1029/1999WR900031
Bolster, C.H., A.L. Mills, G. Hornberger, and J. Herman. 2000. Effect of intrapopulation variability on the long-distance transport of bacteria. Ground
Water 38:370–375. doi:10.1111/j.1745-6584.2000.tb00222.x
Bolt, G.H., and F.A.M. de Haan. 1979. Anion exclusion in soils. In: G.H. Bolt,
editor, Soil chemistry: B. Physico-chemical models. Elsevier, Amsterdam.
p. 233–257.
Bradford, S.A., and M. Bettahar. 2006. Concentration dependent transportof colloids in saturated porous media. J. Contam. Hydrol. 82:99–117.
doi:10.1016/j.jconhyd.2005.09.006
Bradford, S.A., and H. Kim. 2012. Causes and implications of colloid andmicroorganism retention hysteresis. J. Contam. Hydrol. 138–139:83–92.
doi:10.1016/j.jconhyd.2012.06.007
Bradford, S.A., H.N. Kim, B.Z. Haznedaroglu, S. Torkzaban, and S.L. Walker.
2009a. Coupled factors influencing concentration-dependent colloidtransport and retention in saturated porous media. Environ. Sci. Technol.
43:6996–7002. doi:10.1021/es900840d
Bradford, S.A., V.L. Morales, W. Zhang, R.W. Harvey, A.I. Packman, A.
Mohanram, and C. Welty. 2013a. Transport and fate of microbial
pathogens in agricultural settings. Crit. Rev. Environ. Sci. Technol.
43:775–893. doi:10.1080/10643389.2012.710449
Bradford, S.A., J. Šimůnek, M. Bettahar, Y.F. Tadassa, M.Th. van Genuchten, andwww.agronomy.org • www.crops.org • www.soils.org

S.R. Yates. 2005a. Straining of colloids at textural interfaces. Water Resour.
Res. 41:W10404. doi:10.1029/2004WR003675
Bradford, S.A., J. Šimůnek, M. Bettahar, M.Th. van Genuchten, and S.R. Yates.
2003. Modeling colloid attachment, straining, and exclusion in saturated
porous media. Environ. Sci. Technol. 37:2242–2250. doi:10.1021/
es025899u
Bradford, S.A., J. Šimůnek, and S.L. Walker. 2006a. Transport and straining of E.
coli O157:H7 in saturated porous media. Water Resour. Res. 42:W12S12.
Bradford, S.A., Y.F. Tadassa, and Y. Jin. 2006b. Transport of coliphage in thepresence and absence of manure suspension. J. Environ. Qual. 35:1692–
1701. doi:10.2134/jeq2006.0036
Bradford, S.A., and N. Toride. 2007. A stochastic model for colloid transport anddeposition. J. Environ. Qual. 36:1346–1356. doi:10.2134/jeq2007.0004
Bradford, S.A., and S. Torkzaban. 2008. Colloid transport and retention in
unsaturated porous media: A review of interface-, collector-, and porescale processes and models. Vadose Zone J. 7:667–681. doi:10.2136/
vzj2007.0092
Bradford, S.A., and S. Torkzaban. 2012. Colloid adhesive parameters forchemically heterogeneous porous media. Langmuir 28:13643–13651.
doi:10.1021/la3029929
Bradford, S.A., S. Torkzaban, H. Kim, and J. Šimůnek. 2012. Modeling colloid
and microorganism transport and release with transients in solution ionicstrength. Water Resour. Res. 48:W09509. doi:10.1029/2012WR012468
Bradford, S.A., S. Torkzaban, F. Leij, J. Šimůnek, and M.Th. van Genuchten.
2009b. Modeling the coupled effects of pore space geometry and velocity
on colloid transport and retention. Water Resour. Res. 45:W02414.
Bradford, S.A., S. Torkzaban, and A. Shapiro. 2013b. A theoretical analysis ofcolloid attachment and straining in chemically heterogeneous porous
media. Langmuir 29:6944–6952. doi:10.1021/la4011357
Bradford, S.A., S. Torkzaban, and J. Šimůnek. 2011a. Modeling colloid transportand retention in saturated porous media under unfavorable attachment
conditions. Water Resour. Res. 47:W10503. doi:10.1029/2011WR010812
Bradford, S.A., S. Torkzaban, and A. Wiegmann. 2011b. Pore-scale simulations todetermine the applied hydrodynamic torque and colloid immobilization.
Vadose Zone J. 10:252–261. doi:10.2136/vzj2010.0064
Bradford, S.A., M.Th. van Genuchten, and J. Šimůnek. 2005b. Modeling of
colloid transport and deposition in porous media. In: S. Torkzaban and
S.M. Hassanizadeh, editors, Proceedings of a Workshop on HYDRUS:
Advanced modeling of water flow and solute transport in the vadose zone,
Utrecht, the Netherlands. 17–19 Oct. 2005. Univ. of Utrecht, Utrecht, theNetherlands. p. 1–5.
Burdine, N.T. 1953. Relative permeability calculations from pore size distribution
data. J. Pet. Technol. 5:71–78.
Camesano, T.A., and B.E. Logan. 1998. Influence of fluid velocity and cellconcentration on the transport of motile and non-motile bacteria in porous
media. Environ. Sci. Technol. 32:1699–1708. doi:10.1021/es970996m
Cardenas, M.B. 2008. Three-dimensional vortices in single pores and their effects
on transport. Geophys. Res. Lett. 35:L18402. doi:10.1029/2008GL035343
Cey, E.E., and D.L. Rudolph. 2009. Field study of macropore flow processes
using tension infiltration of a dye tracer in partially saturated soils. Hydrol.
Processes 23:1768–1779. doi:10.1002/hyp.7302
Cey, E.E., D.L. Rudolph, and J. Passmore. 2009. Influence of macroporosity
on preferential solute and colloid transport in unsaturated field soils. J.
Contam. Hydrol. 107:45–57. doi:10.1016/j.jconhyd.2009.03.004
Charles, K.J., F.C. Souter, D.L. Baker, C.M. Davies, J.F. Schijven, D.J. Roser, et al.
2008. Fate and transport of viruses during sewage treatment in a moundsystem. Water Res. 42:3047–3056. doi:10.1016/j.watres.2008.02.032
Chatterjee, J., and S.K. Gupta. 2009. An agglomeration-based model for colloid
filtration. Environ. Sci. Technol. 43:3694–3699. doi:10.1021/es8029973
Chen, G., and M. Flury. 2005. Retention of mineral colloids in unsaturated
porous media as related to their surface properties. Colloids Surf. A
256:207–216. doi:10.1016/j.colsurfa.2005.01.021
Chen, K.C., R.M. Ford, and P.T. Cummings. 1998. Perturbation expansion of
Alt’s cell balance equations reduces to Segel’s one-dimensional equations
for shallow chemoattractant gradients. SIAM J. Appl. Math. 59:35–57.
doi:10.1137/S0036139996301283
Cheng, T., and J.E. Saiers. 2009. Mobilization and transport of in situ colloids
during drainage and imbibition of partially saturated sediments. Water
Resour. Res. 45:W08414.
Cherrey, K.D., M. Flury, and J.B. Harsh. 2003. Nitrate and colloid transport
through coarse Hanford sediments under steady state, variably saturated
flow. Water Resour. Res. 39:1165. doi:10.1029/2002WR001944
Chiang, H.-W., and C. Tien. 1985a. Dynamics of deep-bed filtration: I. Analysisof two limiting situations. AIChE J. 31:1349–1359. doi:10.1002/
aic.690310814
435

Chiang, H.-W., and C. Tien. 1985b. Dynamics of deep-bed filtration: II.
Experiment. AICHE J. 31:1360–1371. doi:10.1002/aic.690310815
Choi, N.-C., D.-J. Kim, and S.-B. Kim. 2007. Quantification of bacterial mass
recovery as a function of pore-water velocity and ionic strength. Res.
Microbiol. 158:70–78. doi:10.1016/j.resmic.2006.09.007
Chrysikopoulos, C.V., and E.T. Vogler. 2004. Estimation of time dependent virus
inactivation rates by geostatistical and resampling techniques: Application
to virus transport in porous media. Stochastic Environ. Res. Risk Assess.
18:67–78. doi:10.1007/s00477-003-0130-z
Contois, D.E. 1959. Kinetics of bacterial growth: Relationship between
population density and specific growth rate of continuous cultures. J. Gen.
Microbiol. 21:40–50. doi:10.1099/00221287-21-1-40
Cook, K.L., and C.H. Bolster. 2007. Survival of Campylobacter
jejuni and Escherichia coli in groundwater during prolonged
starvation at low temperatures. J. Appl. Microbiol. 103:573–583.
doi:10.1111/j.1365-2672.2006.03285.x
Corapcioglu, M.Y., and H. Choi. 1996. Modeling colloid transport in unsaturated
porous media and validation with laboratory column data. Water Resour.
Res. 32:3437–3449. doi:10.1029/95WR02693
Cortis, A., T. Harter, L. Hou, E.R. Atwill, A.I. Packman, and P.G. Green. 2006.
Transport of Cryptosporidium parvum in porous media: Long-term elution
experiments and continuous time random walk filtration modeling. Water
Resour. Res. 42:W12S13.
Crane, S.R., and J.A. Moore. 1986. Modeling enteric bacterial die-off: A review.
Water Air Soil Pollut. 27:411–439. doi:10.1007/BF00649422
Crist, J.T., J.F. McCarthy, Y. Zevi, P. Baveye, J.A. Throop, and T.S. Steenhuis. 2004.
Pore-scale visualization of colloid transport and retention in partly saturated
porous media. Vadose Zone J. 3:444–450. doi:10.2136/vzj2004.0444
Crist, J.T., Y. Zevi, J.F. McCarthy, J.A. Throop, and T.S. Steenhuis. 2005.
Transport and retention mechanisms of colloids in partially saturated
porous media. Vadose Zone J. 4:184–195. doi:10.2136/vzj2005.0184
Dabroś, T., and T.G.M. Van De Ven. 1982. Kinetics of coating by colloidal particles.
J. Colloid Interface Sci. 89:232–244. doi:10.1016/0021-9797(82)90137-0
Dean, D.M., and M.E. Foran. 1992. The effect of farm liquid waste application
on tile drainage. J. Soil Water Conserv. 47:368–369.
DeFlaun, M.F., C.J. Murray, W. Holben, T. Scheibe, A. Mills, T. Ginn, et al. 1997.
Preliminary observations on bacterial transport in a Coastal Plain aquifer.
FEMS Microbiol. Rev. 20:473–487. doi:10.1111/j.1574-6976.1997.
tb00331.x
DeNovio, N.M., J.E. Saiers, and J.N. Ryan. 2004. Colloid movement in
unsaturated porous media: Recent advances and future directions. Vadose
Zone J. 3:338–351. doi:10.2136/vzj2004.0338
Derjaguin, B., and L. Landau. 1941. Theory of the stability of strongly charged
lyophobic sols and of the adhesion of strongly charged particles in solutionsof electrolytes. Acta Physicochim. URSS 14:633–662.
de Roda Husman, A.M., W.J. Lodder, S.A. Rutjes, J.F. Schijven, and P.F.M.
Teunis. 2009. Long-term inactivation study of three enteroviruses in
artificial surface and groundwaters, using PCR and cell culture. Appl.
Environ. Microbiol. 75:1050–1057. doi:10.1128/AEM.01750-08
Deshpande, P.A., and D.R. Shonnard. 1999. Modeling the effects of systematic
variation in ionic strength on the attachment kinetics of Pseudomonas
fluorescens UPER-1 in saturated sand columns. Water Resour. Res.
35:1619–1627. doi:10.1029/1999WR900015
Dhawan, S., L.E. Erickson, and L.T. Fan. 1993. Model development andsimulation of bioremediation in soil beds with aggregates. Ground Water
31:271–284. doi:10.1111/j.1745-6584.1993.tb01819.x
Duffadar, R.D., and J.M. Davis. 2007. Interaction of micrometer-scale particles
with nanotextured surfaces in shear flow. J. Colloid Interface Sci. 308:20–
29. doi:10.1016/j.jcis.2006.12.068
Duffadar, R.D., and J.M. Davis. 2008. Dynamic adhesion behavior of micrometerscale particles flowing over patchy surfaces with nanoscale electrostatic
heterogeneity. J. Colloid Interface Sci. 326:18–27. doi:10.1016/j.
jcis.2008.07.004
Elimelech, M., J. Gregory, X. Jia, and R.A. Williams. 1995. Particle deposition
and aggregation: Measurement, modeling, and simulation. ButterworthHeinemann, Oxford, UK.
Elimelech, M., M. Nagai, C.-H. Ko, and J.N. Ryan. 2000. Relative insignificance ofmineral grain zeta potential to colloid transport in geochemically heterogeneous
porous media. Environ. Sci. Technol. 34:2143–2148. doi:10.1021/es9910309
Evans, M.R., and J.D. Owens. 1972. Factors affecting the concentration of
faecal bacteria in land-drainage water. J. Gen. Microbiol. 71:477–485.
doi:10.1099/00221287-71-3-477
Foppen, J.W., G. Lutterodt, W.F. Röling, and S. Uhlenbrook. 2010. Towards
understanding inter-strain attachment variations of Escherichia coli
during transport in saturated quartz sand. Water Res. 44:1202–1212.
doi:10.1016/j.watres.2009.08.034
436

Foppen, J.W.A., and J.F. Schijven. 2006. Evaluation of data from the literatureon the transport and survival of Escherichia coli and thermotolerant
coliforms in aquifers under saturated conditions. Water Res. 40:401–426.
doi:10.1016/j.watres.2005.11.018
Ford, R.M., and R.W. Harvey. 2007. Role of chemotaxis in the transport ofbacteria through saturated porous media. Adv. Water Resour. 30:1608–
1617. doi:10.1016/j.advwatres.2006.05.019
Fox, G.A., M.M. Marvin, J.A. Guzman, C.K. Hoang, R.W. Malone, R.S. Kanwar,
and M.J. Shipitalo. 2012. E. coli transport through surface-connectedbiopores identified from smoke injection tests. Trans. ASABE 55:2185–
2194. doi:10.13031/2013.42511
Fuller, M.E., H. Dong, B.J. Mailloux, T.C. Onstott, and M.F. DeFlaun. 2000.
Examining bacterial transport in intact cores from Oyster, Virginia: Effectof sedimentary facies type on bacterial breakthrough and retention. Water
Resour. Res. 36:2417–2431. doi:10.1029/2000WR900075
Gabriel, J.P., F. Saucy, and L.F. Bersier. 2005. Paradoxes in the logistic equation?
Ecol. Modell. 185:147–151. doi:10.1016/j.ecolmodel.2004.10.009
Gaillard, J.-F., C. Chen, S.H. Stonedahl, B.L.T. Lau, D.T. Keane, and A.I.
Packman. 2007. Imaging of colloidal deposits in granular porous media
by X-ray difference micro-tomography. Geophys. Res. Lett. 34:L18404.
doi:10.1029/2007GL030514
Gao, B., J.E. Saiers, and J. Ryan. 2006. Pore-scale mechanisms of colloid
deposition and mobilization during steady and transient flow
through unsaturated granular media. Water Resour. Res. 42:W01410.
doi:10.1029/2005WR004233
Garbrecht, K., G.A. Fox, J.A. Guzman, and D. Alexander. 2009. E. coli transport
through soil columns: Implications for bioretention cell removal efficiency.
Trans. ASABE 52:481–486. doi:10.13031/2013.26841
Gargiulo, G., S. Bradford, J. Šimůnek, P. Ustohal, H. Vereecken, and E. Klumpp.
2007a. Bacteria transport and deposition under unsaturated conditions:
The role of the matrix grain size and the bacteria surface protein. J. Contam.
Hydrol. 92:255–273. doi:10.1016/j.jconhyd.2007.01.009
Gargiulo, G., S.A. Bradford, J. Šimůnek, P. Ustohal, H. Vereecken, and E.
Klumpp. 2008. Bacteria transport and deposition under unsaturated flow
conditions: The role of water content and bacteria surface hydrophobicity.
Vadose Zone J. 7:406–419. doi:10.2136/vzj2007.0068
Gargiulo, G., S.A. Bradford, J. Šimůnek, H. Vereecken, and E. Klumpp. 2007b.
Transport and deposition of metabolically active and stationary phase
Deinococcus radiodurans in unsaturated porous media. Environ. Sci.
Technol. 41:1265–1271. doi:10.1021/es062854a
Gerke, H.H. 2006. Preferential flow descriptions for structured soils. J. Plant
Nutr. Soil Sci. 169:382–400. doi:10.1002/jpln.200521955
Gerke, H.H., and M.Th. van Genuchten. 1993a. A dual-porosity model for
simulating the preferential movement of water and solutes in structured
porous media. Water Resour. Res. 29:305–319. doi:10.1029/92WR02339
Gerke, H.H., and M.Th. van Genuchten. 1993b. Evaluation of a first-order watertransfer term for variably saturated dual-porosity flow models. Water
Resour. Res. 29:1225–1238. doi:10.1029/92WR02467
Gharasoo, M., F. Centler, P. Regnier, H. Harms, and M. Thullner. 2012. A reactive
transport modeling approach to simulate biogeochemical processes inpore structures with pore-scale heterogeneities. Environ. Modell. Softw.
30:102–114. doi:10.1016/j.envsoft.2011.10.010
Ginn, T.R. 2000a. On the distribution of multicomponent mixtures overgeneralized exposure time in subsurface flow and reactive transport:
Batch and column applications involving residence-time distributions
and non-Markovian reaction kinetics. Water Resour. Res. 36:2895–2903.
doi:10.1029/2000WR900171
Ginn, T.R. 2000b. On the distribution of multicomponent mixtures overgeneralized exposure time in subsurface flow and reactive transport:
Theory and formulations for residence-time-dependent sorption/
desorption with memory. Water Resour. Res. 36:2885–2893.
doi:10.1029/2000WR900170
Ginn, T.R. 2002. A travel time approach to exclusion on transport in porous
media. Water Resour. Res. 38(4). doi:10.1029/2001WR000865
Ginn, T.R., B.D. Wood, K.E. Nelson, T.D. Scheibe, E.M. Murphy, and T.P.
Clement. 2002. Processes in microbial transport in the natural subsurface.
Adv. Water Resour. 25:1017–1042. doi:10.1016/S0309-1708(02)00046-5
Grolimund, D., and M. Borkovec. 2006. Release of colloidal particles in natural
porous media by monovalent and divalent cations. J. Contam. Hydrol.
87:155–175. doi:10.1016/j.jconhyd.2006.05.002
Guber, A.K., D.R. Shelton, and Y.A. Pachepsky. 2005. Transport and retention ofmanure-borne coliforms in soil. Vadose Zone J. 4:828–837. doi:10.2136/
vzj2004.0097
Guzman, J.A., and G.A. Fox. 2011. Implementation of biopore and soil fecal
bacteria fate and transport routines in the Root Zone Water Quality
Model (RZWQM). Trans. ASABE 55:73–84. doi:10.13031/2013.41263
Journal of Environmental Quality

Hahn, M., and C.R. O’Melia. 2004. Deposition and reentrainment of equivalenceof Brownian particles in porous media under unfavorable conditions:
Some concepts and applications. Environ. Sci. Technol. 20:1123–1130.
Harmand, B., E. Rodier, M. Sardin, and J. Dodds. 1996. Transport andcapture of submicron particles in a natural sand: Short column
experiments and a linear model. Colloids Surf. A 107:233–244.
doi:10.1016/0927-7757(95)03366-1
Harvey, R.W., and S.P. Garabedian. 1991. Use of colloid filtration theory inmodeling movement of bacteria through a contaminated sandy aquifer.
Environ. Sci. Technol. 25:178–185. doi:10.1021/es00013a021
Harvey, R.W., and H. Harms. 2002. Transport of microorganisms in theterrestrial subsurface: In situ and laboratory methods. In: C.J. Hurst et al.,editors, Manual of environmental microbiology. ASM Press, Washington,
DC. p. 753–776.
Harvey, R.W., D.W. Metge, N. Kinner, and N. Mayberry. 1996. Physiologicalconsiderations in applying laboratory-determined buoyant densities topredictions of bacterial and protozoan transport in groundwater: Resultsof in-situ and laboratory tests. Environ. Sci. Technol. 31:289–295.
doi:10.1021/es960461d
Harvey, R.W., and J.N. Ryan. 2004. Use of PRD1 bacteriophage in groundwater
viral transport, inactivation, and attachment studies. FEMS Microbiol.
Ecol. 49:3–16. doi:10.1016/j.femsec.2003.09.015
Herzig, J.P., D.M. Leclerc, and P.L. Goff. 1970. Flow of suspensions throughporous media: Application to deep filtration. Ind. Eng. Chem. 62:8–35.
doi:10.1021/ie50725a003
Himathongkham, S., S. Bahari, H. Riemann, and D. Cliver. 1999. Survivalof Escherichia coli O157:H7 and Salmonella typhimurium in cow
manure and cow manure slurry. FEMS Microbiol. Lett. 178:251–257.
doi:10.1111/j.1574-6968.1999.tb08684.x
Hornberger, G.M., A.L. Mills, and J.S. Herman. 1992. Bacterial transport inporous media: Evaluation of a model using laboratory observations. Water
Resour. Res. 28:915–923. doi:10.1029/91WR02980
Hosseini, S.A., and T. Tosco. 2013. Transport and retention of high concentrated
nano-Fe/Cu particles through highly flow-rated packed sand column.
Water Res. 47:326–338. doi:10.1016/j.watres.2012.10.002
Ives,
K.J.
1970.
Rapid
filtration.
Water
Res.
4:201–223.
doi:10.1016/0043-1354(70)90068-0
Ives, K.J., and V. Pienvichitr. 1965. Kinetics of the filtration of dilute suspensions.
Chem. Eng. Sci. 20:965–973. doi:10.1016/0009-2509(65)80094-X
Jarvis, N.J. 2007. Review of non-equilibrium water flow and solutetransport in soil macropores: Principles, controlling factors andconsequences for water quality. Eur. J. Soil Sci. 58:523–546.
doi:10.1111/j.1365-2389.2007.00915.x
Jin, Y., and M. Flury. 2002. Fate and transport of viruses in porous media. Adv.
Agron. 77:39–102.
John, D.E., and J.B. Rose. 2005. Review of factors affecting microbial survival
in groundwater. Environ. Sci. Technol. 39:7345–7356. doi:10.1021/
es047995w
Johnson, P.R., and M. Elimelech. 1995. Dynamics of colloid deposition in porous
media: Blocking based on random sequential adsorption. Langmuir
11:801–812. doi:10.1021/la00003a023
Johnson, W.P., K.A. Blue, B.E. Logan, and R.G. Arnold. 1995. Modelingbacterial detachment during transport through porous media as aresidence-time-dependent process. Water Resour. Res. 31:2649–2658.
doi:10.1029/95WR02311
Johnson, W.P., X. Li, and S. Assemi. 2007. Deposition and re-entrainment
dynamics of microbes and non-biological colloids during non-perturbed
transport in porous media in the presence of an energy barrier to deposition.
Adv. Water Resour. 30:1432–1454. doi:10.1016/j.advwatres.2006.05.020
Jucker, B.A., H. Harms, S.J. Hug, and A.J.B. Zehnder. 1997. Adsorption ofbacterial surface polysaccharides on mineral oxides is mediated by hydrogenbonds. Colloids Surf. B 9:331–343. doi:10.1016/S0927-7765(97)00038-6
Jury, W.A., W.R. Gardner, and W.H. Gardner. 1991. Soil physics. John Wiley &Sons, New York.
Kanti Sen, T., and K.C. Khilar. 2006. Review on subsurface colloids and colloidassociated contaminant transport in saturated porous media. Adv. Colloid
Interface Sci. 119:71–96. doi:10.1016/j.cis.2005.09.001
Khilar, K.C., and H.S. Fogler. 1998. Migrations of fines in porous media. Kluwer
Acad. Publ., Dordrecht, the Netherlands.
Kildsgaard, J., and P. Engesgaard. 2002. Tracer tests and image analysis of
biological clogging in a two-dimensional sandbox experiment. Ground
Water Monit. Rem. 22:60–67. doi:10.1111/j.1745-6592.2002.tb00313.x
Kim, H.N., S.A. Bradford, and S.L. Walker. 2009a. Escherichia coli O157:H7
transport in saturated porous media: Role of solution chemistry and surface
macromolecules. Environ. Sci. Technol. 43:4340–4347. doi:10.1021/
es8026055
www.agronomy.org • www.crops.org • www.soils.org

Kim, H.N., Y. Hong, I. Lee, S.A. Bradford, and S.L. Walker. 2009b. Surface
characteristics and adhesion behavior of Escherichia coli O157:H7: Roleof extracellular macromolecules. Biomacromolecules 10:2556–2564.
doi:10.1021/bm900516y
Kim, H.N., S.L. Walker, and S.A. Bradford. 2010a. Macromolecule mediatedtransport and retention of Escherichia coli O157:H7 in saturated porous
media. Water Res. 44:1082–1093. doi:10.1016/j.watres.2009.09.027
Kim, H.N., S.L. Walker, and S.A. Bradford. 2010b. Coupled factors influencing
the transport and retention of Cryptosporidium parvum oocysts insaturated porous media. Water Res. 44:1213–1223. doi:10.1016/j.
watres.2009.09.041
Kim, M.K., S.B. Kim, and S.J. Park. 2008. Bacteria transport in an unsaturated
porous media: Incorporation of air–water interface area model intotransport modelling. Hydrol. Processes 22:2370–2376. doi:10.1002/
hyp.6799
Köhne, J.M., S. Köhne, and J. Šimůnek. 2006. Multi-process herbicide transport
in structured soil columns: Experiment and model analysis. J. Contam.
Hydrol. 85:1–32. doi:10.1016/j.jconhyd.2006.01.001
Köhne, J.M., S. Köhne, and J. Šimůnek. 2009. A review of model applications forstructured soils: A. Water flow and tracer transport. J. Contam. Hydrol.
104:4–35. doi:10.1016/j.jconhyd.2008.10.002
Kolakowski, J.E., and E. Matijevic. 1979. Particle adhesion and removal in model
systems: 1. Monodispersed chromium hydroxide on glass. J. Chem. Soc.,
Faraday Trans. I 75:65–78. doi:10.1039/f19797500065
Krupp, H.K., J.W. Biggar, and D.R. Nielsen. 1972. Relative flow rates of salt
and water in soil. Soil Sci. Soc. Am. Proc. 36:412–417. doi:10.2136/
sssaj1972.03615995003600030016x
Kumar, D., S. Bhattacharya, and S. Ghosh. 2013. Weak adhesion at the mesoscale:Particles at an interface. Soft Matter 9:6618–6633. doi:10.1039/
c3sm00097d
Kussell, E., R. Kishony, N.Q. Balaban, and S. Leibler. 2005. Bacterial persistence:
A model of survival in changing environments. Genetics 169:1807–1814.
doi:10.1534/genetics.104.035352
Kuznar, Z.A., and M. Elimelech. 2007. Direct microscopic observation of particle
deposition in porous media: Role of the secondary energy minimum.
Colloids Surf. A 294:156–162. doi:10.1016/j.colsurfa.2006.08.007
Landkamer, L.L., R.W. Harvey, T.D. Scheibe, and J.N. Ryan. 2013. Colloidtransport in saturated porous media: Elimination of attachment efficiency
in a new colloid transport model. Water Resour. Res. 49:2952–2965.
doi:10.1002/wrcr.20195
Lang, N.L., and S.R. Smith. 2007. Influence of soil type, moisture content andbiosolids application on the fate of Escherichia coli in agricultural soil undercontrolled laboratory conditions. J. Appl. Microbiol. 103:2122–2131.
doi:10.1111/j.1365-2672.2007.03490.x
Lazouskaya, V., and Y. Jin. 2008. Colloid retention at air–water interface
in a capillary channel. Colloids Surf. A 325:141–151. doi:10.1016/j.
colsurfa.2008.04.053
Lazouskaya, V., Y. Jin, and D. Or. 2006. Interfacial interactions and colloid
retention under steady flows in a capillary channel. J. Colloid Interface Sci.
303:171–184. doi:10.1016/j.jcis.2006.07.071
Lenhart, J.J., and J.E. Saiers. 2003. Colloid mobilization in water-saturated
porous media under transient chemical conditions. Environ. Sci. Technol.
37:2780–2787. doi:10.1021/es025788v
Li, X., Z. Li, and D. Zhang. 2010a. Role of low flow and backward flow zones
on colloid transport in pore structures derived from real porous media.
Environ. Sci. Technol. 44:4936–4942. doi:10.1021/es903647g
Li, X., C.-L. Lin, J.D. Miller, and W.P. Johnson. 2006a. Pore-scale observationof microsphere deposition at grain-to-grain contacts over assemblagescale porous media domains using X-ray microtomography. Environ. Sci.
Technol. 40:3762–3768. doi:10.1021/es0525004
Li, X., C.-L. Lin, J.D. Miller, and W.P. Johnson. 2006b. Role of grain-to-grain
contacts on profiles of retained colloids in porous media in the presenceof an energy barrier to deposition. Environ. Sci. Technol. 40:3769–3774.
doi:10.1021/es052501w
Li, X., T.D. Scheibe, and W.P. Johnson. 2004. Apparent decreases in colloid
deposition rate coefficients with distance of transport under unfavorable
deposition conditions: A general phenomenon. Environ. Sci. Technol.
38:5616–5625. doi:10.1021/es049154v
Li, Z., D. Zhang, and X. Li. 2010b. Tracking colloid transport in porous mediausing discrete flow fields and sensitivity of simulated colloid deposition to
space discretization. Environ. Sci. Technol. 44:1274–1280. doi:10.1021/
es9027716
Liang, Y., S. A. Bradford, J. Šimůnek, H. Vereecken, and E. Klumpp. 2013.
Sensitivity of the transport and retention of stabilized silver nanoparticles
to physicochemical factors. Water Res. 47:2572–2582. doi:10.1016/j.
watres.2013.02.025
437

Ma, H., J. Pedel, P. Fife, and W.P. Johnson. 2009. Hemispheres-in-cell geometry
to predict colloid deposition in porous media. Environ. Sci. Technol.
43:8573–8579. doi:10.1021/es901242b
Martins, J.M.F., S. Majdalani, E. Vitorge, A. Desaunay, A. Navel, V. Guiné, et al.
2013. Role of macropore flow in the transport of Escherichia coli cells in
undisturbed cores of a brown leached soil. Environ. Sci.: Processes Impacts
15:347–356. doi:10.1039/c2em30586k
Mays, D.C., and J.R. Hunt. 2005. Hydrodynamic aspects of particle clogging
in porous media. Environ. Sci. Technol. 39:577–584. doi:10.1021/
es049367k
McCarthy, J., and J. Zachara. 1989. Subsurface transport of contaminants.
Environ. Sci. Technol. 23:496–502.
McDowell-Boyer, L.M., J.R. Hunt, and N. Sitar. 1986. Particle transport
through porous media. Water Resour. Res. 22:1901–1921. doi:10.1029/
WR022i013p01901
McGechan, M.B., and D.R. Lewis. 2002. Transport of particulate and colloidsorbed contaminants through soil: 1. General principles. Biosyst. Eng.
83:255–273. doi:10.1006/bioe.2002.0125
McGechan, M.B., and A.J.A. Vinten. 2003. Simulation of transport through soilof E. coli derived from livestock slurry using the MACRO model. Soil Use
Manage. 19:321–330. doi:10.1079/SUM2003321
McGechan, M.B., and A.J.A. Vinten. 2004. Simulating transport of E. coli
derived from faeces of grazing livestock using the MACRO model. Soil
Use Manage. 20:195–202. doi:10.1079/SUM2004254
Meinders, J.M., J. Noordmans, and H.J. Busscher. 1992. Simultaneous monitoringof the adsorption and desorption of colloidal particles during deposition
in a parallel plate flow chamber. J. Colloid Interface Sci. 152:265–280.
doi:10.1016/0021-9797(92)90026-I
Mishra, S., J. Jeevan, C.K. Ramesh, and L. Banwari. 2001. In situ bioremediation
potential of an oily sludge-degrading bacterial consortium. Curr.
Microbiol. 43:328–335. doi:10.1007/s002840010311
Mohamed, M., K. Hatfield, and I.V. Perminova. 2007. Evaluation of Monod
kinetic parameters in the subsurface using moment analysis: Theory andnumerical testing. Adv. Water Resour. 30:2034–2050. doi:10.1016/j.
advwatres.2007.04.006
Molin, S., and V. Cvetkovic. 2010. Microbial risk assessment in heterogeneous
aquifers: 1. Pathogen transport. Water Resour. Res. 46:W05518.
Monod, J. 1942. Recherches sur la croissance des cultures bactériennes. Hermann,
Paris.
Morohashi, M., Y. Ohashi, S. Tani, K. Ishii, M. Itaya, H. Nanamiya, et al. 2007.
Model-based definition of population heterogeneity and its effects on
metabolism in sporulating Bacillus subtilis. J. Biochem. 142:183–191.
doi:10.1093/jb/mvm121
Mostafa, M., and P.J. Van Geel. 2007. Conceptual models and simulations
for biological clogging in unsaturated soils. Vadose Zone J. 6:175–185.
doi:10.2136/vzj2006.0033
Mualem, Y. 1976. A new model for predicting the hydraulic conductivity ofunsaturated porous media. Water Resour. Res. 12:513–522. doi:10.1029/
WR012i003p00513
Murphy, E.M., and T.R. Ginn. 2000. Modeling microbial processes in porous
media. Hydrogeol. J. 8:142–158. doi:10.1007/s100409900043
Nelson, K.E., and T.R. Ginn. 2005. Colloid filtration theory and the Happel
sphere-in-cell model revisited with direct numerical simulation of colloids.
Langmuir 21:2173–2184. doi:10.1021/la048404i
Oliver, D.M., P.M. Haygarth, C.D. Clegg, and L. Heathwaite. 2006. Differential
E. coli die-off patterns associated with agricultural matrices. Environ. Sci.
Technol. 40:5710–5716. doi:10.1021/es0603249
Oliver, D.M., T. Page, A.L. Heathwaite, and P.M. Haygarth. 2010. Re-shaping
models of E. coli population dynamics in livestock faeces: Increased bacterial
risk to humans? Environ. Int. 36:1–7. doi:10.1016/j.envint.2009.08.006
Oliver, J.D. 2010. Recent findings on the viable but nonculturable state inpathogenic bacteria. FEMS Microbiol. Rev. 34:415–425.
O’Melia, C.R., and W. Ali. 1978. The role of retained particles in deep bed
filtration. Prog. Water Technol. 10:167–182.
Pachepsky, Y.A., A.M. Sadeghi, S.A. Bradford, D.R. Shelton, A.K. Guber,
and T. Dao. 2006. Transport and fate of manure-borne pathogens:
Modeling perspective. Agric. Water Manage. 86:81–92. doi:10.1016/j.
agwat.2006.06.010
Pang, L. 2009. Microbial removal rates in subsurface media estimated frompublished studies of field experiments and large intact soil cores. J. Environ.
Qual. 38:1531–1559. doi:10.2134/jeq2008.0379
Pang, L., M. McLeod, J. Aislabie, J. Šimůnek, M. Close, and R. Hector. 2008.
Modeling transport of microbes in ten undisturbed soils under effluent
irrigation. Vadose Zone J. 7:97–111. doi:10.2136/vzj2007.0108
Parker, J.C., and R.J. Lenhard. 1987. A model for hysteretic constitutive relations
438

governing multiphase flow: 1. Saturation–pressure relations. Water Resour.
Res. 23:2187–2196. doi:10.1029/WR023i012p02187
Passmore, J.M., D.L. Rudolph, M.M.F. Mesquita, E.E. Cey, and M.B. Emelko.
2010. The utility of microspheres as surrogates for the transport of E. coli
RS2g in partially saturated agricultural soil. Water Res. 44:1235–1245.
doi:10.1016/j.watres.2009.10.010
Peleg, M., and M.B. Cole. 1998. Reinterpretation of microbial survival curves.
Crit. Rev. Food Sci. Nutr. 38:353–380. doi:10.1080/10408699891274246
Pérez-Paricio, A., and J. Carrera. 1999. Clogging handbook. European
Commonwealth, Brussels.
Petterson, S.R., P.F.M. Teunis, and N.J. Ashbolt. 2001. Modeling virus
inactivation on salad crops using microbial count data. Risk Anal.
21:1097–1108. doi:10.1111/0272-4332.216178
Philip, J.R. 1968. The theory of absorption in aggregated media. Aust. J. Soil Res.
6:1–19. doi:10.1071/SR9680001
Pot, V., J. Šimůnek, P. Benoit, Y. Coquet, A. Yra, and M.-J. Martínez-Cordón.
2005. Impact of rainfall intensity on the transport of two herbicides inundisturbed grassed filter strip soil cores. J. Contam. Hydrol. 81:63–88.
doi:10.1016/j.jconhyd.2005.06.013
Powelson, D.K., C.P. Gerba, and M.T. Yahya. 1993. Virus transport andremoval in waste-water during aquifer recharge. Water Res. 27:583–590.
doi:10.1016/0043-1354(93)90167-G
Proctor, R.A., C. von Eiff, B.C. Kahl, K. Becker, P. McNamara, M. Herrmann,and G. Peters. 2006. Small colony variants: A pathogenic form of bacteriathat facilitates persistent and recurrent infections. Nat. Rev. Microbiol.
4:295–305. doi:10.1038/nrmicro1384
Rajagopalan, R., and C. Tien. 1976. Trajectory analysis of deep-bed filtration
with the sphere-in-cell porous media model. AIChE J. 22:523–533.
doi:10.1002/aic.690220316
Rathfelder, K.M., J.R. Lang, and L.M. Abriola. 2000. A numerical model(MISER) for the simulation of coupled physical, chemical and biologicalprocesses in soil vapor extraction and bioventing systems. J. Contam.
Hydrol. 43:239–270. doi:10.1016/S0169-7722(00)00086-3
Ray, C., T.W. Soong, Y.Q. Lian, and G.S. Roadcap. 2002. Effect of floodinduced chemical load on filtrate quality at bank filtration sites. J. Hydrol.
266:235–258. doi:10.1016/S0022-1694(02)00168-3
Redman, J.A., S.B. Grant, T.M. Olson, and M.K. Estes. 2001. Pathogen filtration,
heterogeneity, and the potable reuse of wastewater. Environ. Sci. Technol.
35:1798–1805. doi:10.1021/es0010960
Reynolds, P.J., P. Sharma, G.E. Jenneman, and M.J. McInerney. 1989. Mechanismsof microbial movement in subsurface materials. Appl. Environ. Microbiol.
55:2280–2286.
Richards, L.A. 1931. Capillary conduction of liquids through porous mediums.
Physics 1:318–333. doi:10.1063/1.1745010
Rockhold, M.L., R.R. Yarwood, and J.S. Selker. 2004. Coupled microbial andtransport processes in soils. Vadose Zone J. 3:368–383. doi:10.2136/
vzj2004.0368
Rotem, E., A. Loinger, I. Ronin, I. Levin-Reisman, C. Gabay, N. Shoresh, et al.
2010. Regulation of phenotypic variability by a threshold-based mechanism
underlies bacterial persistence. Proc. Natl. Acad. Sci. 107:12541–12546.
doi:10.1073/pnas.1004333107
Russell, T.L., K.M. Yamahara, and A.B. Boehm. 2012. Mobilization andtransport of naturally occurring enterococci in beach sands subject totransient infiltration of seawater. Environ. Sci. Technol. 46:5988–5996.
doi:10.1021/es300408z
Ryan, J.N., and M. Elimelech. 1996. Colloid mobilization andtransport in groundwater. Colloids Surf. A 107:1–56.
doi:10.1016/0927-7757(95)03384-X
Ryan, J.N., and P.M. Gschwend. 1994. Effects of ionic strength and flow rate on
colloid release: Relating kinetics to intersurface potential energy. J. Colloid
Interface Sci. 164:21–34. doi:10.1006/jcis.1994.1139
Saiers, J.E., and J.J. Lenhart. 2003. Colloid mobilization and transport within
unsaturated porous media under transient-flow conditions. Water Resour.
Res. 39:1019.
Sanin, S.L., F.D. Sanin, and J.D. Bryers. 2003. Effect of starvation on the adhesive
properties of xenobiotic degrading bacteria. Process Biochem. 38:909–
914. doi:10.1016/S0032-9592(02)00173-5
Schäfer, A., H. Harms, and A.J.B. Zehnder. 1998. Bacterial accumulation at the
air–water interface. Environ. Sci. Technol. 32:3704–3712. doi:10.1021/
es980191u
Scheibe, T.D., and B.D. Wood. 2003. A particle-based model of size or anion
exclusion with application to microbial transport in porous media. Water
Resour. Res. 39(4):1080. doi:10.1029/2001WR001223
Schijven, J.F., P. Berger, and I. Miettinen. 2003. Removal of pathogens, surrogates,
indicators and toxins using riverbank filtration. In: C. Ray et al., editors,
Bank filtration for water supply. Springer, New York. p. 73–116.
Journal of Environmental Quality

Schijven, J.K., and S.M. Hassanizadeh. 2000. Removal of viruses by soil passage:
Overview of modeling, processes, and parameters. Crit. Rev. Environ. Sci.
Technol. 30:49–127. doi:10.1080/10643380091184174
Schijven, J.F., and S.M. Hassanizadeh. 2002. Virus removal by soil passage at field
scale and groundwater protection of sandy aquifers. Water Sci. Technol.
46:123–129.
Schijven, J.F., and J. Šimůnek. 2002. Kinetic modeling of virus transport
at the field scale. J. Contam. Hydrol. 55:113–135. doi:10.1016/
S0169-7722(01)00188-7
Semenov, A.V., L. van Overbeek, and A.H.C. van Bruggen. 2009. Percolationand survival of Escherichia coli O157:H7 and Salmonella enterica serovar
Typhimurium in soil amended with contaminated dairy manure or slurry.
Appl. Environ. Microbiol. 75:3206–3215. doi:10.1128/AEM.01791-08
Shapiro, A.A. 2007. Elliptic equation for random walks: Application to transportin microporous media. Physica A 375:81–96.
Shapiro, A.A., and P.G. Bedrikovetsky. 2010. A stochastic theory for deep bed
filtration accounting for dispersion and size distributions. Physica A
389:2473–2494. doi:10.1016/j.physa.2010.02.049
Sharma, P.K., M.J. McInerney, and R.M. Knapp. 1993. In situ growth andactivity and modes of penetration of Escherichia coli in unconsolidated
porous materials. Appl. Environ. Microbiol. 59:3686–3694.
Shen, C., Y. Huang, B. Li, and Y. Jin. 2010. Predicting attachment efficiency
of colloid deposition under unfavorable attachment conditions. Water
Resour. Res. 46:W11526. doi:10.1029/2010WR009218
Shen, C., B. Li, Y. Huang, and Y. Jin. 2007. Kinetics of coupled primary- andsecondary-minimum deposition of colloids under unfavorable chemical
conditions. Environ. Sci. Technol. 41:6976–6982. doi:10.1021/es070210c
Sheng, P., and M. Zhou. 1992. Immiscible-fluid displacement: Contact-line
dynamics and the velocity-dependent capillary pressure. Phys. Rev. A
45:5694. doi:10.1103/PhysRevA.45.5694
Sim, Y., and C.V. Chrysikopoulos. 1996. One-dimensional virus transport inporous media with time-dependent inactivation rate coefficients. Water
Resour. Res. 32:2607–2611. doi:10.1029/96WR01496
Simoni, S.F., H. Harms, T.N.P. Bosma, and A.J.B. Zehnder. 1998. Population
heterogeneity affects transport of bacteria through sand columns at low
flow rates. Environ. Sci. Technol. 32:2100–2105. doi:10.1021/es970936g
Šimůnek, J., C. He, L. Pang, and S.A. Bradford. 2006. Colloid-facilitated solutetransport in variably saturated porous media: Numerical model andexperimental verification. Vadose Zone J. 5:1035–1047. doi:10.2136/
vzj2005.0151
Šimůnek, J., N.J. Jarvis, M.Th. van Genuchten, and A. Gärdenäs. 2003. Review
and comparison of models for describing non-equilibrium and preferential
flow and transport in the vadose zone. J. Hydrol. 272:14–35. doi:10.1016/
S0022-1694(02)00252-4
Šimůnek, J., and M.Th. van Genuchten. 2008. Modeling nonequilibrium flow
and transport processes using HYDRUS. Vadose Zone J. 7:782–797.
doi:10.2136/vzj2007.0074
Šimůnek, J., M.Th. van Genuchten, and M. Šejna. 2008. Development andapplications of the HYDRUS and STANMOD software packages andrelated codes. Vadose Zone J. 7:587–600. doi:10.2136/vzj2007.0077
Soleimani, S., P.J. Van Geel, O.B. Isgor, and M.B. Mostafa. 2009. Modeling of
biological clogging in unsaturated porous media. J. Contam. Hydrol.
106:39–50. doi:10.1016/j.jconhyd.2008.12.007
Spielman, L.A., and S.K. Friedlander. 1974. Role of the electrical double layer inparticle deposition by convective diffusion. J. Colloid Interface Sci. 46:22–
31. doi:10.1016/0021-9797(74)90021-6
Stumm, W., J.J. Morgan, and J.I. Drever. 1981. Aquatic chemistry. John Wiley &Sons, New York.
Stuyfzand, P.J. 1989. Hydrology and water quality aspects of Rhine
bank groundwater in the Netherlands. J. Hydrol. 106:341–363.
doi:10.1016/0022-1694(89)90079-6
Taneda, S. 1979. Visualization of separating Stokes flows. J. Phys. Soc. Jpn.
46:1935–1942. doi:10.1143/JPSJ.46.1935
Taylor, S.W., P.C.D. Milly, and P.R. Jaffé. 1990. Biofilm growth and the relatedchanges in the physical properties of a porous medium: 2. Permeability.
Water Resour. Res. 26:2161–2169. doi:10.1029/WR026i009p02161
Tessier, G. 1942. Croissance des populations bactériennes et quantité d’aliment
disponible. Rev. Sci. Paris 3208:209–214.
Thullner, M., L. Mauclaire, M.H. Schroth, W. Kinzelbach, and J. Zeyer. 2002a.
Interaction between water flow and spatial distribution of microbial
growth in a two-dimensional flow field in saturated porous media. J.
Contam. Hydrol. 58:169–189. doi:10.1016/S0169-7722(02)00033-5
Thullner, M., M.H. Schroth, J. Zeyer, and W. Kinzelbach. 2004. Modeling ofa microbial growth experiment with bioclogging in a two-dimensional
saturated porous media flow field. J. Contam. Hydrol. 70:37–62.
doi:10.1016/j.jconhyd.2003.08.008
www.agronomy.org • www.crops.org • www.soils.org

Thullner, M., J. Zeyer, and W. Kinzelbach. 2002b. Influence of microbial growthon hydraulic properties of pore networks. Transp. Porous Media 49:99–
122. doi:10.1023/A:1016030112089
Tien, C. 1989. Granular filtration of aerosols and hydrosols. Butterworths,
London.
Tong, M., X. Li, C.N. Brow, and W.P. Johnson. 2005. Detachment-influenced
transport of an adhesion-deficient bacterial strain within water-reactive
porous media. Environ. Sci. Technol. 39:2500–2508. doi:10.1021/
es049013t
Tong, M., H. Ma, and W.P. Johnson. 2008. Funneling of flow into grain-to-grain
contacts drives colloid–colloid aggregation in the presence of an energy
barrier. Environ. Sci. Technol. 42:2826–2832. doi:10.1021/es071888v
Torkzaban, S., S.A. Bradford, and S.L. Walker. 2007. Resolving the coupledeffects of hydrodynamics and DLVO forces on colloid attachment toporous media. Langmuir 23:9652–9660. doi:10.1021/la700995e
Torkzaban, S., S.M. Hassanizadeh, J.F. Schijven, and A.M. de Roda Husman.
2006a. Virus transport in saturated and unsaturated sand columns. Vadose
Zone J. 5:877–885. doi:10.2136/vzj2005.0086
Torkzaban, S., S.M. Hassanizadeh, J.F. Schijven, and H.H.J.L. van den
Berg. 2006b. Role of air–water interfaces on retention of viruses
under unsaturated conditions. Water Resour. Res. 42:W12S14.
doi:10.1029/2006WR004904
Torkzaban, S., Y. Kim, M. Mulvihill, J. Wan, and T. Tokunaga. 2010a. Transportand deposition of functionalized CdTe nanoparticles in saturated
porous media. J. Contam. Hydrol. 118:208–217. doi:10.1016/j.
jconhyd.2010.10.002
Torkzaban, S., H.N. Kim, J. Šimůnek, and S.A. Bradford. 2010b. Hysteresis ofcolloid retention and release in saturated porous media during transientsin solution chemistry. Environ. Sci. Technol. 44:1662–1669. doi:10.1021/
es903277p
Torkzaban, S., S.S. Tazehkand, S.L. Walker, and S.A. Bradford. 2008. Transportand fate of bacteria in porous media: Coupled effects of chemical
conditions and pore space geometry. Water Resour. Res. 44:W04403.
doi:10.1029/2007WR006541
Torkzaban, S., J. Wan, T.K. Tokunaga, and S.A. Bradford. 2012. Impacts ofbridging complexation on the transport of surface-modified nanoparticles
in saturated sand. J. Contam. Hydrol. 136–137:86–95. doi:10.1016/j.
jconhyd.2012.05.004
Tosco, T., and R. Sethi. 2010. Transport of non-Newtonian suspensions of highly
concentrated micro- and nanoscale iron particles in porous media: A
modeling approach. Environ. Sci. Technol. 44:9062–9068. doi:10.1021/
es100868n
Tosco, T., A. Tiraferri, and R. Sethi. 2009. Ionic strength dependent transportof microparticles in saturated porous media: Modeling mobilization andimmobilization phenomena under transient chemical conditions. Environ.
Sci. Technol. 43:4425–4431. doi:10.1021/es900245d
Tufenkji, N. 2007. Modeling microbial transport in porous media: Traditional
approaches and recent developments. Adv. Water Resour. 30:1455–1469.
doi:10.1016/j.advwatres.2006.05.014
Tufenkji, N., D.R. Dixon, R. Considine, and C.J. Drummond. 2006. Multiscale Cryptosporidium/sand interactions in water treatment. Water Res.
40:3315–3331. doi:10.1016/j.watres.2006.07.036
Tufenkji, N., and M. Elimelech. 2004. Correlation equation for predicting
single-collector efficiency in physicochemical filtration in saturated porous
media. Environ. Sci. Technol. 38:529–536. doi:10.1021/es034049r
Tufenkji, N., and M. Elimelech. 2005a. Breakdown of colloid filtration theory:
Role of the secondary energy minimum and surface charge heterogeneities.
Langmuir 21:841–852. doi:10.1021/la048102g
Tufenkji, N., and M. Elimelech. 2005b. Spatial distributions of Cryptosporidium
oocysts in porous media: Evidence for dual mode deposition. Environ. Sci.
Technol. 39:3620–3629. doi:10.1021/es048289y
Tufenkji, N., J.A. Redman, and M. Elimelech. 2003. Interpreting deposition
patterns of microbial particles in laboratory-scale column experiments.
Environ. Sci. Technol. 37:616–623. doi:10.1021/es025871i
Tufenkji, N., J.N. Ryan, and M. Elimelech. 2002. The promise of bank filtration.
Environ. Sci. Technol. 36:422A –428A. doi:10.1021/es022441j
Unc, A., and M.J. Goss. 2004. Transport of bacteria from manure andprotection of water resources. Appl. Soil Ecol. 25:1–18. doi:10.1016/j.
apsoil.2003.08.007
van Genuchten, M.Th., and P.J. Wierenga. 1976. Mass transfer studies in sorbing
porous media: I. Analytical solutions. Soil Sci. Soc. Am. J. 40:473–480.
doi:10.2136/sssaj1976.03615995004000040011x
Veerapaneni, S., J. Wan, and T.K. Tokunaga. 2000. Motion of particles in film
flow. Environ. Sci. Technol. 34:2465–2471. doi:10.1021/es9912731
Verhulst, P.F. 1838. Notice sur la loi que la population suit dans son accroissement.
Corresp. Math. Phys. 10:113–121.
439

Verwey, E.J.W., and J.T.G. Overbeek. 1948. Theory of the stability of lyophobic
colloids. Elsevier, Amsterdam.
Vidali, M. 2001. Bioremediation: An overview. Pure Appl. Chem. 73:1163–
1172. doi:10.1351/pac200173071163
Walker, S.L., J.A. Redman, and M. Elimelech. 2004. Role of cell surface
lipopolysaccharides in Escherichia coli K12 adhesion and transport.
Langmuir 20:7736–7746. doi:10.1021/la049511f
Wan, J., and T.K. Tokunaga. 1997. Film straining of colloids in unsaturated
porous media: Conceptual model and experimental testing. Environ. Sci.
Technol. 31:2413–2420. doi:10.1021/es970017q
Wan, J., T.K. Tokunaga, and C.-F. Tsang. 1995. Bacterial sedimentation
through a porous medium. Water Resour. Res. 31:1627–1636.
doi:10.1029/95WR01255
Wan, J., and J.L. Wilson. 1994a. Colloid transport in unsaturated porous media.
Water Resour. Res. 30:857–864. doi:10.1029/93WR03017
Wan, J.M., and J.L. Wilson. 1994b. Visualization of the role of the gas–waterinterface on the fate and transport of colloids in porous media. Water
Resour. Res. 30:11–23. doi:10.1029/93WR02403
Wang, M., and R.M. Ford. 2009. Transverse bacterial migration induced bychemotaxis in a packed column with structured physical heterogeneity.
Environ. Sci. Technol. 43:5921–5927. doi:10.1021/es901001t
Wang, M., R.M. Ford, and R.W. Harvey. 2008. Coupled effect of chemotaxis andgrowth on microbial distributions in organic-amended aquifer sediments:
Observations from laboratory and field studies. Environ. Sci. Technol.
42:3556–3562. doi:10.1021/es702392h
Wang, Y., S.A. Bradford, and J. Šimůnek. 2013. Transport and fate of
microorganisms in soils with preferential flow under different solution
chemistry conditions. Water Resour. Res. 49:2424–2436. doi:10.1002/
wrcr.20174
Weiss, W.J., E.J. Bouwer, R. Aboytes, M.W. LeChevallier, C.R. O’Melia, B.T.
Le, and K.J. Schwab. 2005. River filtration for control of microorganisms
results from field monitoring. Water Res. 39:1990–2001. doi:10.1016/j.
watres.2005.03.018
Weiss, M., Y. Lüthi, J. Ricka, T. Jörg, and H. Bebie. 1998. Colloidal particles
at solid–liquid interfaces: Mechanisms of desorption kinetics. J. Colloid
Interface Sci. 206:322–331. doi:10.1006/jcis.1998.5636
Williams, V., and M. Fletcher. 1996. Adhesion and transport through porous
media of Pseudomonas fluorescens is affected by lipopolysaccharide
composition. Appl. Environ. Microbiol. 62:100–104.
Wissmeier, L., and D.A. Barry. 2009. Effect of mineral reactions on the hydraulicproperties of unsaturated soils: Model development and application. Adv.
Water Resour. 32:1241–1254. doi:10.1016/j.advwatres.2009.05.004
Xu, L.C., and B.E. Logan. 2006. Adhesion forces between functionalized latex
microspheres and protein-coated surfaces evaluated using colloid probe
atomic force microscopy. Colloids Surf. B 48:84–94. doi:10.1016/j.
colsurfb.2006.01.012

440

Xu, S., B. Gao, and J.E. Saiers. 2006. Straining of colloidal particles
in saturated porous media. Water Resour. Res. 42:W12S16.
doi:10.1029/2006WR004948
Yao, K.-M., M.T. Habibian, and C.R. O’Melia. 1971. Water and waste water
filtration: Concepts and applications. Environ. Sci. Technol. 5:1105–
1112. doi:10.1021/es60058a005
Yoon, J.S., J.T. Germaine, and P.J. Culligan. 2006. Visualization of particle
behavior within a porous medium: Mechanisms for particle filtration andretardation during downward transport. Water Resour. Res. 42:W06417.
doi:10.1029/2004WR003660
Yuan, H., and A.A. Shapiro. 2010. Modeling non-Fickian transport andhyperexponential deposition for deep bed filtration. Chem. Eng. J.
162:974–988. doi:10.1016/j.cej.2010.07.003
Yuan, H., and A.A. Shapiro. 2011. A mathematical model for non-monotonic
deposition profiles in deep bed filtration systems. Chem. Eng. J. 166:105–
115. doi:10.1016/j.cej.2010.10.036
Yukalov, V.I., E.P. Yukalova, and D. Sornette. 2009. Punctuated evolution due
to delayed carrying capacity. Physica D 238:1752–1767. doi:10.1016/j.
physd.2009.05.011
Zevi, Y., A. Dathe, B. Gao, W. Zhang, B.K. Richards, and T.S. Steenhuis.
2009. Transport and retention of colloidal particles in partially saturated
porous media: Effect of ionic strength. Water Resour. Res. 45:W12403.
doi:10.1029/2008WR007322
Zevi, Y., A. Dathe, J.F. McCarthy, B.K. Richards, and T.S. Steenhuis. 2005.
Distribution of colloid particles onto interfaces in partially saturated sand.
Environ. Sci. Technol. 39:7055–7064. doi:10.1021/es048595b
Zevi, Y., B. Gao, W. Zhang, V.L. Morales, M.E. Cakmak, E.A. Medrano, et al.
2012. Colloid retention at the meniscus–wall contact line in an open
microchannel. Water Res. 46:295–306. doi:10.1016/j.watres.2011.09.046
Zhang, P., W.P. Johnson, T.D. Scheibe, K.-H. Choi, F.C. Dobbs, and B.J.
Mailloux. 2001. Extended tailing of bacteria following breakthrough at
the Narrow Channel Focus Area, Oyster, Virginia. Water Resour. Res.
37:2687–2698. doi:10.1029/2000WR000151
Zhang, Q., S.M. Hassanizadeh, A. Raoof, M.Th van Genuchten, and S.M. Roels.
2012. Modeling virus transport and remobilization during transientpartially saturated flow. Vadose Zone J. 11(2). doi:10.2136/vzj2011.0090
Zhang, W., V.L. Morales, M.E. Cakmak, A.E. Salvucci, L.D. Geohring, A.G.
Hay, et al. 2010. Colloid transport and retention in unsaturated porous
media: Effect of colloid input concentration. Environ. Sci. Technol.
44:4965–4972. doi:10.1021/es100272f
Zheng, W., L.-P. Wang, D. Or, V. Lazouskaya, and Y. Jin. 2012. Role of mixed
boundaries on flow in open capillary channels with curved air–waterinterfaces. Langmuir 28:12753–12761. doi:10.1021/la302833p

Journal of Environmental Quality