Advances in Water Resources 25 (2002) 477–495

www.elsevier.com/locate/advwatres

Review

Considerations for modeling bacterial-induced changes in

hydraulic properties of variably saturated porous media
a,b,*
M.L. Rockhold , R.R. Yarwood a, M.R. Niemet c, P.J. Bottomley d, J.S. Selker a,*

a
Department of Bioengineering, Gilmore Hall, Oregon State University, Corvallis, OR 97331, USA
b
Pacific Northwest National Laboratory, Box 999, Richland, WA 99352, USA
c
CH2M Hill, 2300 NW Walnut Blvd., Corvallis, OR 97330, USA
d
Department of Microbiology, Nash Hall, Oregon State University, Corvallis, OR 97331, USA
Received 28 June 2001; received in revised form 20 December 2001; accepted 29 December 2001

Abstract
Bacterial-induced changes in the hydraulic properties of porous media are important in a variety of disciplines. Most of the
previous research on this topic has focused on liquid-saturated porous media systems that are representative of aquifer sediments.
Unsaturated or variably saturated systems such as soils require additional considerations that have not been fully addressed in the
literature. This paper reviews some of the earlier studies on bacterial-induced changes in the hydraulic properties of saturated porous
media, and discusses characteristics of unsaturated or variably saturated porous media that may be important to consider when
modeling such phenomena in these systems. New data are presented from experiments conducted in sand-packed columns with
initially steady unsaturated flow conditions that show significant biomass-induced changes in pressure heads and water contents and
permeability reduction during growth of a Pseudomonas fluorescens bacterium. Ó 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Bioremediation; Unsaturated porous media; Surface tension; Fluid-media scaling

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

2. Liquid-saturated porous media systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478

3. Unsaturated or variably saturated systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

3.1. Hydraulic properties of variably saturated porous media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482

4. Surface tension effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

5. Contact angle effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

6. Density and viscosity effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

7. Fluid-media scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

8. Composite media model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490

9. Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492

*
Corresponding authors. Address: Department of Bioengineering, Gilmore Hall 116 (M.L. Rockhold)/240 (J.S. Selker), Oregon State University,
Corvallis, OR 97331, USA. Tel.: +1-541-737-5410 (M.L. Rockhold)/+1-541-737-6304 (J.S. Selker); fax: +1-541-737-2082.
E-mail addresses: rockhold@engr.orst.edu (M.L. Rockhold), selkerj@engr.orst.edu (J.S. Selker).

0309-1708/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved.
PII: S 0 3 0 9 - 1 7 0 8 ( 0 2 ) 0 0 0 2 3 - 4
478 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

1. Introduction show the affects of biomass growth on pressure head and

water content distributions in unsaturated sand. Finally,
Bacterial-induced changes in the hydraulic properties several methods are discussed that can be used for
of porous media have been studied for various appli- modeling bacterial-induced changes in the hydraulic
cations ranging from enhanced oil recovery, to water properties of variably saturated systems. These methods
and wastewater treatment, to bioremediation of con- include fluid-media scaling, and a composite media
taminated soils and aquifer systems. Biodegradation of model for hydraulic properties.
anthropogenic contaminants in soils and aquifers in-
volves many complex interactions between physical,
chemical, and biological processes. Improved under-
standing of these processes and interactions is necessary 2. Liquid-saturated porous media systems
to achieve more effective bioremediation in field appli-
cations. Various conceptual and mathematical models have
Several conditions are needed for biodegradation been developed to describe substrate utilization or con-
and effective bioremediation [3]. One of these is that the taminant biodegradation and bacterial growth and
environment must be conducive to the proliferation of transport in saturated porous media systems. Three
the microorganisms of interest. Although proliferation different approaches have been used most often for this
of microorganisms is necessary, it can also have detri- type of modeling [6]. These are: (1) the biofilm model,
mental effects. For example, biomass accumulation can (2) the microcolony model, and (3) the strictly macro-
result in clogging of pore space and well bore bio- scopic model. A biofilm can be loosely defined as the
fouling at nutrient injection wells [44]. This biofouling layers of bacterial cells and associated extracellular
can restrict or prevent further injection of nutrients, material that form on a surface. The biofilm modeling
which can reduce the effectiveness of a bioremediation approach assumes that the attached biomass forms a
system. In the oil industry, however, selective plugging continuous biofilm of uniform thickness covering all
of pore space has been used to enhance oil recovery solid particles [70–73]. The microcolony modeling ap-
during water injection. In situ microbial growth in proach assumes that bacteria attach to soil or aquifer
liquid-saturated systems can selectively plug high per- solids in discrete colonies, each with an effective surface
meability zones and tends to drive an initially hetero- area through which substrates diffuse [50,83,84]. The
geneous permeability field toward homogeneity [33,55]. biofilm and microcolony modeling approaches have
An open question is if microbial growth and accumu- both been used to explicitly account for possible
lation in heterogeneous, unsaturated porous media substrate diffusional limitations through an attached
systems will manifest greater heterogeneity, or if it will biomass phase. The strictly macroscopic modeling ap-
have a homogenizing effect as seen in saturated sys- proach assumes that bacteria can attach and grow in the
tems. porous media but makes no other assumptions about
The objectives of this paper are to review some of the the spatial structure or geometry of the attached bio-
earlier studies on bacterial-induced changes in the hy- mass. In this approach it is usually assumed that no
draulic properties of saturated porous media, and to diffusional limitations exist in the biomass and that it is
discuss characteristics of unsaturated or variably satu- fully penetrated by substrate, nutrients, contaminant,
rated porous media that may be important to consider etc. It has been shown that with certain assumptions, the
when modeling such phenomena in these systems. Pre- biofilm and microcolony models can be reduced to the
viously published work on conceptual and mathematical strictly macroscopic model [6,58,83]. Recent literature
models and experimental studies of biomass growth and suggests that the macroscopic modeling approach is
accumulation in saturated porous media is reviewed to most commonly used [17,44,52].
identify some of the issues and progress to date. Char- A number of experimental studies have been con-
acteristics of variably saturated or unsaturated systems ducted to provide data to support the use of the different
are discussed to identify additional processes that may conceptual and mathematical models described above,
need to be considered for modeling changes in the hy- and to evaluate the effects of microbial growth and bio-
draulic properties of variably saturated porous media. mass accumulation on the effective porosity and per-
New data from column experiments are presented that meability of saturated porous media. Taylor and Jaffe
 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495 479

[70] conducted experiments in water-saturated, sand-

packed column reactors using bacteria isolated from
primary sewage and activated sludge from a treatment
plant. They used methanol as a substrate, at concen-
trations of 7.2 and 5.6 mg/l, and observed reductions in
saturated hydraulic conductivity, Ks , of more than 3
orders of magnitude at the influent ends of their col-
umns as a result of biomass accumulation. The mean
particle diameter of the sand used in their experiments
was 0.7 mm. Their data suggest an upper limit to the
reduction of Ks of about 3.5 orders of magnitude. They
hypothesized that this upper limit represents a balance
between growth and accumulation of attached biomass,
and biomass loss to the water phase resulting from fluid
shear. Taylor et al. [73] and Taylor and Jaffe [71] de-
veloped models for permeability reduction and changes
in dispersivity based on the concept of bacteria forming
biofilms that uniformly cover the grains of the porous
media.
Vandevivere and Baveye [75,76] showed that an aer-
obic bacterial strain, Arthrobacter AK19, was able to
reduce the Ks of saturated sand columns by 3–4 orders
of magnitude within one week when grown on glucose
concentrations as low as 10 mg/l. They determined that
the production of extracellular polymeric substances
(EPS) was not necessary to induce severe clogging. They Fig. 1. SEM images of Arthrobacter AK19 taken in sand at different
noted that EPS (polysaccharides) were produced and magnification (A and B) under conditions of O2 limitation by Van-
appeared to cause additional reduction in Ks when the devivere and Baveye [75] (with permission).
carbon to nitrogen (C:N) ratio was high [77], but EPS
seemed to be absent from the clogged layers when the Rittmann [58] notes that regardless of the character-
C:N ratio was low (<39). The mean particle diameter of istics of the attached biomass, net accumulation is
the sand used in their experiments was 0.09 mm. controlled by four processes: growth, deposition, decay
Fig. 1 shows scanning electron microscope (SEM) (or death), and detachment. Growth is generally as-
images of Arthrobacter AK19 taken in sand [76]. Van- sumed to be proportional to the rate of substrate utili-
devivere and Baveye [76] noted that there was no evi- zation and to the amount of biomass already present.
dence in their SEM photographs of the bacterium Deposition is controlled by the concentration of the
forming biofilms that uniformly covered the pore walls. aqueous-phase biomass and physicochemical properties
Instead, their experiments indicated that the cells grew of the fluid-media system. Biomass decay is assumed to
in interstitial spaces where they formed large aggregates. be proportional to the amount of active biomass. De-
They contend that permeability reduction in saturated tachment is generally assumed to be primarily a function
porous media systems is caused mainly by the accumu- of the amount of attached biomass, hydrodynamic shear
lation of bacterial aggregates at pore constrictions where stress, and growth rate [45,56,69]. Lawrence et al. [36]
they form local plugs that impede water flow [74–76]. studied the surface colonization behavior of a Pseudo-
The two primary modes of accumulation of attached monas fluorescens bacterium and determined that it
bacteria that have been conceptualized and observed in could be subdivided into the following sequential pha-
saturated systems––continuous biofilm vs. cell aggre- ses: motile attachment phase, reversible attachment
gates––raises questions as to what mode of accumula- phase, irreversible attachment phase, growth phase, and
tion is most prevalent under what conditions, and how recolonization phase. These colonization phases may
to best represent this accumulation in terms of its effect differ between bacterial strains.
on porosity and permeability reductions. The answers to Rittmann [58] recognized that different studies have
these questions are problematic, and depend on the type used different types of bacteria, different substrates, dif-
of bacteria and the environmental conditions. No uni- ferent flow rates, and porous media with different mean
versally applicable model has been developed for satu- grain sizes. He attempted to explain and reconcile some
rated porous media systems. Moreover, no attempts of the differences in the characteristics of the attached
have been made to develop a model that is applicable to biomass that have been observed in previous studies
both saturated and unsaturated systems. by using the concept of normalized surface loading
480 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495

[30,31,57,82] to standardize results. Normalized surface and permeability caused by biomass accumulation in
loading curves can be generated using the biofilm model saturated porous media. Their equations are based on
of Rittmann and McCarty [59,60], which was developed macroscopic estimates of average biomass concentra-
under the assumption that a given biofilm is at steady tions and are thus appropriate for use in the macro-
state and the substrate is completely mixed. Rittmann scopic approaches for modeling substrate utilization.
[58] attempted to establish guidelines for the range of Their results are comparable to the biofilm model results
values of normalized surface loading that can be ex- obtained by Taylor et al. [73]. Clement et al. [17] used a
pected to lead to the formation of continuous biofilms cut-and-random-rejoin model of porous media [51,73]
versus discontinuous cell aggregates by comparing and derived the following equations for relative changes
computed values of normalized surface loading with the in permeability and specific surface area due to biomass
observed characteristics of the attached biomass that accumulation
were reported in previous studies.
19=6
Vandevivere [74] developed a model to estimate hy- kb nf
¼ 1 ð3Þ
draulic conductivity reduction in saturated porous k0 /
media systems that incorporates both the uniform bio-
2=3
film accumulation and cell aggregate clogging mecha- Mb nf
¼ 1 ð4Þ
nisms. He developed the following expression from an M0 /
analysis of several data sets [18,70,75] where kb and k0 are the permeabilities of the biomass-


Ks
2 a affected porous medium and the ‘‘clean’’ porous me-
¼ F ðBÞð1  BÞ þ ½1  F ðBÞ ð1Þ dium, and Mb and M0 are the specific surface areas of the
Ks a þ B  aB
biomass-affected and clean porous media, respectively.
where Values of specific surface area were computed by
"
2 # Clement et al. [17] to facilitate comparisons with the
B biofilm model of Taylor et al. [73]. The volume of sand-
F ðBÞ ¼ exp  0:5 ð2Þ
Bc associated (attached) biomass/bulk volume of porous
media was estimated from
and where Ks
=Ks is the ratio of the saturated hydraulic
conductivity of the biomass-affected porous medium to Xf qb
nf ¼ ð5Þ
the saturated hydraulic conductivity of the ‘‘clean’’ po- qf
rous medium, B ¼ 1  ðnb =/Þ, which is the volume
where Xf is the mass of microbial cells per unit mass of
fraction of pore space occupied by bacterial colonies, nb
porous medium, qb is the bulk density of the porous
is the porosity of the biomass-affected porous medium,
medium, and qf is the density of the microbial cells.
and / is the original porosity. The parameter a is the
Clement et al. [17] calculated the porosity reduction
value of Ks
=Ks when the porous medium is completely
from a simple volume balance
filled with biomass (B ¼ 1), and Bc is an empirical pa-
rameter that controls how quickly the system ap- n b ¼ /  nf ð6Þ
2
proaches the value of a. The term, ð1  BÞ in (1)
represents the clogging of a bundle of capillary tubes by where nb is again the porosity of the biomass-affected
continuous biofilms that reduce the effective diameter of porous medium. Note that (6) implies that the attached
the tubes. Vandevivere [74] refers to this as the ‘‘biofilm’’ biomass phase is non-porous. With the assumptions
model. The term, ½a=ða þ B  aBÞ, in (1) represents the used in their derivations, Clement et al. [17] found that
formation of discrete plugs in some of the tubes in the Eqs. (3) and (4) resulted from using either the van Ge-
capillary bundle. Vandeviviere [74] refers to this as nuchten [78] or Brooks and Corey [11] models of water
the ‘‘plug’’ model. The two terms are combined as a retention, both of which were used to infer the pore-size
weighted average function of the volume fraction of the distributions of the porous media. However, Clement
total porosity occupied by biomass. Based on the maxi- et al. [17] ignored possible changes in the pore-size dis-
mum permeability reductions observed in earlier studies, tribution of the porous media and only accounted for
an average value of a ¼ 0:00025 was suggested to be reductions in the maximum pore radius.
adequate for most practical purposes [74]. Alternatively, Eq. (1) from Vandeviviere [74] is plotted in Fig. 2 with
the a parameter can be determined experimentally. Note data from Cunningham et al. [18] and Vandevivere
that unlike the previous models that have been proposed and Baveye [75]. Also plotted are the ‘‘plug’’ and ‘‘bio-
in the literature, a porous and permeable attached bio- film’’ models from Vandevivere [74], and Eq. (3) from
mass phase is implicitly assumed by the use of non-zero Clement et al. [17]. Eq. (3) contains no empirical pa-
values of the a parameter in (1). rameters and is essentially equivalent to a biofilm model.
Clement et al. [17] developed analytical expressions The empirical parameter, Bc , in (2) was fit to the data
for modeling changes in porosity, specific surface area, sets depicted in Fig. 2 by Vandevivere [74]. He noted
 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495 481

clusion is also supported by a number of other recent

studies [8,42,43,85].

3. Unsaturated or variably saturated systems

Differences in the behavior of bacteria in unsaturated

or variably saturated porous media such as soils, relative
to fully water-saturated porous media such as aquifers
are due, in part, to the presence of air–water interfaces.
Wan et al. [81] showed that preferential sorption of
bacteria can occur on air–water interfaces relative to
solid–water interfaces. This preferential sorption was
shown to be proportional to air saturation. Wan et al.
[81] suggest that sorption onto air–water interfaces is
controlled primarily by bacterial cell surface hydro-
phobicity and that this sorption is essentially irrevers-
ible. In addition to the hydrophobicity mechanism,
preferential growth of aerobic bacteria might also occur
at air–water interfaces due to oxygen limitations, espe-
cially during high substrate loading conditions. Such
limitations could result in oxygen gradients that favor
the migration of motile aerobic microorganisms to air–
Fig. 2. Models for hydraulic conductivity or permeability reduction in water interfaces via chemotaxis.
saturated porous media as a function of the volume fraction of pore The adaptive nature of microorganisms complicates
space occupied by bacterial colonies, B. Data for P. aeruginosa in 0.7 the quantification of their behavior and interactions.
mm sand is from Cunningham et al. [18], and data for Arthrobacter in
0.09 mm sand is from Vandevivere and Baveye [75,76].
This adaptive nature is more apparent in unsaturated or
variably saturated porous media systems than in satu-
rated systems due to the additional degree of freedom.
that the coarser the texture of the porous media, the For example, Roberson and Firestone [61] and Chenu
greater the fitted value of Bc , and suggested that this [15] demonstrated that some bacteria respond to soil
observation warranted additional research to obtain drying by increasing the production of EPS which
independent estimates of Bc for various systems. Van- buffers cells from desiccation and also apparently in-
devivere [74] also noted that any practical use of (1) creases the rates of cell attachment to porous media.
would require the simultaneous modeling of water flow, EPS can also have a tremendous water-holding capacity
transport and utilization of substrate, and biomass [15].
growth and accumulation. Table 1 lists some of the properties of unsaturated or
Reaching a consensus on a conceptual model for how variably saturated porous media systems that may
bacteria attach, accumulate, and alter porosity and change due to the accumulation of biomass or due to the
permeability in porous media is impeded by the diffi- generation of bi-products of microbial metabolism, such
culty of observing them in situ under realistic environ- as biosurfactants. These properties include the surface
mental conditions, and by the fact that different bacteria tension at the gas–liquid interface, the solid–liquid
respond to changing environmental conditions differ- contact angle, the bulk solution density and viscosity,
ently [13,19,47]. De Beer and Schramm [19] studied the and the effective pore structure of the combined porous
microbial ecology of microenvironments and mass media/biomass system. The volume and composition of
transfer characteristics in biofilms using a combination the gas phase may also change as oxygen or other gases
of microsensor and molecular techniques. They cite are consumed and carbon dioxide or other gases are
earlier work in which confocal microscopy was used to generated during microbial metabolism [37]. Gas gen-
study biofilms and to identify highly complex structures eration and entrapment thus provides an additional
within them. These structures contained layers and mechanism for reducing permeability, in both saturated
clusters of cells, as well as voids or pores [20,21,36]. De and unsaturated porous media [14,67]. The processes
Beer et al. [21] determined that the biofilm volumes in that we believe are most influential in the alteration of
their study were up to 50% void spaces. The primary the hydraulic properties of variably saturated porous
conclusion of De Beer and Schramm [19] was that due to media, and methods for modeling their changes in flow
the porous nature of biofilms, convection can be a sig- and transport models, are discussed in more detail in the
nificant transport mechanism through them. This con- following sections.
482 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495

Table 1 interface, and r is the effective radius of curvature of a

Possible effects of biomass accumulation and associated bi-product cylindrical capillary tube or spherical pore. The inter-
formation on hydraulic and transport properties of variably saturated
porous media
facial tensions, rsg and rls , and the effective radius of
curvature of the liquid–gas interfaces, R2 are difficult to
Location of adsorption or Possible effects
accumulation
measure. Therefore, Eqs. (7) and (8) are usually not used
directly, but are expressed in terms of more easily
Gas–liquid interface Decreased surface tension
Increased gas–liquid interfacial area measured variables such as the liquid–gas interfacial
Changes in gas–liquid mass transfer tension, rlg , and an apparent contact angle, c, between
rates the liquid–gas interface and the solid. Young’s equation
Solid–liquid interface Decrease in porosity and permeability relates the three interfacial tensions to the apparent
Changes in apparent contact angle contact angle at equilibrium
Liquid–liquid interface Changes in interfacial tensions rsg ¼ rls þ rlg cos c ð9Þ
(e.g. water–NAPL)
Increased solubility of NAPL Eqs. (8) and (9) can be combined to yield what is com-
Bulk aqueous phase Increased viscosity monly known as the Laplace equation
Increased solution density
Increased solubility of substrates
2rlg cos c
pc ¼ ð10Þ
r
Cell-to-cell (or particle) Physical filtration and pore clogging
aggregation When expressed on the basis of an equivalent height of
Decrease in porosity and permeability water, Eq. (10) becomes
2rlg cos c
h¼ ð11Þ
Dqgr
3.1. Hydraulic properties of variably saturated porous
media where h is the pressure head (negative for unsaturated
porous media), which is equivalent to the height to
Unlike liquid-saturated porous media systems, un- which water would rise in a capillary tube when its lower
saturated or variably saturated porous media contain a end is in contact with a free water surface, and Dq is the
gas phase which is frequently assumed to be intercon- density difference between the aqueous and gas phases.
nected and at constant, atmospheric pressure. The water The density of the gas phase is usually considered to be
content (or saturation) and hydraulic conductivity of negligible relative to the aqueous phase.
variably saturated porous media are non-linear func- Various empirical models have been developed to
tions of the capillary pressure, rather than being con- describe pressure–saturation relations, such as that
stants as in saturated systems. To aid in this discussion, given by Brooks and Corey [11]
the equations that relate the capillary pressure to surface    k
tension and other interfacial forces are reviewed. hr
Se ¼ hhws h ¼ hhb for h P hb
The pressure difference, Dp, between a gas and liquid
r ð12Þ
Se ¼ 1 for h < hb
phase across their shared interface is related to the
curvature of the interface by the well-known Young– where Se is the effective saturation, hr is the residual or
Laplace equation irreducible water content, hs is the saturated water

 content or porosity (/), hb is the air-entry pressure,
1 1
Dp ¼ pg  pl ¼ rlg þ ð7Þ which is a measure of the maximum pore size forming a
R1 R2
continuous network of flow channels through the po-
where pg is the pressure in the gas phase, pl is the pres- rous medium, and k is a pore-size distribution index.
sure in the liquid phase, rlg is the surface tension at the The relative permeability, kr , or hydraulic conductivity,
liquid–gas interface, and R1 and R2 are the principal K, of a porous medium can be represented using models
radii of curvature of the solid surface (e.g. sand grain) such as that given by Burdine [12] or Mualem [51].
and the liquid–gas interfaces, respectively. In capillary When combined with the Brooks–Corey model, the
tubes and porous media, this pressure difference is Burdine model can be expressed as
usually referred to as the capillary pressure, pc , which K e
can also be defined as kr ¼ ¼ ðSe Þ ð13Þ
Ks
 
2 rsg  rls or
Dp pc ¼ ð8Þ
r  h g
kr ¼ b
h
for h P hb
where rsg is the interfacial tension at the solid–gas in- ð14Þ
terface, rls is the interfacial tension at the liquid–solid kr ¼ 1 for h < hb
 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495 483

where Ks is the hydraulic conductivity of the porous

medium when fully saturated with liquid, and where
e ¼ 2=k þ 3, and g ¼ 2 þ 3k.
The van Genuchten [78] model is also commonly used
to represent the water retention characteristics of vari-
ably saturated porous media
1
Se ¼ n m ð15Þ
½1 þ ðahÞ 

where a, n, and m are empirical parameters that affect

the shape of the water retention function. Van Ge-
nuchten [78] combined (15) with the Mualem [51]
hydraulic conductivity model to derive closed-form ex-
pressions for the hydraulic conductivity of unsaturated
porous media. These expressions for hydraulic conduc-
tivity are given by Eqs. (16) and (17),
m 2
KðSe Þ ¼ Ks Se‘ ½1  ð1  Se1=m Þ  ð16Þ
mn n m 2
Ks f1  ðahÞ ½1 þ ðahÞ  g
KðhÞ ¼ n m‘
ð17Þ
½1 þ ðahÞ 

as a function of effective saturation and pressure head, Fig. 3. Water retention data and fitted retention functions for pure
respectively, where ‘ is a pore-interaction term that is xanthan (data from Chenu [15]), a clay soil (model parameters from
Leij et al. [38]), clean 40/50 grade Accusandâ , and repacked, biomass-
often assumed to be equal to 0.5, and m ¼ 1  1=n
affected 40/50 grade Accusandâ . The continuous curves represent fits
[51,78]. Further discussion on these equations is pro- of the Brooks–Corey and van Genuchten water retention models to the
vided by van Genuchten et al. [79]. data.
Fig. 3 shows the measured water retention charac-
teristics (primary drainage) of a 40/50 grade of quartz
sand (Accusandâ , Unimin, Co.) measured in our labo- the columns at a flow rate of 7 cm/h, with the lower
ratory, a clay soil [38], and xanthan, a pure polysac- boundary maintained at a pressure head of 0 cm. These
charide isolated from the soil bacterium, Xanthomonas boundary conditions resulted in unsaturated conditions
sp. [15]. Xanthan is widely used in modifying the vis- in the upper halves of the columns with saturated con-
cosity of processed foods, in stabilizing suspensions, ditions below. Pressure heads and apparent volumetric
and in oil field recovery operations [5]. The remarkable water contents within the columns were measured dur-
water holding capacity of xanthan is clearly evident ing the experiment using the tensiometers and TDR
from Fig. 3. This large water holding capacity has po- probes, respectively.
tentially significant implications for the ability of bac- After one week, water began to pond on the surface
teria to modify the hydraulic properties of variably of the columns, indicating that the saturated hydraulic
saturated porous media through their production of conductivity of the sand at the surface of the columns
EPS. was reduced from its original value of 317 cm/h to less
The water retention characteristics of the clean 40/50 than 7 cm/h. After ponding started, the supply of in-
Accusand shown in Fig. 3 are plotted with data repre- fluent to the tops of the columns was stopped and the
senting the same sand after a Pseudomonas fluorescens upper unsaturated portions of the columns were de-
HK44 bacterium was allowed to grow in the sand in our structively sampled. Samples were oven-dried at 50 °C
laboratory for one week. The sand was originally for two days to determine gravimetric water contents.
wet-packed into duplicate, segmented, acrylic columns The oven-dried, biomass-affected sand formed aggre-
that were instrumented with tensiometers with pressure gates which were broken up and passed through a 40
transducers, and time-domain reflectometry (TDR) mesh (0.425 mm) screen prior to repacking in Tempe
probes, for measurement of pressure heads and apparent cells (Soil Measurement Systems, Inc.) for water reten-
volumetric water contents, respectively. The sand was tion measurements. The sand-packed Tempe cells were
wet-packed into the columns which contained a cell- vacuum saturated prior to initiating water retention
solution with a concentration of approximately 108 measurements. Comparisons of the data representing
CFU/ml (where CFU refers to a colony-forming unit). the clean and biomass-affected sands in Fig. 3 indicates
A steady flux of a minimal mineral salts (MMS) solution that the biomass had a significant impact on the water
containing 250 mg/l glucose was applied to the tops of retention characteristics of the porous media. The
484 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495

properties of the sand shown in Figs. 3 and 4 are dis-

cussed below.

4. Surface tension effects

Many bacterial cell surface polymers are amphipathic,

containing strongly hydrophobic and hydrophilic moi-
eties that tend to concentrate at gas–liquid interfaces [5].
As noted previously, cell hydrophobicity provides a
mechanism for sorption of bacterial cells at gas–liquid
interfaces. Bacterial cells may also secrete compounds
such as polypeptides that can behave like surfactants.
Adsorption of bacteria and surfactants at gas–liquid
interfaces tends to reduce the interfacial free energy and
thus the surface tension. If sorption can be taken to be
instantaneous, the Gibbs adsorption equation can po-
tentially be used to relate observed changes in surface
tension to the concentration of adsorbed cells and/or
surfactants at gas–liquid interfaces [2]. Recent work by
Docoslis et al. [24] indicates that the hydrophobic or
hydrophilic nature of solutes is also an important con-
sideration when measuring surface tensions of aqueous
Fig. 4. Water retention characteristics for primary wetting and drain- solutions.
age of clean 40/50 grade Accusandâ , and water retention data mea-
Fig. 5 shows the apparent surface tensions at the gas–
sured by tensiometry and TDR in columns during growth of a
Pseudomonas fluorescens HK44 bacterium on glucose under steady flow liquid interface for different concentrations of station-
conditions. Note that the times correspond to times following the in- ary-phase Pseudomonas fluorescens HK44 suspended in
troduction of glucose into the columns and the symbols for the tran- MMS. The surface tensions shown in Fig. 5 were mea-
sient data represent 10 h increments (except for the final time of 168 h). sured using a DuNo€ uy ring tensiometer (CSC Scientific
Co., Inc., Fairfax, VA). Fig. 5 suggests that an ap-
proximately linear decrease in surface tension of less
wettability of the sand was apparently reduced, but the
effective residual water content of the biomass-affected
sand was also increased.
Fig. 4 shows the water retention characteristics of the
40/50 Accusandâ corresponding to primary drainage
and wetting, along with data collected from the tensi-
ometers and TDR probes in our laboratory during the
experiment described above. Since steady flow was
maintained during the experiment, the changes in pres-
sure head and water content that occurred in the bio-
mass-affected sand depicted in Fig. 4 (transient data)
were likely due to changes in contact angle and/or sur-
face tension. Pressure heads increased at all measured
depths during the experiment, while increases in the
apparent volumetric water content occurred primarily in
the upper 3 cm of the columns. Measurements made on
sand samples from the columns indicated that little or
no EPS was produced under the conditions of the col-
umn experiment. The data shown in Fig. 3, however,
represent the biomass-affected sand after it was oven
dried and repacked. Changes in the water retention
characteristics of the biomass-affected sand shown in
Fig. 3 are apparently due to changes that occurred Fig. 5. Apparent surface tension as a function of aqueous phase cell
during drying. Some of the possible causes for the ob- concentrations for the Pseudomonas fluorescens HK44 bacterium
served, biomass-induced changes in the hydraulic (error bars represent standard deviation of three measurements).
 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495 485

than 1 mN/m occurs over an almost three-order-of- 5. Contact angle effects

magnitude increase in cell concentrations ( 106 –109
CFU/ml) for this particular bacterium in stationary The changes in saturation that are depicted in Fig. 4
phase. These data suggest that surface tension lowering could also have resulted, in part, from changes in the
due to sorption of the cells themselves may be relatively apparent contact angle at solid–liquid interfaces as the
insignificant. However, Deziel et al. [23] conducted a solids became coated by biofilms. Table 2 lists some
study of a Pseudomonas aeruginosa 19SJ bacterium ac- physicochemical properties of various bacteria and latex
tively growing on the polycyclic aromatic hydrocarbon, particles, including apparent contact angles (wetting).
naphthalene, and reported a reduction in surface tension The contact angle data shown in Table 2 from Wan et al.
from 74 to 33 mN/m as a result of biosurfactant [81] were measured at the junction of the drop of an
production by the bacterium. They did not report the aqueous solution, a bacterial surface formed on micro-
actual cell concentrations that were used in their ex- porous filter paper, and the atmosphere using a contact
periments, but the contrast between their results and the angle goniometer. The values reported by Wan et al. [81]
data in Fig. 5 suggest that surface tension lowering ef- represent the means of more than 15 measurements for
fects might be related to the production of surface-active each bacterium examined. The contact angle in water-
agents during active metabolism. This conclusion is wet porous media is generally assumed to be equal to
dependent, however, on the type (and metabolic state) 0°, whereas a contact angle of 30° can be inferred
of the bacteria, the type of substrate, and on the pres- from data for water imbibition into dry capillary tubes.
ence or absence of various trace elements [35]. The data shown in Table 2 clearly indicate that bacteria
Deziel et al. [23] determined that the presence of the are capable of altering the wettability of surfaces, and
intermediate metabolite, salicylate, reduced the delay or thus changing the water retention characteristics of po-
lag time before accumulation of biosurfactant (glyco- rous media (see Eq. (11)). Further discussion on contact
lipid––rhamnose) in the P. aeruginosa 19SJ bacterium. angle effects is given in a later section on fluid-media
They also determined that the production of biosurfac- scaling.
tants in their experiments increased the apparent aque- Decreases in liquid saturation that result from low-
ous solubility of naphthalene by more than a factor of 3 ering of surface tension and changes in apparent contact
over its normal solubility in water. They suggested that angles would also tend to create more gas–liquid inter-
biosurfactant production by bacteria is a self-stimulat- facial area. Increased gas–liquid interfacial area poten-
ing process in which the solubilizing effect of biosurf- tially provides additional sites for cell and biosurfactant
actants increases the availability of insoluble substrates, adsorption, as well as more surface area for exchange of
which in turn promotes further growth and utilization oxygen and other gases between the aqueous and gas
of the substrates. Hammel and Ratledge [28] suggest, phases. Adsorption of a macromolecular film at the gas–
however, that surfactant production by microorganisms liquid interface can, however, effectively decrease the
may be nothing more than a method of removing sur- mass transfer rates of gases across the interface [2,5]. All
plus fatty acids. of these factors may need to be considered for accurate
In unsaturated porous media, reduced surface tension modeling of biodegradation processes in variably satu-
due to adsorption of cells and/or surfactants at gas– rated porous media.
liquid interfaces could lead to lower liquid saturations. Bailey and Ollis [5] note that the adsorption of mac-
Sch€afer et al. [64] monitored liquid contents and pres- romolecular films at gas–liquid interfaces can also result
sures in unsaturated column experiments during trans- in stagnant, rigid interfaces. From a fluid mechanics
port of two types of soil bacteria under non-growth perspective, the nature of the gas–liquid interface in
conditions. They observed slight increases in liquid
saturation during their experiments, but stated that the Table 2
increase was not caused by a change in surface tension Selected physicochemical properties of bacteria and colloids
of the liquid in the presence of bacteria. From the pre- Bacteria or Size (lm) Contact angle, Zeta potential,
viously cited results, and without regard to other fac- Colloid cw (deg) f (mV)
tors, the accumulation of biosurfactants would tend to Arthrobacter 1:0  0:8 77.1  2.5 56.3
lower surface tension and lead to lower liquid satura- sp. S-139a
tion. However, desaturation effects due to surface ten- P. cepacia 1:3  0:8 24.7  3.1 12.1
sion lowering may also be strongly dependent upon the 3N3Aa
Rhodococcus 3:0  0:9 95.1  1.7 44.8  1.4
boundary conditions and dimensionality of the experi-
sp. C125b
mental system. Local reductions in surface tension and P. putida mt2b 2:2  0:9 38.2  1.5 13.4  1.0
desaturation of a porous medium should result in lower Latex particlesc 0.22 127  5 36
unsaturated hydraulic conductivity, which effectively a
From Wan et al. [81].
increases the resistance to flow. This could then lead to b
From Sch€afer et al. [64].
c
increases in upstream saturations, as illustrated in Fig. 4. From Wan and Wilson [80].
486 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495

unsaturated porous media is subject to debate as to Happel and Brenner [29] review various equations
whether it more closely resembles a no-slip (e.g. the that have been used for calculating the apparent vis-
static wall of a capillary tube) or a slip boundary (e.g. cosity of liquids containing solid particles in suspension.
the dynamic gas–liquid interface at the surface of a Einstein [25] formula can be used to calculate the ap-
flowing river), or some combination of the two. Exper- parent viscosity of a dilute suspension of spherical par-
imental data from Sch€ ugerl [66] and Wan et al. [81] ticles
provide support for the argument of a limited slip

5
boundary condition. l ¼ l0 1 þ /m ð19Þ
2
where l0 is the viscosity of the particle-free suspending
6. Density and viscosity effects liquid. Brodnyan [10] proposed the following equation
for the viscosity of concentrated solutions of ellipsoidal
As cell concentrations increase in the bulk aqueous particles
" #
phase during growth of bacteria, the apparent viscosity 2:5/m þ 0:399ðp  1Þ1:48 /m
and density of the liquid-cell suspension may increase. l ¼ l0 exp ð20Þ
1  c/m
Several studies have demonstrated the importance of
solution density on transport in saturated porous media where the value 2.5 comes from the Einstein formula
systems. Istok and Humphrey [32], for example, con- (19), the constants 0.399 and 1.48 were determined em-
ducted two-well tracer tests in a homogeneous physical pirically from experimental data, p ¼ a1 =a2 where a1 and
aquifer model and observed significant gravity-induced a2 are the dimensions of the major and minor axis of the
plume sinking with bromide concentrations as low as 50 ellipsoidal particle, respectively, and c is an experimen-
mg/l. Murphy et al. [52] determined that accounting for tally determined constant that ranges in value from 1.35
density differences as low as 0.1% was significant for to 1.91.
accurately modeling breakthrough of CaCl2 and ben- Eqs. (18)–(20) are plotted in Fig. 6, using values of
zoate in a flow cell containing saturated porous media p ¼ 4:0 and 1.0, and c ¼ 1:68 for Eq. (20). With an av-
with bimodal heterogeneities and benzoate-degrading erage cell density of 1.1 g/cm3 , changes in the density of
bacteria. the liquid-cell suspension are relatively small, increasing
The affects of density differences in unsaturated po- by only 1% for a 10% increase in the volume fraction of
rous media are usually assumed to be less significant cells in suspension. Fig. 6 indicates that the potential for
than in saturated porous media because of the lack of changes in the apparent relative viscosity are much more
buoyancy effects. Ouyang and Zheng [53] conducted significant than changes in density, especially for ellip-
numerical experiments to determine the significance of soidal particles. A value of p ¼ 1 in the Brodnyan [10]
density effects on transport in unsaturated soil. They model (20) corresponds to spherical particles, and yields
determined that solution density had a negligible affect values that are similar to Einstein’s results from (19).
on the transport of the chemical aldicarb (relatively low The differences between the apparent relative viscosities
aqueous solubility), but had a significant affect on the predicted by (19) and (20) are substantial, however,
transport of the chemical acephate (relatively high when p ¼ 4. This value of p corresponds to ellipsoidal
aqueous solubility). particles whose major axes are four times larger than
Evaluation of the significance of changes in bulk so- their minor axes, which is within the range of possible
lution density due to bacterial cells is straightforward. dimensions for rod-shaped bacteria.
Bouwer and Rittmann [9] report that bacterial cell In many natural environments, low nutrient avail-
densities range from about 1.01 to 1.13 g/cm3 , with an ability will limit bacterial cell growth and population
average value of about 1.1 g/cm3 . If cells are assumed to densities so that changes in solution density and vis-
behave approximately like solid particles, and if the cosity due to the accumulation of cells will be relatively
liquid-cell suspension is viewed as a continuum, the small and probably negligible. However, under high
average density of a bacterial cell and the volume frac- nutrient loading conditions, such as might occur in a
tion of cells in suspension can be used to estimate the bioremediation scenario, these changes may be signifi-
density and apparent viscosity of the liquid-cell sus- cant.
pension. The density of the liquid-cell suspension, q, can Murphy et al. [52] noted that physical heterogeneities
be calculated from tend to amplify density and viscosity differences in sat-
q ¼ /m qm þ ð1  /m Þq0 ð18Þ urated porous media systems. Furthermore, they noted
that macroscopic continuum models of flow and trans-
where /m is the volume fraction of cells (or particles) in port may be taxed beyond their theoretical capability
suspension, and qm and q0 are the densities of the cells when density and viscosity effects are significant because
and the cell-free liquid, respectively. these effects may be due to microscopic pore-scale in-
 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495 487

Fig. 6. Relative density and relative apparent viscosity as a function of the volume fraction of particles (bacterial cells) in suspension. The parameter
p represents the ratio of the dimensions of the major and minor axis of an ellipsoidal particle.

stabilities arising from the density and viscosity varia- angle, liquid density, and viscosity on the hydraulic
tions that cannot be adequately resolved using conti- properties of a variably saturated porous medium
nuum models. The same argument applies to variably can be accounted for approximately in continuum
saturated or unsaturated porous media systems, al- flow and transport models by fluid-media scaling [49].
though the effects of density should be significantly less Changes in the air-entry pressure of a porous medium
in unsaturated systems owing to the lack of buoyancy (see Eq. (12)) can be estimated by taking ratios of (11),
effects and the mitigating effects of capillarity. which yields
Pore-scale instabilities may also be induced in vari-


ably saturated or multi-fluid systems by a microscopic r q0
h
b ¼ hb b ð21Þ
phenomenon known as the Marangoni effect, which r0 q
refers to the carrying of bulk material through motions
energized by surface tension gradients [2]. Marangoni where h
b is a scaled air-entry pressure, r and r0 are
instabilities are often associated with temperature gra- surface tensions at the gas–liquid interface, and q and q0
dients that alter or create surface tension gradients [63]. are liquid densities, for the liquid-cell suspension and
However, such instabilities could also result from con- cell-free liquid (subscript 0), respectively, and b is a
centration gradients that might arise in variably satu- contact angle scaling factor. Surface tension and density
rated or multi-fluid systems due to solute displacement, can be measured as a function of bacterial cell concen-
substrate consumption, microbial growth, and/or bio- trations, or estimated using Eqs. (18)–(20). Changes in
surfactant production. Such instabilities could provide a surface tension due to biosurfactant production may be
potential mechanism for rapid spreading of surfactants more difficult to quantify, however, since biosurfactant
across gas–liquid interfaces. This mechanism could re- production will depend on several other factors in ad-
sult in desaturation of a variably saturated porous me- dition to cell concentration.
dium much more rapidly and extensively than would be Taking ratios of (11) implies that the contact angle
predicted by standard continuum models of flow and scaling factor b ¼ cos c= cos c0 . This will be referred to
transport. as ‘‘simple’’ contact angle scaling. Using simple contact
angle scaling in (21) is not strictly valid for non-zero
contact angles because it violates the assumption of
7. Fluid-media scaling geometric similitude [49]. As noted previously, in sub-
surface environments it is typically assumed that porous
In spite of the potential theoretical limitations noted media are water-wet so that the effective contact angle is
above, the effects of changes in surface tension, contact constant and approximately equal to 0°. If this is the
488 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495

case, then b  1. However, if a porous medium becomes

coated by biofilms, the assumption of a zero contact
angle may no longer be appropriate because the biofilms
may effectively change the wettability of the coated
particle surfaces [1].
According to (9), at equilibrium, distinct contact
angles can only occur at the point of contact between
three separate phases––e.g. solid, liquid, and gas. This
situation only occurs in porous media when the wetting
fluid (usually water) is contained in discrete pendular
rings that develop around the contact points between
the solid particles (mineral grains), and when the rest of
the particle surfaces are in direct contact with the non-
wetting fluid (usually air) [22,48]. If the wettability of the
Fig. 7. Schematic diagram of a pendular ring of liquid around the
particles is altered by biofilm formation, the determi- contact between two spherical particles, with relevant geometric terms.
nation of contact angle scaling factors for use in (21)
may require an evaluation of the configuration of pen-
dular water in the porous media. The liquid saturation corresponding to a given capillary
Frankenfield and Selker [26] developed the following pressure in a random packing of identical spherical
equations to describe surface area and volume rela- particles can be calculated from the volume of a single
tionships for a single pendular ring of liquid forming pendular ring (given by 24) using equations from
around the contact point between two equal-sized Gvirtzman and Roberts [27]. Noting that liquid satu-
spherical particles ration, S, is equal to the volumetric water content di-
vided by porosity, these equations yield
Als ¼ 4pR2 ð1  cos uÞ ð22Þ

 3Vp
1  cos u S¼ ½26:49ð1  /Þ  10:73 ð27Þ
Alg ¼ 4pR2 fx½ð1  cos uÞ cot x 8/pR3
sin x
þ sin u  ð1  cos uÞg ð23Þ where / is the porosity. Eqs. (22)–(27) can be used to


calculate pressure–saturation relations for imbibition of
Vp ¼ 2pR3 ð1  cos uÞ2 1 þ cot x sin u þ cot x any liquid into a dry porous medium consisting of uni-
form, spherical particles of size R, for any contact angle.


 
sin u 1  cos u x Note, however, that these equations are only applicable
 1  cos u  þ
cos x sin x cos x for a finite range of values of the angle u (see Fig. 7)
ð24Þ such that individual pendular rings do not overlap with
each other or with other particles.
where Als and Alg are the interfacial areas between the Eqs. (22)–(27) are collectively referred to here and in
liquid and solid phases, and the liquid and gaseous Fig. 8 as the ‘‘FS’’ model. Fig. 8 shows pressure head–
phases, respectively, and where Vp is the volume of the saturation relations calculated from the FS model for
pendular ring. The angle u defines the size of the pen- c ¼ 0° and 30° for a 40/50 grade of Accusandâ packed
dular ring and R is the radius of the solid particles (as- to a porosity of 0.33. The median grain diameter (d50 ),
sumed uniform). A schematic of a pendular ring with uniformity coefficient (d60 =d10 ), and particle sphericity
relevant geometric terms is shown in Fig. 7. The term x for this sand are 0:359  0:01 mm, 1:2  0:018, and 0.9,
is defined by the size of the pendular ring and the con- respectively [65]. Also shown in Fig. 8 is a plot of the
tact angle as x ¼ p=2  u  c. data representing values computed for c ¼ 0° that have
Frankenfield and Selker [26] used the following ex- been scaled to c ¼ 30° using (21) with simple contact
pression to relate changes in the surface energy of a angle scaling (b ¼ cos c= cos c0 ). The solution density
pendular ring, DEp , to changes in the interfacial areas and viscosity are assumed to be constant. As shown in
and contact angle Fig. 8, simple contact angle scaling results in the under-
estimation of the pressure head, relative to the FS
DEp ¼ rlg ðDAlg þ DAls cos cÞ ð25Þ
model, for non-zero contact angles at all saturations.
The capillary pressure at a liquid–gas interface can be New contact angle scaling factors, b ¼ Pc ðcÞ=Pc ð0Þ,
calculated by dividing the change in surface energy of a were computed using the FS model and are plotted as a
pendular ring by the change in its volume [41] function of saturation (27) in Fig. 9. The solution den-
sity and viscosity were again assumed to be constant.
DEp Unlike simple contact angle scaling in which the scaling
pc ¼ ð26Þ
DVp factors are only a function of the ratios of the cosines of
 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495 489

proposed a ‘‘curvature correction factor’’ to adjust the

results obtained from simple contact angle scaling. Like
simple contact angle scaling, the correction factor pro-
posed by Melrose yields scaling factors that are inde-
pendent of saturation. This correction factor results in
smaller values of the scaling factors (or larger pressure
corrections) relative to simple contact angle scaling.
However, the scaling factors proposed by Melrose tend
to overestimate pressure heads at low saturations, and
underestimate pressure heads at higher saturations, rel-
ative to the FS model [26]. We assume that contact angle
scaling based on the FS model is more accurate than
either simple contact angle scaling or the method used
by Melrose [48]. However, the applicability of the FS
model has yet to be tested and may be limited by the fact
that it relies on the assumption of uniform, spherical
particles.
Accounting for changes in solution density, viscosity,
and surface tension is relatively straightforward. How-
ever, the foregoing discussion suggests that accurately
accounting for the effects of changes in contact angle is
Fig. 8. Water retention curves calculated using the FS model corre-
more complex. Additional difficulties arise when con-
sponding to imbibition into dry porous media with contact angles,
c ¼ 0° and 30°. Also shown is a curve that is scaled from the results for sideration is given to the various types of hysteresis that
c ¼ 0° to c ¼ 30° using simple contact angle scaling (see description in can also occur in the pressure–saturation–permeability
text). relations for variably saturated porous media, and how
biomass growth and accumulation might induce addi-
tional hysteretic phenomena. For the sake of brevity, the
topic of hysteresis will not be discussed in detail here.
Excellent papers on this topic can be found elsewhere
[39,40,54].
It may be difficult to distinguish between changes in
saturation that are due to changes in surface tension
relative to those due to changes in contact angle.
However, if the production of biosurfactants causes a
lowering of surface tension, then this effect should be
apparent locally, as well as downstream of the region in
which the biosurfactant is being produced. On the other
hand, if changes in saturation are due primarily to
changes in contact angle resulting from attached bio-
mass altering the wettability of the porous media, then
this effect should be local to the area colonized by the
bacteria.
Changes in the saturated hydraulic conductivity of a
biomass-affected porous medium due to changes in so-
lution density and viscosity can be estimated from



l0 q
Ks
¼ Ks ð28Þ
l q0
Fig. 9. Contact angle scaling factors, b, calculated as a function of where Ks
is the scaled value of the saturated hydraulic
wetting fluid saturation for c ¼ 30° with the FS model and with simple
conductivity. Eq. (28) results from the definition of in-
contact angle scaling.
trinsic permeability, k ¼ Ks l0 =q0 g, by taking ratios of
the solution viscosities and densities.
the contact angles, the scaling factors determined from Eq. (28) is plotted as a function of the volume frac-
the FS model are a function of both the contact angles tion of particles in suspension in Fig. 10, using the
and saturation. This is probably more realistic, but also density and viscosity changes predicted by (18)–(20).
makes the FS model more difficult to apply. Melrose [48] Fig. 10a indicates that density and viscosity changes
490 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495

Fig. 10. Relative hydraulic conductivity as a function of volume fraction of particles (or bacterial cells) in suspension. The parameter p represents the
ratio of the dimensions of the major and minor axis of an ellipsoidal particle.

caused by increases in aqueous-phase bacterial concen- phase could effectively lead to a composite porous media
trations could potentially decrease hydraulic conduc- system with both primary and secondary porosity.
tivity by 18–42% if the volume fraction of cells in Furthermore, data by Chenu [15] and others indicate
suspension is 10%. Fig. 10b shows the potential changes that the EPS produced by some bacteria can have a
in hydraulic conductivity due to density and viscosity tremendous water-holding capacity, which could also
over a smaller, and probably more realistic range of cell alter the hydraulic properties of a variably saturated
concentrations. Brodnyan’s [10] model for ellipsoidal porous medium.
particles predicts a decrease in hydraulic conductivity of A simple composite media model can be used to
almost 4.5% resulting from density and viscosity in- represent such systems. If the porous medium is sand,
creases corresponding to a volume fraction of 1% par- for example, the porosity of a composite porous medium
ticles in solution. Changes in surface tension, contact consisting of the sand with a porous, attached biomass
angle, liquid density, and viscosity are all assumed to phase can be calculated from
have no affect on the pore-size distribution index, k, in
(12). hcomp
s ¼ hsand
s  nf ð1  hbio
s Þ ð29Þ

where nf is defined by (5), and hbio s is the assumed po-

rosity of the attached biomass phase. An equation
8. Composite media model analogous to (29) has been used previously to estimate
the porosity of sediment assemblages containing mix-
Thus far we have only considered the possible effects tures of sand and clay [34,46].
of changes in the liquid-cell suspension and wettability The volumetric liquid content of a composite porous
on the effective hydraulic properties of variably satu- medium whose porosity is given by (29) can be calcu-
rated porous media. Accumulation of biomass attached lated as a function of pressure head, h, from
to solid particles will also affect the hydraulic properties. (" # )
As noted previously, several studies have observed comp sand hsand
w ðhÞ bio
hw ðhÞ ¼ hw ðhÞ  nf  hw ðhÞ ð30Þ
bacterial cells that formed clusters or aggregates with hsand
s
void spaces that made up to an estimated 50% of their
occupied volume [19–21]. The SEM photographs of Eq. (30) implicitly assumes that the capillary pressure in
Vandevivere and Baveye [76] also show the formation the attached biomass phase is equal to that of the sur-
of porous bacterial aggregates (see Fig. 1). This type of rounding porous media. The hydraulic conductivity of
infilling of the original pore space with a porous biomass the composite porous medium can be approximated by
 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495 491

" !#b
concentrations. However, non-destructive, in situ de-
nf
K comp
ðhcomp
w Þ ¼K sand
ðhsand
w Þ 1 þ K bio ðhbio
w Þnf termination of biovolume or attached biomass concen-
hsand
s trations is also extremely difficult. As an alternative, the
ð31Þ saturated hydraulic conductivity of an attached biomass
phase could be estimated from an assumed porosity and
where K sand and K bio are the hydraulic conductivities of median cell size using the Kozeny–Carmen equation [7].
the sand and the attached biomass phase, respectively, The water retention characteristics of an attached bio-
as a function of the volumetric water content of each mass phase could be estimated from the average cell
phase, and b is an empirical parameter. If the attached density and an assumed cell-size distribution using a
biomass phase is assumed to be non-porous and im- model such as that given by Arya and Paris [4]. Another
permeable, then hbio
s and K bio would be equal to zero. alternative would be to simply assume that the hydraulic
For this case, if the b parameter is taken as equal to properties of the attached biomass phase are similar to a
19=6, and the porous medium is saturated, then (29) and clay-textured soil.
(31) reduce to (6) and (3), respectively. Fig. 11 shows an example of the composite hydraulic
Eqs. (29)–(31) are applicable to variably saturated properties of the 40/50 Accusandâ containing different
conditions. However, calculation of the liquid content volume fractions of attached biomass (vfb), based on
(or saturation) and unsaturated hydraulic conductivity (29)–(31). van Genuchten [78] model is used in Fig. 11 to
in this composite media model requires models for the represent the attached biomass phase, with parameters
liquid retention characteristics and hydraulic conduc- that correspond to a clay-textured soil from Leij et al.
tivities of both the original porous medium, as well as [38]. The parameters used to represent the clay (or bio-
the attached biomass phase. Models such as those given mass) component with the van Genuchten [78] model
by Brooks and Corey [11], van Genuchten [78], or others are: hs ¼ 0:51, hr ¼ 0:102, a ¼ 0:021 cm1 , n ¼ 1:2, Ks ¼
could be used for this purpose. Due to the fragility of 1:08 cm/h. The parameters used to represent the sand
microbial aggregates and biofilms, the independent de- component with the Brooks and Corey [11] and Burdine
termination of the parameters in these models would [12] models are: hs ¼ 0:37, hr ¼ 0:028, hb ¼ 21:6 cm,
be difficult. Therefore, application of (29)–(31) would k ¼ 5:84, and Ks ¼ 317 cm/h.
probably require that the parameters for the attached The effects of the attached biomass become most
biomass phase be determined experimentally using ob- apparent in the composite media model at relatively
served liquid saturation and pressure data, combined high biomass concentrations. Thus the use of such a
with measurements of biovolume or attached biomass model may be unnecessary in most cases, particularly in

Fig. 11. Composite media model of volumetric water content and hydraulic conductivity as a function of pressure head for different vfb.
492 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495

low nutrient environments. Nevertheless, Eqs. (29)–(31) bacteria, the substrate type and loading rate, surface and
provide a means of accounting for the possible effects of solution chemistries, and the flow rate. Several concep-
the accumulation of an attached biomass phase on the tual and mathematical models have been proposed for
hydraulic properties of variably saturated porous media. describing biomass-induced porosity and permeability
Eqs. (29)–(31) can also be used in conjunction with (21) reduction in saturated systems, with different assump-
and (22) to simultaneously account for the effects of tions about the morphology of the attached biomass
changes in surface tension, contact angle, solution vis- phase. No universally applicable model has yet been
cosity and density, and infilling of the original pore developed for saturated porous media systems. More-
space by a porous biomass phase. Note that a similar over, no attempts have been made prior to this one to
approach could also be applied in geochemical modeling develop or propose a model that is applicable to both
to account for primary porosity reduction and second- saturated and unsaturated systems.
ary porosity formation and changes in hydraulic prop- Unsaturated or variably saturated porous media are
erties that might develop in variably saturated porous considerably more complicated than fully water-satu-
media during mineral precipitation/dissolution reac- rated systems, due to the fact that the water content and
tions. hydraulic conductivity are non-linear functions of cap-
The composite-media model given in (29)–(31) does illary pressure rather than being constants as in satu-
not explicitly consider changes in the actual pore-size rated systems. Unsaturated systems are also complicated
distribution of the porous media. An alternative to this by the presence of gas–liquid interfaces. Previous studies
model would be to discretize the water retention and have shown that preferential sorption of bacteria can
hydraulic conductivity functions representing the clean occur at gas–liquid interfaces, relative to solid–liquid
porous media, and to account for biomass accumulation interfaces. This preferential sorption at gas–liquid in-
by explicitly changing the corresponding discretized terfaces has been attributed to bacterial cell surface hy-
form of the pore-size distribution. A hydraulic conduc- drophobicity.
tivity model such as that given by Childs and Collis- Sorption of cells at gas–liquid interfaces, and the
George [16] or others could be used in such a scheme to production of surface-active compounds or biosurfac-
calculate relative permeability from a water retention tants during microbial metabolism, can result in lower-
function represented by piece-wise linear curve segments ing of surface tension and desaturation of variably
[62,68]. The water retention and hydraulic conductivity saturated porous media. Desaturation tends to create
functions for the biomass-affected porous media could more gas–liquid interfacial area that provides additional
then be represented in numerical flow and transport sites for sorption of bacterial cells and surfactants. Ac-
models with tabular data, using table entries that are cumulation of cells and macromolecules at gas–liquid
updated dynamically during a simulation. A potential interfaces can also reduce the mass transfer rates of
problem with this approach would be deciding how to gases across gas–liquid interfaces. The solid–liquid
distribute the biomass within the water-filled pores. contact angle, and hence the wettability of a porous
After this decision was made, however, the altered pore- medium may also change as it becomes coated by bio-
size distribution could be readily used to recompute films. These effects are unique to unsaturated porous
the water retention characteristics and hydraulic con- media systems and may be important to consider for
ductivity of the biomass-affected porous media. This applications such as bioremediation, and for the design
approach might be more rigorous than the composite- of septic and water treatment systems.
media model, but it would also be more difficult to in- Additional changes that may be caused by the accu-
corporate, and less efficient to use in numerical flow and mulation of bacterial cells in unsaturated or variably
transport models. From a practical perspective, con- saturated porous media include increases in the viscosity
sidering the uncertainties associated with how biomass and density of the bulk solution. Density effects should
would actually be distributed within the pore space, the be much less significant in unsaturated porous media
development and implementation of more rigorous ap- than in saturated porous media, however, due to the
proaches is probably unnecessary. lack of buoyancy effects and the mitigating effects of
capillarity. Gas generation and entrapment may also
play a role in permeability reduction, in both saturated
and unsaturated porous media, as bacteria metabolize
9. Summary and conclusions substrates and generate carbon dioxide or other gases.
Very little effort has been made previously to address
Bacterial growth and accumulation in porous media these issues for unsaturated porous media systems, from
systems is important in a variety of disciplines because it either a measurement or modeling perspective. Several
typically results in the reduction of the porosity and simple expressions are discussed in this paper that can be
permeability of the porous media. The characteristics of used to model changes in the apparent viscosity and
the accumulated biomass are dependent on the type of density of liquid-cell suspensions given the average cell
 M.L. Rockhold et al. / Advances in Water Resources 25 (2002) 477–495 493

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