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ArticleInfluence of Tension-Driven Flow on the Transport of AFFF in
Unsaturated Media
Faran Vahedian, Jeff A. K. Silva,* Jirí̌ Š imůnek, and John E. McCray
Cite This: https://doi.org/10.1021/acsestwater.3c00611

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sı Supporting Information*

ABSTRACT: Per- and polyfluoroalkyl substances, and other chemicals in aqueous
fire-fighting foam (AFFF), accumulate at air−water interfaces in the vadose zone,
reducing interfacial tension and potentially causing tension-driven flow (TDF).
This study investigates the importance of TDF on AFFF lateral spreading in thevadose zone using bench-scale column experiments and numerical modeling.
Understanding AFFF spreading beyond an original spill footprint would enhancesite conceptual models, wherein understanding the contaminant source zone iscritical. Our experiments demonstrate that AFFF exhibits noteworthy TDF,
characterized by substantial lateral water flow and AFFF spreading, causing
variations in moisture content, which alters capillary pressure and hydraulicconductivity. The modified HYDRUS model accurately simulated experiments and was then used to simulate site-scale AFFF sourcezone dynamics. The numerical investigation demonstrated that TDF could lead to a significant increase in the surface footprint of an
AFFF source zone, where wetter conditions yield a 6-fold increase compared to an initial spill, while drier soils exhibit a 4-fold
expansion. The footprint expansion occurs over decades, which is highly relevant for our conceptual understanding of both historicand relatively new AFFF spills. This study highlights that the lateral flow of AFFF due to TDF is an important transport mechanismthat controls the AFFF source zone.
KEYWORDS: AFFF transport, PFAS, tension-driven flow, vadose zone dynamics, numerical modeling

1. INTRODUCTION
The extensive application of aqueous film-forming foams(AFFF) containing per- and polyfluoroalkyl substances(PFAS) for extinguishing hydrocarbon-based fires, along withother surfactants and solvents, has led to their widespread
distribution in a variety of environmental media.1−4 AFFF
solutions can infiltrate into the vadose zone and become amajor reservoir for PFAS release and thus serve as a long-termsource of groundwater contamination.5−7 PFAS-contaminatedaquifers that also serve as a drinking water source can result ina primary PFAS exposure route for humans.8−12
The transport behavior of PFAS/AFFF in the vadose zone ismore complicated than that in groundwater, and complicating
factors include the accumulation or adsorption of PFAS andother AFFF components at air−water interfaces (AWIs).
Adsorption of solutes at AWIs can impact the flow by causing
retardation due to interfacial partitioning but also by changing
the interfacial tension (IFT), also called surface tension forair−water systems, which affects capillary pressure and soil
moisture, and thereby unsaturated hydraulic conductivity.
Thus, changes in the IFT from AFFF or PFAS can cause
tension-driven flow (TDF) of water and associated solutes,13−15 and thus PFAS and AFFF.
AFFF solutions include many components such as surfaceactive solvents, surfactants (including high concentrations ofPFAS), and wettability modifiers, each having distinctly© XXXX American Chemical Society

different interactions with environmental fluid and solidinterfaces, affecting the unsaturated transport of PFAS and
AFFF.7,16−19 AFFF is also a mobile source of PFAS in thevadose zone. Thus, the movement of both PFAS and AFFF in
the vadose zone is of high interest. To date, much attention has
been focused on PFAS transport in aquifers10,20−26 rather thanon the AFFF solutions as a source of PFAS contamination.
However, given that AFFF solutions are one of the importantsources of PFAS, it is equally important to understand AFFF
flow within the vadose zone environment, particularly
regarding the understanding of PFAS source dynamics. All
guidance on conceptual model development for contaminatedsites highlights the importance of understanding the nature of
the source (geometry, mass distribution, etc.),1,27,28 and proper
characterization of the source is essential for contaminanttransport modeling simulations.
The effects of TDF have been studied previously,13,29−31
with a focus on the transport of single-component surface
active agents as IFT sorbents, causing water movement andReceived: October 5, 2023
Revised: January 7, 2024
Accepted: January 8, 2024A

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TDF in unsaturated porous media. These studies demonstrated that the presence of the surfactant in unsaturated media
creates concentration-dependent surface tension gradients
between surfactant-free and surfactant-impacted zones, whichcauses capillary pressure gradients and moisture transition
across the media.30,32−34 Costanza-Robinson and Henry35
modified the HYDRUS-1D model (publicly unavailable) toinclude the impact of surfactant-induced flow on IFT changes
and subsequent impacts on water movement. They concluded
that surfactant-induced flow significantly affects the air−waterinterfacial areas (increasing the magnitude up to 43%), withobvious implications for vadose-zone fluid physics. In contrast,
other studies offered a differing perspective based on theirunsaturated column experiments, asserting that the influence of
surfactant-induced flow on air−water interfacial areas was
negligible within the context of their modeling.17,34,36−38 For
example, Zeng and Gou’s34 and Zeng et al.’s38 studies on
surfactant-induced flow (SIF), akin to TDF in this paper,
focused on PFAS transport rather than bulk AFFF transport.
Both studies found minimal TDF impact on vertical movement
and observed prolonged leaching within their PFAS concentration ranges (Zeng and Gou34 used PFAS concentrations lessthan 1000 mg/L, and Zeng et al.38 used PFOA concentrationsof up to 1 mg/L). To the best of our knowledge, no literature
has attempted to simulate bulk AFFF, let alone utilizing amodel with experimentally validated TDF based on actual
AFFF, as demonstrated in this study. Consequently, thespecific impacts of TDF on the actual AFFF movement havenot been systematically investigated.
Our current study aims to contribute to the ongoing
discourse by investigating and clarifying the role of TDF on
AFFF transport. Our research investigates a genuine AFFF thatwas collected from a contaminated site, which contained adiverse array of PFAS/non-PFAS surfactants, solvents, andwettability modifiers. We conducted benchtop experiments
and numerical modeling to explore the impact of TDF on
AFFF movement in unsaturated porous media. First, we
conducted benchtop experiments to characterize the relationship between AFFF concentration (not PFAS concentration)
and air−water interfacial tension. Then, we conductedhorizontal column experiments to measure the TDF-induced
AFFF lateral movement based on measurements of moisture
content. A major goal was to utilize data from the laboratory
study to evaluate the performance of the HYDRUS 5.03
vadose-zone flow and transport simulator, which now
incorporates AFFF-induced TDF. The modification of
HYDRUS to simulate bulk AFFF transport, rather thantransport of single, specific constituents, is a significant
advancement in modeling realistic PFAS transport in thevadose zone. To obtain some important model input
parameters, such as the dispersivity, we conducted parallel
experiments with isopropyl alcohol (IPA), an IFT-reducing
fluid that does not sorb to soil. Finally, the experimentally
validated HYDRUS model is used to better understand thelateral spreading of a field-scale AFFF source zone.
These results shed light on the potential impact of interfacial
TDF and lateral spreading of AFFF solutions in the vadosezone, particularly in relation to source-zone footprints but also
because of the impacts on important hydraulic parameters suchas unsaturated hydraulic conductivity. In this paper, we firstpresent materials and methodology, encompassing the experiments described above, as well as HYDRUS model parametrization. Subsequently, findings from both experimental

Articleand model performance evaluations are presented. The
validated model was then used to conduct field-scale
simulations, which gave insights into the importance of TDF
on AFFF source zone dynamics. Finally, the summary
encapsulates the key insights garnered from the study as wellas limitations of the study.

2. MATERIALS AND METHODOLOGY
Experiments were performed using the following fluids:
simulated groundwater (SGW), IPA as a nonreactive surface
tension-reducing solute (i.e., it does not sorb to soil ordegrade), and AFFF collected from Peterson Space Force Base.
IPA is used here as a conservative surface tension-reducing
tracer for comparison. The porous media used in all
experiments was a 30-mesh silica sand (U.S.Silica) that wasrinsed with SGW and dried in a laboratory oven prior to use.
The test columns were prepared from acrylic tubing with an
inner diameter of 4.5 cm and a length of 10 cm. The AFFF
concentrate was diluted to 1 and 0.1% v/v (10,000 and 1000mg/L), and the IPA was diluted to 70 and 7% v/v (700,000
and 70,000 mg/L), using SGW with dissolved ions composedof NaHCO3 (96 mg/L), CaSO4·2H2O (60 mg/L), MgSO4,(60 mg/L), and KCl (4 mg/L).
2.1. TDF Evaluation. Tension-driven pore-water redistribution was assessed following the approach outlined by Silva
et al.39 for AFFF solutions, building upon prior studies
conducted by Karkare et al.40 and Henry et al.41 for waterinsoluble and water-soluble surface-active alcohols, respectively. The experimental setup consisted of preparing two
samples of unsaturated sand for each half of the column. The
left-hand side of the column contains SGW (water side) at agiven moisture content, while the right-hand side of thecolumn contains either IPA or AFFF solutions (IPA/AFFFside) at the same moisture content (Figure 1). All experiments

Figure 1. Apparatus used in TDF experiments (with equal initialmoisture content on each side).

were performed in a horizontal position (i.e., to minimize
gravity flow) at room temperature (19−21 °C), with the same
initial moisture content, with sealed ends to prevent outflow,
isolate the TDF effects, and rule out other factors that mightcause flow. Additional details on the experiment can also befound in the Supporting Information, Section S1. The IPA and
AFFF experiments were each performed in triplicate, to ensure
reliability and reproducibility of the results. However, for thesake of brevity in publication, we present only one set of results
here, while the rest can be found in the Supporting
Information, Figures S1 and S2.
2.2. Numerical Model Formulation and Modification.
This study used the HYDRUS unsaturated flow and transportmodel42 that was modified to incorporate the effects ofsolution concentration-dependent air−water interfacial tenB

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pubs.acs.org/estwaterij yzh( , ) = jjj zzzh0( ,
j 0z
k {

sion, also referred to as surface tension, on solute transport inunsaturated porous media.39 IFT can be decreased bysurfactant solutions (such as AFFF) and cosolvent solutions(such as IPA). The dependence of IFT (σ) on soluteconcentration (Cw) was represented in the model using theLangmuir-Szyszkowski (L-S) equation (Eq)39,43,44 as
=1
0

C y
i
b lnjjj1 + w zzz
a {
k

(1)

where a (ML ) and b (�) are fitting parameters used for
Hydrus model input, σ0 is the surface tension of clean water,
also a HYDRUS model input parameter, and σ is the calculated
interfacial tension of an AFFF (or IPA) solution with aconcentration of Cw (M T−2, J m−2). The IFT for a surfactant
solution such as AFFF remains constant at AFFF concentrations greater than the critical micelle concentration (CMC).
Thus, the relevant scaling factor also remains constant forconcentrations above the CMC at a value associated with the
IFT at the CMC. IPA has IFT-reducing properties but is asolvent rather than a surfactant and thus does not have a CMC.
In the unsaturated zone, water and thus chemical transport
are driven by gravity head and the capillary pressure head (h).
For our horizontal flow experiments, the gravity head isirrelevant. Capillary pressure head (h) depends on surface
tension as follows

=

Se( ,

0) =

[Se( ) 1/ m

1]1/ n1=(1 + ( h0)n )m
r

s

,

0)

(4)

K ( ) d(h + z)
ne
dx

(5)

(1

Se1/ m)m ]2(6)−1

where Ks is the saturated hydraulic conductivity (L T ).
Equation 1 through 6 above demonstrate how changes ininterfacial tension due to sorption of surface-acting solutes at
the AWI influence the pressure head and K(θ) in the equationsof flow implemented in HYDRUS.
HYDRUS uses the advection-dispersion equation with firstorder reactions to describe the retention of solutes in thevadose zone. The simplest expression for describing theretention of solutes in the vadose zone is the following linear,reversible form of the retardation factor (Rf) equation, which
includes solid-phase sorption and adsorption at the AWI for
surface active solutes like IPA, some AFFF components, and
PFAS compounds46

(3a)

b KD

Rf = 1 +

r

0) =

q
=
ne

K ( ) = K sSe 0.5[1(2)1hh 0 (

where z is the elevation (gravity) head, υ is the average linear
pore-water velocity [L/T], q is the Darcy flux [L/T], ne is theeffective porosity available for water flow, and d(h + z)/dx isthe hydraulic gradient of the total water potential in the lateral(x) direction (i.e., the direction of water flow). For a horizontal
experiment, dz/dx = 0 and the total gradient is reduced to dh/
dx. The unsaturated hydraulic conductivity function, K(θ), is
given by the van Genuchten-Mualem45 relationshipwhere the subscript o annotates water without a surface-acting
agent, ρ is the density of water (M L−3), g is the gravitational
acceleration constant (L T−2), and r (L) is the radius ofcurvature of the AWI. The radius of curvature of the AWI is
fundamentally related to the pore size distribution, which isrelated to pore size and grain size distribution.
HYDRUS, like most unsaturated zone models, does not
attempt to replicate the impact of pore-scale physics on
capillary head, but rather uses the van Genuchten45 empiricaleq 3a to relate moisture content to capillary pressure head (ho)h0 ( ,

0) =where αh is the pressure-head scaling factor (�) (note: this is
not the same parameter as the van Genuchten α parameter
described above with eq 1). As the AFFF or IPA solution
concentrations change in the model simulation, eq 4 calculates
a new value for IFT, and the scaling factor in HYDRUS is
automatically adjusted during the simulation per eq 4.
For water, surfactant, or cosolvent solution, velocity in
HYDRUS is calculated from the pressure head gradient using
the unsaturated form of the Darcy equation as follows (where
the flow direction is horizontal, or along the x-direction, forour experiments)−3

ho = 2 0/ gr

Article

(3b)

3

+

K awA aw
(7)

where Kaw (L /L ) is the AWI partitioning coefficient, Aaw (L2/
L3) is the interfacial area of the AWI, ρb is bulk density, and KD(M/L3) is the sorption partitioning coefficient. The term Aaw iscalculated by HYDRUS from soil-water retention curves, as
explained in detail in Silva et al.39,47 Kaw and KD are chemicallyspecific parameters. When retardation is important, thevelocity of specific contaminants given by eq 5 is reduced bya factor of 1/R. This expression, while discussed here, primarily
pertains to solute partitioning and retardation concerning thetransporting fluid. Traditional formulations are designed forwater as the transporting fluid, but in our study using IPA or
AFFF, the bulk concentration serves as the relevant “solute”.
As a result, traditional retardation formulations are notapplicable, a topic explored further in an upcoming section.
Additionally, HYDRUS can implement a more complicatedformulation for retardation than that shown in eq 7. PFAS
sorption to soil and partitioning to the air−water interface hasoften been shown to be nonlinear.39,48,49 Nonlinear partitioning yields a more complex representation of the retardation

where h is the pressure head, θ(h) is the water content for a
specific pressure head, and Se is effective saturation. The van
Genuchten α is an empirical factor that is inversely
proportional to interfacial tension but also may include theimpacts of other physical phenomena, such as grain size
distribution. The parameters m and n are empirical but related
to grain size and distribution, where m = 1−1/n. The
HYDRUS model input parameters include the saturated
volumetric moisture content θs, the residual volumetricmoisture content θr, and fitting parameters α, n, and m, in
addition to the parameters associated with eq 1 above.
For AFFF (or IPA) solutions, as the interfacial tension
decreases with increasing concentration, the magnitude of thecapillary head h (θ, σ) decreases compared to the head of asurfactant-free solution h0 (θ, σ0). Thus, h0 (θ, σ0) can bescaled by the reduced surface tension of a surfactant solution
to obtain the pressure head of that surfactant solution, h (θ, σ)
as follows
C2

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factor that is a function of the concentration versus time
derivative (e.g., Fetter et al.50 for soil sorption). The model
supports various sorption isotherms, including traditional
nonlinear and Langmuir formulations. In HYDRUS, the air−water interfacial partitioning employs the nonlinear Langmuir
formulation, utilizing parameters like the Langmuir partitioning coefficient, KL,aw (L3 M−1), and the maximum interface
concentration, ΓMAX (M L−2) (Silva et al.10).
2.3. HYDRUS Model Input, Measurement, andParameterization. A 1D model is used to simulate theexperiments. The domain has a length of 10 cm, with a nodal
spacing of 0.1 cm. The measured uniform moisture content of
0.18 was assigned as the initial condition throughout thedomain to match the experiment. Zero-flux boundaries wereassigned at both ends of the column domain to match theexperiment. The initial solute (either AFFF or IPA)
concentration was set to zero for the surfactant-free side andset to the concentration used in a particular experiment for thesurfactant-containing side (e.g., AFFF at 0.1 or 1% [1000 or
10,000 mg/L], and IPA at 7 or 70% [7000 or 70,000 mg/L]).
Capillary hysteresis was not considered. The following soil
hydraulic parameters were measured previously for the porous
sandy media used in these experiments.18 The saturated
hydraulic conductivity KS = 6 × 10−4 cm/s, the residual soil
moisture content θr = 0.038, the saturated moisture content θs= 0.315, and bulk density = 1.7 g/cm3. The fitting parametersof the van Genuchten equation, n and α, were estimated to be
3 and 0.07 cm−1,45 respectively, based on hanging-column
capillary pressure experiments.51 The molecular diffusion
coefficient for IPA was designated as 0.036 cm2/h,18 whereas
the molecular diffusion of AFFF, represented by PFOA/PFOS
with a value of 0.021 cm2/h, was acquired from Xing et al.52
since most PFAS components in AFFF have similar diffusion
coefficients. However, diffusion is negligible compared withhydrodynamic dispersion for our experiments. Dispersivity was
fitted during the IPA and AFFF simulations (more details arepresented in the next section).

ArticleFigure 2. Measured surface tension isotherms fitted with the L-S (eq1) scaled-surface tension for TDF simulations. The CMC for AFFF isalso shown in the figure. Note that pure water has a value of about 72
mN/m.

Thus, AFFF is represented here as a pseudo-single-component
species. It is also important to note that the L-S relationship(eq 1) does not represent IFT behavior beyond CMC, where
the surface tension no longer decreases with increasing
surfactant-solution concentration but instead remains constant.
The CMC of AFFF based on the data in Figure 2 cannot be
concisely chosen but is approximately the 0.25% AFFF
concentration. Consequently, for concentrations surpassing
the CMC (depicted in Figure 2 at approximately 2500 mg/L),
a consistent low interfacial tension (IFT, s) value of 17 mN/m
is integrated into the HYDRUS model by using the scaling
equations described above. It is important to highlight that themodel utilizes a minimum IFT input of , resulting in the use0of 0.23 (=17/72) within the model rather than the value of 17
mN/m. The L-S equation was fitted to the AFFF and IPA data
sets, resulting in parameter values of a = 50 mg/L and b = 0.2
for AFFF and a = 8000 mg/L and b = 0.17 for IPA.
3.2. Column Experiment and HYDRUS Model Simulations. 3.2.1. TDF-Induced Flow of IPA. Figure 3 shows theexperimental results for 7 and 70% IPA (and also modeling
results for two additional nonexperimental concentrations, 0.7

3. RESULTS AND DISCUSSION
3.1. Surface Tension Isotherms. Surface tension
isotherms were derived from surface tension measurements
using a du Nouy ring tensiometer (Fisher Surface Tensiomat,
model 21, Fisher Scientific) with standard ring methods53 for
AFFF (from Peterson AFB), which was obtained from
Colorado School of Mines and previously characterized by
Hao et al.,54 and IPA (Figure 2 depicts the results). From these
data, we obtain the parameters a and b in the L-S eq (eq 1),
which are inputs to the modified version of HYDRUS to
calculate concentration-dependent surface tension and thus theimpacted pressure head value in the van Genuchten
equations.45
The primary influence on the TDF is the AFFF-inducedpressure head gradient induced by the reduction in the IFT(eq 1), which in turn drives fluid movement (eqs 2−5). The
HYDRUS-simulated variables are moisture content (including
both water and AFFF solutions) and the bulk AFFF
concentrations. For the experimental study, we focus on the
movement of fluids, so we primarily use moisture content in
our analysis. For the experiments and HYDRUS simulations,because the solute is AFFF, the modeled variable is theconcentration of AFFF (mass per volume of water). The AFFF
contains numerous solutes, whereby not all solutes, and noneof the particular solute concentrations, are precisely known.

Figure 3. Experimental and simulated changes in moisture contents
for IPA solutions.
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pubs.acs.org/estwaterand 40%, which are discussed later). Results of the triplicate
experiments are shown in the Supporting Information, Figure
S1. Based on visual observation of the experiments, theredistribution of pore water occurred relatively rapidly, within
about 2 h, and moisture content measurements wereconducted after 12 h. Note that the TDF-driven moistureredistribution represents the movement of IPA fluid toward thecosolvent-free side.
When surface tension-reducing fluids (i.e., the IPA side, orright side, of the unsaturated column) contact the water side of
the column containing only water, the surface-tension-induced
capillary pressure gradient across the interface of contact drives
a fluid movement from the IPA side (drainage) to the waterside (imbibition), causing an increase in moisture content on
the water side and a decrease on the IPA side. TDF movement
toward the water side is significant for both concentrations of
IPA (7 and 70%). For the 0.7% solution, as IPA moves toward
the water side, the moisture content subsequently reduces toabout 0.155 on the IPA side (less than the initial 0.18) andincreases to about 0.23. For the 70% solution, the behavior
looks similar except that the water content changes are larger(0.12 and 0.275). It is also interesting that the moisture
content redistribution for 7% compared to the initial value issimilar to the redistribution between 7 and 70%. The moisturechanges are not linear with the IPA concentration. This ispartly explained by examining Figure 2, which suggests asimilar IFT difference between water and 7% IPA (70,000 mg/
L) as between the 7 and 70% (700,000 mg/L) IPA solutions.
The nonsymmetric shapes, exhibiting greater water content
changes on the water side, particularly within the initial few
centimeters, are intriguing. This asymmetry is essential for
maintaining a fluid mass balance across the column, especiallyconsidering the more substantial change in moisture content
on the water side compared with the IPA side.
HYDRUS-simulated moisture content values for the IPA
experiments (7 and 70% v/v) are displayed in Figure 3, alongwith simulations for additional IPA concentrations (0.7 and
40%) not used in the experiments. Simulations for initial IPA
concentrations of 7 and 70% v/v over 12 h, corresponding to
the experimental duration, exhibit excellent agreement withmeasured moisture content values, validating the HYDRUS
model for concentration-dependent TDF in IPA (Figure 3).
Only longitudinal dispersivity55 was optimized during the IPA
experiments and determined to be 1.0 cm. However, the fit was
not highly sensitive to this parameter, within the expected
range between about 0.5 and 2 cm, for this 10 cm column,56−58
indicating that the flow in this column was primarily advective(logical because the sandy media used here is very
homogeneous). The Supporting Information, Figure S3, andassociated text, shows a model sensitivity study conducted forthe dispersivity parameter versus our experimental data.
Because dispersivity is porous media-specific, not chemicalspecific, this dispersivity value for the relatively conservative
IPA experiments was then used for subsequent modeling of the
AFFF solutions.
The model can now be used to further examine the TDF
behavior in the experiments. Minimal TDF is observed for thesimulated 0.7% IPA, aligning with the slight IFT decrease seenin Figure 2 compared to water. The simulated 40% IPA
solution behaves as expected, showing a moisture content
distribution profile intermediate to the 7 and 70% solution.
The nonsymmetric shapes of the curve and relative moisture
distribution between the different IPA concentrations are not

Articleeasily explained using the experimental data alone. However,this is not surprising given the highly complex processes
required to simulate TDF. Unlike most contaminants, the flowof AFFF is concentration-dependent because of the relationship between IFT and concentration (which is highly
nonlinear), the relationships between IFT and capillarypressure head, and the relationship between capillary headand moisture content (which is also highly nonlinear). These
interacting and nonlinear processes render it impossible todescribe TDF behavior without a model that incorporates
these complex processes. Thus, a more detailed discussion of
the dynamic physical processes causing TDF-induced movement of IPA in unsaturated media is useful. The discussion also
largely applies for AFFF, which is discussed in more detail in
the next section.
Initially, we present a summary of water flow physics inunsaturated media (eqs 3a−6). Equation 3a simplifies thephysics-based LaPlace eq 2, indicating that the capillary head is
directly proportional to the IFT and inversely proportional to
the radius of curvature (r) of the AWI. The radius of thecurvature term is linked to the moisture content, where higher
moisture contents correspond to smaller radii of curvaturecompared to dry conditions with larger radii. It is not feasible
to measure IFT or the AWI radius of curvature in practicalsituations, whereas the moisture content is measurable. Thus,
HYDRUS and nearly all vadose zone models use the empiricalvan Genuchten equation, wherein the pressure head is simply afunction of water content and the van Genuchten a., which isinversely proportional to IFT. AWI partitioning also influences
the radius of curvature of the AWI as it reduces the IFT. In
turn, IFT is a function of cosolvent/surfactant concentration
via the L-S relationship in eq 1. Thus, the capillary pressure
head is also a function of cosolvent/surfactant concentration
via the IFT vs concentration relationship (eq 1 and Figure 2).
The relationship is expressed through the van Genuchten aparameter, integrating IPA or AFFF concentrations into
unsaturated flow and transport physics for bulk fluids.
Equations 1, 3a, 4, 5, and 6 encapsulate these intricate
processes in the model. Notably, molecular diffusion wasdeemed insignificant in the IPA movement, even with asubstantial concentration shift across the 7% IPA boundary;simulations with zero diffusion yielded consistent results.
The initial head difference induces flow from the IPA side to
the water side, as discussed previously. As IPA flow continues
toward the water side, the moisture content on the IPA side
declines and the moisture content on the water side increases.
This also dilutes the IPA concentration from the initial value(7 or 70%) as the IPA moves, resulting in declining
concentrations, which result in increasing IFT relative to theinitial IPA value (but less than the initial water value).
Consequently, van Genuchten a (eq 3a) decreases across thewater side, contributing to an increasing (more negative)
capillary head. To maintain a constant capillary head, moisture
content must increase across the water side, resulting in an
increasing Se in eq 3a and contributing to a decreasing (lessnegative) capillary head. These processes continue until thecapillary head is constant and flow stops. The no-flow
boundaries on the end of the column ultimately prevent
further dilution of the IPA concentration and force the fluids inthe column to achieve a steady-state condition. The
unsaturated hydraulic conductivity (eq 6) impacts the rate of
the bulk fluid flow across the column.
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Additionally, the relationship between the capillary pressure
head (and thus the IFT scaled capillary pressure head) andmoisture content is highly nonlinear (eq 3a). Large pressurehead changes induce small moisture content changes at low
moisture levels, while small pressure head changes causesignificant moisture content changes at intermediate to higher
moisture values. This behavior is pronounced in sandy
materials, where the h vs q curve exhibits a “bench-like”
shape. (e.g., Jury and Horton59 and Fetter et al.50). Thus, themoisture content changes significantly with small pressure
gradients at intermediate to higher levels but requires larger
pressure gradients at low moisture values. The complex andnonlinear processes governing surfactant or cosolvent movement in unsaturated media necessitate a model for accurately
describing dynamic IPA and AFFF movement due to TDF.
3.2.2. TDF-Induced Flow of AFFF. Figure 4 shows theresults of experiments conducted to investigate AFFF-induced

ArticleAFFF side to the water side. The magnitude of redistribution
was similar to, but somewhat less than, the 7% IPA solution
and nearly as much as for 70% IPA. This result is logicalbecause the IFT of the 1% AFFF solution is similar to, butsomewhat greater than, the 7% IPA solution and somewhat
less than the 70% solution. The physical dynamics of TDF of
AFFF are the same as explained for IPA above. The model
simulations for the experimental concentrations of AFFF arealso shown in Figure 4.
The simulated values for water content match theexperimental data quite well for both the 1 and 0.1% AFFF
solutions. It is remarkable that the excellent model fits were
determined without input-parameter calibration, which demonstrates the rigor of the HYDRUS model modification withthe appropriate physical processes. The soil hydraulicparameters were previously measured (as discussed above),
and the dispersivity value was obtained from the IPA
experiments. For both AFFF and IPA, the model successfully
simulates all of the experimental TDF experiments. The fit isexcellent for the 1% solution and is satisfactory for the 0.1%
IPA, although not as good as the other IPA and AFFF model
fits, possibly because the data on the water side near the end of
the column have a slight declining moisture content comparedto the other AFFF and IPA data sets at the same location
within the column. The experimental and model results for the
0.1% solution are somewhat counterintuitive. The 0.1% AFFF
shows a small redistribution of moisture even though the initial
IFT reduction for 1% solution is substantial (Figure 2).
The behavior is due to dilution of AFFF as it mobilizes
toward the water side. The 0.1% AFFF or 1000 mg/L would
impart a substantial reduction in IFT by itself, butconcentrations approaching several hundred mg/L do notcause dramatic IFT reductions (Figure 2). Figure 5 shows how
AFFF concentration vs distance evolves for 0.1% AFFF and 1%
AFFF as the AFFF mobilized toward the water side. Note thatconcentrations along the column were not measured in theexperiments, but the model can be used to investigate TDF
behavior using concentration profiles. First, the simulations
demonstrate that steady movement of AFFF, and thus TDF,
occurs with the first few hours of the experiment as observed
visually. Figure 5a demonstrates that the concentrations are
below a few hundred mg/L after the first 2 cm from the initialwater-AFFF boundary, where IFT reductions, compared towater, are only 5 to 15%. Thus, the IFT reductions are not

Figure 4. Experimental and simulated changes in moisture contents
for AFFF solutions.

TDF with 0.1 and 1% solutions for AFFF (results of thetriplicate experiments are shown in Figures S2). The 0.1%
solution is not practically realistic for a source zone because
fire-fighting foam typically contains AFFF at concentrations ofseveral percents. However, it is relevant for AFFF on thefringes of a source zone to ensure proper model performance
evaluation. A small fluid redistribution was observed for the
0.1% AFFF solution in the experiments. The 1% AFFF
solution demonstrated a significant moisture-content redistribution. That is, substantial AFFF movement is from the

Figure 5. Simulated concentration along the experimental column for (a) AFFF 0.1% and (b) AFFF 1%.
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ArticleFigure 6. Simulated concentrations and moisture contents in a hypothetical AFFF-source area after TDF for a 3% AFFF solution with different
initial moisture contents. The top two panels depict wetter initial conditions (θ = 0.28), and the bottom two panels show drier initial conditions (θ= 0.08).

given soil by up to 2 orders of magnitude (from 3.45 × 10−4 to2.70 × 10−6 cm/s) across the column (eq 6). It should be
noted that no parameters in the unsaturated hydraulic function
were calibrated to fit the data. Rather, it uses the same input
parameters as measured for the capillary pressure head vsmoisture content relationship (eq 3a).
Similar redistributions occurring in an actual source zone
could have substantial implications for the downward movement of the AFFF phase (eq 5), in addition to the lateral TDF.
A 2-order-of-magnitude change in K(θ) would result in a 2order-of-magnitude change in the rate of movement of AFFFin the vadose zone compared to not considering the impact of
TDF on the moisture content. While these concepts were not
relevant to the bench experiments performed for this study,
which looked primarily at the final moisture content rather
than the rate of change, they are highly relevant tounderstanding the multidimensional transport of AFFFs andtheir travel times or times to reach a steady state.
In the following numerical investigations, we aim to examine
the implications of a spill involving 3% AFFF (the usualprescribed application strength of firefighting foam). The
HYDRUS-1D model is used to explore hypothetical lateral
movement only within an AFFF source zone. The goal of thisnumerical investigation is to understand the impact ofincluding or neglecting TDF-induced flow when developing
conceptual site models (CSMs), where understanding thesource zone is always a critical component. Documents on
CSMs63−66 all state the importance of understanding thesource zone when developing a CSM.
Two initial moisture contents of 28 and 8% are utilized
within a designated area to represent wetter and drier
conditions, etc. The AFFF spill occupies a 10 m zone (AFFFside of Figure 6) adjacent to a subsequent 20 m stretch of
uncontaminated vadose zone (water side of Figure 6). The
conceptual, hypothetical simulations represent a circular AFFF
spill area (source zone) with a 10 m radius, where the outerboundary of this source zone is 3% AFFF. The 10 m radius
represents the original spill footprint, where TDF will induce
AFFF spreading into a larger radius of only water around theoriginal spill footprint. The AFFF concentration representing
the outer boundary of the source zone after spreading isarbitrarily defined to be 600 ng/L AFFF for the following
reasons. AFFF 3% contains approximately 200 mg/L of PFOS

large, limiting TDF. For the 1% solution (Figure 5b), however,the concentrations remain above several hundred mg/L, andtypically greater than 1000 mg/L, throughout the entire
column length, resulting in significant TDF.
As expected, soil sorption and AWI partitioning of bulk
AFFF were not significant. Sensitivity analysis indicated thebest model fit occurred with no retardation (R = 0, eq 7),
detailed in the Supporting Information, Section S4a. Sorption
to clean sands was not anticipated to impact transport,
supported by the introduction and consistent with findings
from other researchers in clean sand experiments.19,49,60
However, the Supporting Information, Section S4a demonstrates that sorption to porous media with substantial sorption
capacity could influence AFFF transport.
Similarly, AWI partitioning was not anticipated tosignificantly impact AFFF transport. AWI partitioning
coefficients estimated from the L-S equation coefficients “a”
and “b” (eq 1, Figure 2) using the method presented by Silva etal.10 and described in Supporting Information, Section S4b
resulted in partitioning coefficients similar to that estimated for
PFOA and considerably smaller than that for PFOS. Other
studies have shown that retardation of PFOA in unsaturated
porous media is not significant relative to PFOS.61,62 Thus, wewould not expect AWI partitioning to cause significant
retardation that would notably influence the AFFF transport.
3.3. Implications. While not addressed directly by ourexperimental design, the rate of fluid movement due to TDF
will be potentially impacted not only by retardation but also by
the changes in pressure head and also changes in unsaturated
hydraulic conductivity relative to water alone. The changes inmoisture content observed in these experiments because of
TDF will substantially impact both parameters. For example, inthese benchtop experiments, for AFFF with a 1% concentration, it was estimated from eq 3a that the capillary pressure
head (h(θ)) decreased by roughly 57% (from −17 to about−26.5 cm) on the water-containing side and increased on thesolution-containing side by 58% (from −17 to about −7 cm),compared to water only. The unsaturated hydraulic conductivity is strongly dependent on moisture content (that is, it
decreases approximately exponentially with a reduction inmoisture content) (eq 6). Moisture content dynamics in theexperiment have been discussed earlier. These TDF-inducedchanges in moisture content resulted in variations in K(θ) for aG

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within 30,000 mg/L of AFFF. The USEPA has proposed amaximum contaminant level of 4 ng/L for PFOS in 2023.67 To
meet this threshold, the AFFF concentration would beapproximately 600 ng/L.
In these simulations, the media properties remain consistent
with those described in the experimental study, except for
dispersivity, which is known to be scale-dependent, whereby arealistic value of 300 cm is assumed for this hypotheticalhomogeneous porous media.56,57 To capture the magnitude
and extent of moisture redistribution across the lateral sourcezone footprint over a long-term steady-state hypothetical
redistribution period, a 20 year period was investigated. Similar
to our experimental studies, we neglected partitioning to thesolid phase as well as AWI.
For AFFF-transport simulations, a free drainage was set on
the water side to allow AFFF to escape the model domain if itreached that boundary; a no-flow boundary was used on the
AFFF side, which is conceptually the center of the AFFF
source zone, simulating a finite AFFF supply (i.e., the initial
AFFF concentration is allowed to deplete). Simulations wereconducted until quasi-steady-state conditions were reachedbased on analysis of concentration and pressure gradientprofiles produced by HYDRUS. The term quasi-steady state isused because very slow spreading would continue indefinitely
due to molecular diffusion.
The results (Figure 6) highlight the significant influence of
TDF-induced movement in the AFFF source zone. Figure 5a,b
presents concentrations versus lateral distance for two different
initial water contents, wetter and drier (initial moisture
contents of 0.28 and 0.08, respectively). The 20 m on theleft in Figure 6 depicts the area initially without AFFF (water
only). The right side 10 m is simulated as 3% AFFF. Under
drier conditions, the AFFF footprint extends due to TDF byapproximately 14.5 m into the original water-only side, fromthe original radius of 10 to 24.5 m. The time to reach quasisteady state is approximately 20 years, transitioning from theoriginal boundary of 3% (30,000 mg/L) to the definedboundary concentration of 600 ng/L.
Assuming a circular source area, the TDF-induced flow
increases the simulated source footprint area for wetter
conditions by a factor of 6 from an initial (and typicallyassumed permanent) area of 314 to 1885 m2. For the drier
scenario, the footprint expands at least 11.5 m, from a radius of
10 m to a radius of about 21.5 m, expanding the simulated
footprint from 314 m2 to nearly 1451 m2, more than a 4-foldincrease. Of course, if an arbitrary lower concentration of
AFFF were chosen as the definition of the outer boundary forthe source zone, the AFFF spreading would result in a larger
AFFF footprint. Wetter initial conditions result in a larger
footprint radius compared to drier conditions, as the wetter
soil holds a greater reservoir of aqueous 3% AFFF. Additionally, higher moisture content leads to faster spreading over a
fixed distance, driven by increased unsaturated hydraulicconductivity and larger pressure gradients (discussed in thesection below). Overall, higher initial moisture contents
accelerate the AFFF source zone spread, expanding the
TDF-induced zone. The 28% moisture content system reacheda near-steady state in several decades (converging lines).
Conversely, drier conditions reach a steady state sooner, taking
about a decade for quasi-equilibrium pressure heads andconcentrations. This occurs at a smaller lateral distancecompared to wetter conditions, likely due to a smaller AFFF

Articlereservoir and very low unsaturated hydraulic conductivity
values causing flow cessation sooner than in wetter conditions.
It is worth noting that while altering the dispersivity had
minimal effect on the model’s fit at the experiment scale, it
played a significant role in field-scale spreading. The
dispersivity influences the resulting surface area of the
footprint, highlighting that the estimates for accurate
dispersivity would be needed to simulate field-scale transportof AFFF. The Supporting Information Figures S4 and S5
provide further details on dispersivity sensitivity analysis.
These results are interesting because an original spill
footprint for traditional contaminants, often ascertained fromsite records or surface infrastructure evidence, is largely
assumed to remain constant over time. However, the resultsof our study demonstrate that a considerable increase in the
AFFF source zone surface footprint should be expected. Ourfindings also suggest that seasonal variations in moisture
content, such as those caused by precipitation or evaporation,
can continuously modify the dimensions of the source zone
over extended periods. Notably, severe droughts or exceptionally wet years could essentially reshape the footprint of thesource zone. Additionally, a similar AFFF spill at different
locations with different climate regimes would result indifferent amounts of AFFF spreading compared with theoriginal spill footprint. This temporal behavior underscores thelong-term behavior and persistence of AFFF in the vadosezone, highlighting the need for targeted AFFF monitoring andassessment to fully understand the implications and potential
risks associated with AFFF contamination.
3.4. Limitations. The primary limitation is the use of alateral 1-D model for simulating field-scale lateral transport ofan AFFF source zone without considering vertical transport.
The absence of gravity in simulations may impact lateralexpansion by reducing the AFFF concentration in the sourcezone due to downward transport, an aspect that has received
limited attention. The robust 3D model used by Zeng andGuo34 and Zeng et al.38 demonstrated minimal impact of TDF
on transport of specific PFAS. However, these studies
simulated individual PFAS rather than actual AFFF transport
from an impacted site. The concentrations of specific PFAS inthese simulations (up to 1 mg/L PFOA in Zeng et al.,38 and1000 mg/L of PFOS in Zeng and Guo34) were notably lower
than the total surface-acting chemical concentrations in our 3%
AFFF (30,000 mg/L, including all constituents, with PFOS
alone at approximately 200 mg/L). Indeed, the results of theseauthors regarding TDF are consistent with our own, where our
0.1% AFFF experimental solution (1000 mg/L total constituents) showed minimal TDF. Unlike other studies, ourmodel was calibrated to actual AFFF data. As discussed earlier,
we anticipate the AFFF movement to differ from that of any
specific PFAS component.
Additionally, several field and modeling studies suggest that
AFFF-phase downward movement is slight and slow, where
the PFAS concentrations that indicate AFFF are confined
primarily to the top tens of centimeters.6,68−71 Using a lateral
1-D model of an AFFF source zone is consistent with theseobservations. In any case, the model modification used here
has not yet been implemented into a publicly available 3-Dmodel, and the 1-D model used in these simulations is
intended for conceptual understanding of lateral transport due
to TDF. We acknowledge that future work should investigate
multidimensional movement of actual AFFF for realistic site
conditions.
H

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The general applicability of our results is also limited
because AFFF-specific model input parameters related to soil
and air−water partitioning have yet to be measured and themethods to do so have not been developed. Currently, onlytransport parameters for specific PFAS have been reported in
the literature. In the few previous modeling studies that haveaddressed this topic (see above), bulk AFFF transport withregard to partitioning has been simulated with surrogate
parameters from specific PFAS, which is not accurate giventhat AFFF consists of numerous components, where specific
PFAS components comprise less than 1% of the bulk AFFF.
Based on the sensitivity studies (described in Supporting
Information, Section S4a), soil sorption is likely an important
influence on TDF flow of AFFF, so additional studies that
attempt to better characterize or estimate the partitioning
coefficients for AFFF would be useful. Currently, the mostrigorous method to obtain transport parameters for actual
AFFF is by using model calibration to experimental data andmodel sensitivity analyses, as we have performed in thisresearch.

Articletypically assumed to be constant over time. For example,
a 3% AFFF solution with an initial moisture content of
0.28 showed over a 6-fold expansion in source zone
surface area, while an initial moisture content of 0.08
exhibited a more than 4-fold increase. Wetter initialconditions led to faster AFFF spreading due to increased
pressure gradients and unsaturated hydraulic conductivity. While many AFFF sites may have endured for overtwo decades, this insight is particularly relevant to newersites, suggesting the potential for continuous expansionof the source-zone footprint over time.
• Guidelines for conceptual model establishment incontaminated sites consistently emphasize comprehending source attributes (e.g., geometry, mass distribution)
because accurate source characterization is crucial forunderstanding the site and developing contaminanttransport models. This study underscores the significance of incorporating TDF effects in evaluating AFFF
source zones and transport. The adapted HYDRUS
model offers a quantitative approach for simulating
TDF-induced changes in AFFF solutes, advancing ourunderstanding and predictive capabilities.
• Overall, the present study has provided fundamental
insights into the primary factors controlling the transportand retention of AFFF in the vadose zone that need tobe considered for site characterization, vadose zonetransport, source-zone remediation, and assessment/
remediation of groundwater pollution risk. However, it is
crucial to recognize that the observed behavior in our
simulations may vary across different soil types or when
AFFF-component sorption significantly influences bulk
AFFF-phase transport.

4. SUMMARY AND CONCLUSIONSThis experimental study investigated the influence of TDF on
the transport of AFFF and IPA (a cosolvent). The numericalmodel HYDRUS, recently modified to account for AFFF
transport, was used to simulate the experiments and thensubsequently to conduct some simple but useful numeral
experiments regarding field-scale AFFF source zone spreading.
The study yielded several significant findings, as follows:• The results demonstrated that the introduction of AFFF
can cause substantial TDF due to the impact on capillarypressure gradients relative to water alone.
• The new version of HYDRUS-1D (HYDRUS 5)
incorporated adjustments to account for TDF andaccurate IFT versus AFFF concentration profiles, evenfor concentrations exceeding the CMC. The model
effectively simulated TDF induced by IPA and AFFF
during horizontal, bench-scale column experiments,
requiring minimal parameter calibration after appropriately characterizing concentration versus IFT relationships for each fluid. Only dispersivity coefficients were
calibrated for IPA experiments and subsequently used
for AFFF simulations, with little impact observed on thesimulation outcomes.
• Sorption to soil was not important in influencing the
TDF of AFFF for our specific clean, sandy porous
media. However, a model sensitivity study showed thatsorption to soils could be important for soils that enablesignificant sorption of PFAS components. This topic
should be investigated in further detail.
• Our model calibration to experimental data, along with asubsequent model sensitivity study, demonstrated thatpartitioning to the air−water interface, while importantfor causing the capillary gradients required to induce
TDF, was not important in the final redistribution of an
AFFF source zone because the AWI partitioning
coefficient of bulk AFFF is relatively small (similar to
PFOA) to cause significant retardation.
• Numerical experiments intended to represent realisticscale AFFF source zones revealed that TDF can cause
lateral AFFF source-zone spreading that is significantly
different from the spill’s original footprint, which is■

ASSOCIATED CONTENT

sı Supporting Information*

The Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acsestwater.3c00611.
Additional experimental details, moisture content
variation in triplicate measurements, sensitivity analysis
on dispersivity, and sensitivity analysis on the impacts ofpartitioning (PDF)■

AUTHOR INFORMATION

Corresponding Author

Jeff A. K. Silva − Arclight Research & Consulting, LLC,
Golden, Colorado 80401, United States; Email: jsilva@
arclightrc.com
Authors

Faran Vahedian − Civil & Environmental Engineering
Department, Colorado School of Mines, Golden, Colorado
80401, United States; orcid.org/0009-0006-2285-6362
Jiří Šimůnek − Department of Environmental Sciences,
University of California, Riverside, California 92521, UnitedStatesJohn E. McCray − Civil & Environmental Engineering
Department, Hydrologic Science and Engineering Program,
Hydrologic Science & Engineering Program, ReNuWit�The
Urban Water Engineering Research Center, Colorado Schoolof Mines, Golden, Colorado 80401, United States;
orcid.org/0000-0001-7481-9965
Complete contact information is available at:I

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https://pubs.acs.org/10.1021/acsestwater.3c00611
Author Contributions

CRediT: Faran Vahedian conceptualization, data curation,
methodology, validation, visualization, writing-original draft;
Jeff A.K. Silva conceptualization, funding acquisition, investigation, methodology, project administration, resources,
supervision, validation, writing-review & editing; Jiri Simunek
software, validation, writing-review & editing; John E. McCray
conceptualization, methodology, writing-review & editing.
Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS
This work was supported by the US Army Corps of Engineers
and the Department of Defense Strategic Environmental
Research and Development Program under Contract no.
W912HQ21C0040. We appreciate the valuable feedback fromthe reviewers.

■

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https://doi.org/10.1021/acsestwater.3c00611
ACS EST Water XXXX, XXX, XXX−XXX