The Influence of Tension-Driven Flow on the Transport of AFFF in Unsaturated Media
Faran Vahediana, Jeff A.K. Silvab, Jiří Šimůnek c, John E. McCrayda Civil & Environmental Engineering Department, Colorado School of Mines, Golden, CO 80401, USA;fvahedian@mines.edu
b Arclight Research & Consulting, LLC, Golden, CO 80401, USA; jsilva@arclightrc.com
cDepartment of Environmental Sciences, University of California, Riverside, CA 92521, USA;jiri.simunek@ucr.edu
dCivil & Environmental Engineering Department, Hydrologic Science and Engineering Program,Hydrologic Science & Engineering Program, ReNuWit—The Urban Water Engineering ResearchCenter, Colorado School of Mines, Golden, CO 80401, USA; jmccray@mines.edu
Corresponding author. Jeff A.K. Silva, jsilva@arclightrc.com, Golden, CO 80401, USA

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Section 1- Additional experimental details
For each experiment, 372 g of dry sand was measured out to provide enough sand to pack thecolumn. Half of the dry sand was mixed with simulated groundwater to attain the designatedgravimetric moisture content (GMC), while the remaining half was blended with either IPA or AFFF
solution to reach an equivalent moisture content. The moisture content was measured gravimetricallyfollowing the methodology outlined by Jury and Horton 1; gravimetric moisture content (GMC) isdetermined by evaluating the ratio of water mass to dry sand mass, which is then scaled by themeasured bulk density to derive the volumetric moisture content (q). The target q was between 0.15
and 0.2 designed to provide enough initial moisture to observe the range of changes in moisture
content. Following several experiments, 0.18 was chosen. The saturated sands were agitated for twominutes, individually sealed, and left to equilibrate for 24 hours to ensure uniform fluid distribution.
They were subsequently mixed again for 2 minutes before packing. The packing process began withpacking the water side of the column and then the IPA / AFFF side using a tamp-and-fill procedure.
The total time for packing the column did not exceed 5 minutes. The columns were capped with avented high-density polyethylene end cap on each end and was then placed in a larger sealedcontainer to maintain the positioning of the pack and minimize evaporation during a given moistureredistribution period. After 12 hours of moisture redistribution, the soil core was carefully extruded
from the columns and segmented into 10 samples, each approximately 1 cm long, to determine themoisture content profile within the columns. The samples were oven-dried at 100°C for 24 hours toobtain the moisture content.

Section 2- Moisture content variation in triplicate measurements
The figures below show the triplicate data for IPA 7% and IPA 70% (Figure S1) and AFFF 0.1% andAFFF 1% (Figure S2). The similarity in the results underscores the robustness of the experimental
data.

Figure S1- Experimental (in triplicate) and simulated change in moisture contents for the 7% IPA
solution (to the left) and 70% IPA solution (to the right).

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Figure S2- Experimental (in triplicate) and simulated change in moisture contents for the 0.1% AFFF
solution (to the left) and the 1% AFFF solution (to the right).
Section 3- Sensitivity analysis on dispersivity
The model required minimal calibration to dispersivity. Therefore, dispersivity was calibrated based on
IPA data to be 1 cm, falling within the range recommended by Gelhar et al.2 To validate this for AFFF,
we conducted a sensitivity analysis by adjusting dispersivity in the model's fit to the experimental
scale (AFFF data). Figure S3 illustrates that varying dispersivity within a reasonable range had
negligible effects on the experimental scale. The model fits closely aligned, with a dispersivity of 1
providing the best description of the data. However, given the minimal differences in the triplicate
experimental data, alternative dispersivity values might better fit the other datasets (AFFF1%-2 orAFFF1%-3).

Figure S3- Evaluating the impact of dispersivity through sensitivity analysis on the experiment-scale.
However, Figure S4 shows that altering the dispersivity within a reasonable range played a significant
role in field-scale spreading. For example, decreasing the dispersion coefficient from 300 cm to 100
cm led to less TDF spreading. In wetter (Figure S4) and drier conditions (Figure S5), the radius
dropped from 4.5 and 5 meters respectively. This alteration will influence the resulting surface area ofthe footprint.

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Figure S4- Evaluating the impact of dispersivity through sensitivity analysis on field-scale spreadingThe left figure depicts the original wetter condition with a dispersivity of 300 cm, while the right one
represents the wetter condition with a dispersivity of 100 cm.

Figure S5- Evaluating the impact of dispersivity through sensitivity analysis on field-scale spreadingThe left figure depicts the original drier condition with a dispersivity of 300 cm, while the right one
represents the drier condition with a dispersivity of 100 cm.

Section 4- Sensitivity analysis on the impacts of partitioning
Section 4a- Sorption to solid-phase
In this study, the model achieved the best fit to data with fitted retardation values of R = 1.0, meaning
the impact of soil and air-water interfacial (AWI) partitioning is not important for AFFF TDF for ourspecific experiments. IPA is known to not sorb to soil (i.e. Costanza-Robinson and Henry(3)); Sorption
or interfacial partitioning studies related to retardation and transport for AFFF have not yet been
published. Given our experimental conditions using clean, well-sorted sandy soil, we do not anticipate
significant AFFF retardation due to interfacial partitioning at the air-water interface. The lack ofimportance of soil sorption aligns with the relatively low concentration of strongly sorbing PFAS in ourAFFF. Previous studies using similar media also demonstrated negligible impacts of soil sorption on
PFAS transport4-6. Indeed, we chose a material that should have little sorption with the intent ofisolating the impacts of TDF due to interfacial partitioning. The expectation was confirmed when theS4

best fit of the HYDRUS model prediction to our data occurred when the sorption coefficient (Kf in thiscase) was zero (i.e., R=1) (Figures S6). However, it is useful to show how sorption might impact theTDF, because PFAS sorbed are removed from the solution and thus not able to contribute to TDF.
In Figure S6, we provide examples illustrating how sorption beyond our observations can affect TDF.
This brief sensitivity study illustrates that while sorption of PFAS and other AFFF constituents can andwill occur, its contribution is not significant to TDF for the AFFF solutions used here. This is because
solution concentrations of the surface-active components in the AFFF solutions remain high, relative
to the sorbed concentrations in our system.

Figure S6- Sensitivity analysis of solid-phase sorption on AFFF Transport. Kd refers to linear sorption
for a range of values to demonstrate effects. Nonlinear sorption uses the Freundlich model (Kf:0.59
L/kg, n: 085) based on the results of Guelfo et al 6.

Section 4b- Partitioning to the air-water interface
We do not anticipate AFFF retardation from AWI partitioning. The best model fit to data (Figure S7) isachieved with R = 1 (Kaw=0). However, as TDF is influenced by the adsorption of PFAS and AFFF
constituents to the air-water interface, leading to reduced surface tension, it is essential to evaluate
TDF sensitivity to varying levels of air-water interfacial adsorption. The relationship between theinterfacial adsorbed concentration (Ꚍ, ML⁻²) and solution concentration (𝐶𝑤, ML⁻³) is simulated in
HYDRUS through the application of the Langmuir-type adsorption isotherm (KL), described by Eq. 4 inSilva et al7. Based on this technique, the relevant air-water partitioning parameters are ΓMAX, themaximum surface concentration (i.e., at the solubility limit) (ML−2), and KL,aw is the Langmuir
partitioning coeﬃcient (L3M −1). KL,aw for AFFF cannot be measured directly. The common approach,followed by most authors, including Silva et al7 and our study, is to separately determine therelationship between surface tension and surfactant concentration using the L-S equation. Thisapproach, as implemented in the main text of the paper (see Equation 1 and Figure 2), allows
estimation of KL,aw from the "a" and "b" parameters, following the methodology described in Silva etal7. Using this technique, we estimated a KL,aw value of 20,000 cm3/g for our AFFF, closely resembling

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the value of 16,100 cm3/g estimated by Silva et al7 for PFOA. By employing these inputs in HYDRUS,
the outcomes of the sensitivity analysis reveal no discernible impact on the steady-state position of
the moisture content front, as depicted in Figure S7. The predicted moisture front remains the same
regardless of the values used for KL and Γ𝑚𝑎𝑥. Previous researchers, through experimental ormodeling studies, have indicated that the retardation of PFOA in unsaturated media due to air-waterinterfacial (AWI) partitioning is not substantial compared to PFOS5, 8. Therefore, we do not expect
substantial retardation of AFFF due to air-water interfacial (AWI) partitioning, given the similarity of thepartitioning values. The logical and expected outcome of the sensitivity study (Figure S7), where thebest model fit to data was achieved with R = 1.0, supports this understanding. While air-waterinterfacial adsorption remains important for PFAS and AFFF component transport, it does not
significantly contribute to TDF for this AFFF, given the high solution concentrations of the surfaceactive components in the presented cases.

Figure S7. Sensitivity analysis was performed using the estimated KL,aw for the AFFF used in thisstudy. Note that the model results coincided with the original simulation, where R=1

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