Comparison of methods to estimate air-water interfacial areas for evaluating PFAS transport in the vadose zone

When performing calculations or numerical simulations for the fate and transport of PFAS and other surface-active solutes in the vadose zone, accurately representing the relationship between the area of the air-water interfaces (A_aw) as a function of water saturation (S_w), and changes in that relationship resulting from changes in soil texture, are equally important as accurately characterizing interfacial adsorption coefficients and the concentration dependence for PFAS solutes. This is true because the magnitude of the A_aw directly governs the degree of air-water interfacial adsorption, which contributes to the transport retardation of these solutes within unsaturated porous media. Herein, a well-known thermodynamic-based model for predicting the A_aw-S_w relationship is evaluated through comparisons to literature data collected using various measurement techniques for model sands and a limited number of soils using data collected from the current published literature. This predictive model, herein termed the Leverett thermodynamic model (LTM), relies on the characterization of the soil-water retention curve (SWRC) for a given soil, using the van Genuchten (VG) equation for the pressure head-vs-S_w relationship. Therefore, methods to estimate the VG equation parameters are also compared as to the A_aw-S_w relationships predicted. Comparisons suggest that the LTM provides the best estimate of the actual A_aw-S_w relationships for water containing non-surface-active solutes. Because PFAS solutes are also surface-active, A_aw measurement methods utilizing surface-active tracers are considered to provide the most accurate representation of the A_aw-S_w relationship for these solutes. Differences between A_aw-S_w relationships derived from tracer methods and the LTM are described in relation to media surface roughness effects. Based on the available literature data, a practical empirical model is proposed to adjust the LTM prediction to account for the effects of surface roughness on the magnitude of the A_aw for surface-active solutes. Finally, example retention calculations are performed to demonstrate the sensitivity of the predicted A_aw-S_w relationship on the vadose zone transport of of a representative PFAS, perfluorooctane sulfonate.