The PFAS Module
Note: Using the PFAS module in 1D and 2D projects requires a license for the H1D-Pro add-on module package.
Sorption to (distribution between soil water and) air-water interface
When evaluating the fate and transport of polyfluoroalkyl substances (PFAS) under dynamic vadose zone conditions, one needs to consider sorption to (distribution between soil water and) air-water interface [Silva et al., 2019, 2020, 2021]. In that case, the term accounting for the distribution of a solute between the liquid and gaseous phases is replaced with a new term accounting for solute sorption to the air-water interface as follows:
where Gamma is the interfacial adsorbed concentration (i.e., mass or moles per unit area of the interface, or M/L2), and Aaw is the air-water interfacial area, which has units of [L2/L3] or [1/L]. The air-water interfacial area Aaw is calculated from the pressure head-saturation relationship using equation (8) of Bradford et al. [2015] (also Bradford and Leij [1997]):
where Sigma_aw is the air-water surface tension [M/T2], Paw is the capillary pressure [M/L/T2], theta_s is the saturated water content [L3/L3], ro_w is the density of water [M/L], and g is the gravitational acceleration [L/T2]. The users can specify at input an additional constant, which allows them to linearly scale the interfacial area Aaw.
The interfacial adsorbed concentration (Gamma, mass or moles per unit area of the interface, or M/L2) can be calculated directly using the Freundlich-Langmuir adsorption isotherm as:
where Gamma_max [M/L2] is the maximum surface concentration (i.e., at the solubility limit), and KH [for linear sorption, L3/M1, for Freundlich sorption L^(3Beta)/M^Beta], Beta [-], and KL [L^(3Beta)/M^Beta] are empirical coefficients.
Concentration Dependence of the Soil Hydraulic Functions
The scaling technique, similar to one used to describe the temperature dependence of soil hydraulic properties, is used in HYDRUS to express the concentration dependence of the soil hydraulic functions. The primary impact of surface-active organic solutes on unsaturated flow is through the dependence of soil water pressure head on surface tension. The dependence of surface tension on solute concentration is described according to Adamson and Gast (1997) and Henry et al. (2001).
where a [L3/M1] and b [-] are constants for the compound of interest, sigma(c) the surface tension at concentration c, and sigma_0 the surface tension at the reference concentration.
A similar expression is used to consider the dependence of viscosity as a function of solute concentration (Smith and Gillham, 1999).
where d [L3/M1] and e [-] are constants for the compound of interest, nu(c) the kinematic viscosity at concentration c, and nu_0 is kinematic viscosity at the reference concentration.
References
- Silva, J. A. K., J. Šimůnek, and J. E. McCray, Comparison of methods to estimate air-water interfacial areas for evaluating PFAS transport in the vadose zone, Journal of Contaminant Hydrology, 247, 103984, 13 p., doi: org/10.1016/j.jconhyd.2022.103984, 2022.
- Silva, J. A. K., J. Šimůnek, and J. E. McCray, A modified HYDRUS model for simulating PFAS transport in the vadose zone, Water, 12, 2758, 24 p., doi: 10.3390/w12102758, 2020.
- Šimůnek, J., M. Šejna, G. Brunetti, and M. Th. van Genuchten, The HYDRUS Software Package for Simulating the One-, Two, and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media, Technical Manual I, Hydrus 1D, Version 5.0, PC Progress, Prague, Czech Republic, 334p., 2022. (PDF 3.9MB)
- Šimůnek, J., M. Th. van Genuchten, and M. Šejna, The HYDRUS Software Package for Simulating One-, Two-, and Three-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Porous Media, Technical Manual II, Hydrus 2D/3D. Version 5.0, PC Progress, Prague, Czech Republic, 283 p., 2022. (PDF 3.6MB)