Mathematical modeling of coupled heat and mass transfer with phase transitions in heterogeneous porous soils: mechanism of soil water diffusivity collapse during freezing

Abstract

A mathematical model of coupled heat and mass transfer with water–ice–vapor phase transitions in heterogeneous porous soils is presented. The model comprises the Richards equation, the water vapor diffusion equation, and the heat transfer equation, coupled through a temperature-dependent hydraulic conductivity governed by the Kozeny–Carman relation and thermodynamic phase equilibrium described by the Clapeyron–van Genuchten framework. The study aims to identify the physical mechanism responsible for the suppression of moisture transport during soil freezing and to quantitatively characterize the sharp reduction in the soil moisture diffusion coefficient. An analytical expression for the soil moisture diffusion coefficient is derived, linking the hydraulic conductivity to the specific moisture capacity and determining the rate of moisture redistribution in the soil. The analytical result admits a compact dimensionless form controlled by a single governing parameter that separates two physically distinct limiting regimes of moisture transport degradation: a kinematic regime dominated by geometric pore blockage due to ice formation, and a thermodynamic regime governed by phase inertia associated with the latent heat of the phase transition. Numerical simulations using the finite element method reveal a sharp collapse of the soil moisture diffusion coefficient upon passage of the freezing front, driven by the simultaneous reduction of hydraulic conductivity and a manifold increase in effective moisture capacity. The characteristic magnitude of the collapse and the critical temperature marking the transition between the two regimes are determined analytically. The~results elucidate the physical mechanism of critical moisture transport suppression in freezing porous media and provide a physically based parameterization applicable to thermo-hydrological models of frozen soils, prediction of seasonal freezing processes, and engineering assessment of soil foundation stability under cold-climate conditions.

The manuscript is based on an English-language preprint previously posted on EarthArXiv. The submitted Russian version is substantially revised, expanded, and translated. Full disclosure is provided in the manuscript.