Mathematical Modeling of Coupled Heat and Mass Transfer with Phase Transitions in Heterogeneous Porous Soils: Mechanism of Soil Moisture Diffusivity Collapse during Freezing

Elena M. Avraham

A mathematical model of coupled heat and mass transfer with water–ice–vapor phase transitions in heterogeneous porous soils is developed. 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 moisture transport suppression 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 hydraulic conductivity to specific moisture capacity and governing the rate of moisture redistribution in the soil. It is shown that the behavior of the system can be described in 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. It is established that passage of the freezing front is accompanied by a sharp collapse of the soil moisture diffusion coefficient, caused by the simultaneous reduction of hydraulic conductivity and a manifold increase in the effective moisture capacity of the medium. The characteristic magnitude of the diffusivity reduction and the critical temperature corresponding to the transition between the kinematic and thermodynamic regimes of moisture transport suppression are determined. The results elucidate the physical mechanism of critical moisture transport suppression in freezing porous media and may be used in the development of thermo-hydrological models of frozen soils, prediction of seasonal soil freezing processes, and engineering assessment of soil foundation stability and infrastructure under cold-climate conditions.