Phase transitions in porous media

TL;DR

This paper models water diffusion, freezing, and melting in porous media using complex PDE systems with hysteresis, proving the existence of global solutions under broad conditions.

Contribution

It introduces a comprehensive PDE model incorporating Preisach hysteresis for phase transitions in porous media, establishing global solvability.

Findings

Global solutions exist for the coupled PDE system.

The model captures hysteresis effects in phase transitions.

Mathematical framework applies to thermomechanical porous media.

Abstract

The full quasistatic thermomechanical system of PDEs, describing water diffusion with the possibility of freezing and melting in a visco-elasto-plastic porous solid, is studied in detail under the hypothesis that the pressure-saturation hysteresis relation is given in terms of the Preisach hysteresis operator. The resulting system of balance equations for mass, momentum, and energy coupled with the phase dynamics equation is shown to admit a global solution under general assumptions on the data.