Deformable porous media with degenerate hysteresis in gravity field

TL;DR

This paper extends models of hysteresis in porous media to include viscoelastic solids and gravity-driven moisture flux, proving the existence of solutions using advanced mathematical techniques.

Contribution

It introduces a new model incorporating viscoelasticity and gravity effects in hysteretic porous media and proves solution existence with Orlicz space methods.

Findings

Model successfully incorporates viscoelasticity and gravity effects.

Existence of solutions established mathematically.

Handles degeneracy in pressure-saturation relations.

Abstract

Hysteresis in the pressure-saturation relation in unsaturated porous media, which is due to surface tension on the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation. Solutions to such degenerate equations have been recently constructed by the method of convexification even if the permeability coefficient depends on the hysteretic saturation. The model is extended here to the case that the solid matrix material is viscoelastic and that the system is coupled with a gravity driven moisture flux. The existence of a solution is proved by compact anisotropic embedding involving Orlicz spaces with respect to the time variable.