Effects of an impermeable wall in dissipative dynamics of saturated porous media

TL;DR

This paper investigates how an impermeable wall affects the formation and dynamics of fluid-rich bubbles in saturated porous media during consolidation, using a Cahn-Hilliard-like PDE model with different boundary conditions.

Contribution

It introduces a phase transition model incorporating boundary effects and provides analytical insights into interface positioning during fluid segregation.

Findings

Impermeable boundary influences bubble formation and position.

Analytic expression for interface location in phase coexistence.

Dynamics differ significantly with boundary permeability.

Abstract

A phase transition model for porous media in consolidation is studied. The model is able to describe the phenomenon of fluid-segregation during the consolidation process, i.e., the coexistence of two phases differing from fluid content inside the porous medium under static load. Considering pure Darcy dissipation, the dynamics is described by a Cahn-Hilliard-like system of partial differential equations (PDE). The goal, here, is to study the dynamics of the formation of stationary fluid-rich bubbles. The evolution of the strain and fluid density profiles of the porous medium is analyzed in two physical situation: fluid free to flow through the boundaries of the medium and fluid flow prevented at one of the two boundaries. Morover, an analytic result on the position of the interface between the two phases is provided.