Modeling the diffusion of a fluid in a strained solid: a comparison between different formats

TL;DR

This paper compares different modeling formats for fluid diffusion in strained solids, revising Bowen's approach and demonstrating their equivalence within mixture theory, enhancing understanding of porous media behavior.

Contribution

It revises Bowen's model and proves its equivalence to recent formats for fluid diffusion in strained solids using mixture theory.

Findings

Revised Bowen's format for porous media

Proved equivalence of different modeling approaches

Enhanced understanding of fluid diffusion in strained solids

Abstract

We revise the format proposed by Bowen in [R.~M. Bowen. Int. J. Eng. Sci., 18(9):1129--1148, 1980.] to describe incompressible porous media by use of the theory of mixtures. We then show that this format is equivalent the those proposed more recently to model the diffusion of a fluid in a strained solid.