Compression Effects in Heterogeneous Media

TL;DR

This paper investigates how compression effects behave in heterogeneous media near maximal packing, deriving limiting equations that depend on the relative importance of bulk viscosity, revealing memory effects in dense regimes.

Contribution

It introduces a convergence analysis from compressible Brinkman equations with singular pressures to two-phase models, highlighting the role of bulk viscosity in memory effects.

Findings

Convergence of solutions to two-phase Brinkman equations

Memory effects depend on bulk viscosity importance

Limit models capture dense regime behaviors

Abstract

We study in this paper compression effects in heterogeneous media with maximal packing constraint. Starting from compressible Brinkman equations, where maximal packing is encoded in a singular pressure and a singular bulk viscosity, we show that the global weak solutions converge (up to a subsequence) to global weak solutions of the two-phase compressible/incompressible Brinkman equations with respect to a parameter $\varepsilon$ which measures effects close to the maximal packing value. Depending on the importance of the bulk viscosity with respect to the pressure in the dense regimes, memory effects are activated or not at the limit in the congested (incompressible) domain.