Homogenization of the Stokes type model in porous media with slip boundary conditions

TL;DR

This paper investigates the limiting behavior of Stokes-type fluid flows in porous media with slip boundary conditions, using two-scale convergence under periodic assumptions to derive homogenization results.

Contribution

It provides a rigorous homogenization result for Stokes flows with slip boundary conditions in porous media, extending previous models to include boundary slip effects.

Findings

Proved convergence of Stokes flows with slip boundary conditions in periodic porous media.

Derived effective equations describing macroscopic flow behavior.

Validated the homogenization approach using two-scale convergence.

Abstract

This work is devoted to the study of the limiting behaviour of the Stokes type fluid flows in porous media. The boundary conditions here are of the Fourier-Neumann's type on the boundary of the holes. Under the periodic hypothesis on the structure of the medium and on the coefficients of the viscosity tensor, one convergence result is proved. Our approach is the well known two-scale convergence method.