Newtonian fluid flow in a thin porous medium with non-homogeneous slip boundary conditions

TL;DR

This paper analyzes the asymptotic behavior of Newtonian fluid flow in a thin, perforated porous medium with non-homogeneous slip boundary conditions, revealing different limit systems depending on boundary parameters.

Contribution

It extends the unfolding method to derive the asymptotic limits of Stokes flow in thin porous media with complex boundary conditions.

Findings

Different limit systems depending on slip parameter gamma.

Asymptotic velocity and pressure profiles characterized.

Methodology applicable to similar fluid-structure interaction problems.

Abstract

We consider the Stokes system in a thin porous medium $\Omega_\varepsilon$ of thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe non-homogeneous slip boundary conditions depending on a parameter $\gamma$. The aim is to give the asymptotic behavior of the velocity and the pressure of the fluid as $\varepsilon$ goes to zero. Using an adaptation of the unfolding method, we give, following the values of $\gamma$, different limit systems.