# Bingham flow in porous media with obstacles of different size

## TL;DR

This paper develops a homogenization framework for Bingham fluid flow in porous media with obstacles of varying sizes, leading to a nonlinear Darcy law describing the effective flow behavior.

## Contribution

It introduces a general compactness result for perforated domains with different-sized obstacles and applies it to derive a nonlinear Darcy law for Bingham fluids.

## Key findings

- Homogenization of Bingham flow in media with mixed obstacle sizes
- Derivation of a nonlinear Darcy law as the effective model
- Establishment of a compactness result using unfolding operators

## Abstract

By using the unfolding operators for periodic homogenization, we give a general compactness result for a class of functions defined on bounded domains presenting perforations of two different size. Then we apply this result to the homogenization of the flow of a Bingham fluid in a porous medium with solid obstacles of different size. Next we give the interpretation of the limit problem in term of a non linear Darcy law.