# Analysis of the roughness regimes for micropolar fluids via homogenization

## TL;DR

This paper investigates how micropolar fluid flows behave in thin, rough domains with oscillating boundaries, revealing three distinct regimes based on the relative scale of domain thickness and boundary oscillations, and deriving generalized Reynolds equations for each.

## Contribution

It introduces a comprehensive asymptotic analysis of micropolar fluids in rough thin domains, identifying three regimes and deriving corresponding generalized Reynolds equations considering microstructure effects.

## Key findings

- Identification of three distinct flow regimes based on boundary and thickness scales.
- Derivation of generalized Reynolds equations incorporating microstructure effects.
- Establishment of asymptotic behavior of micropolar fluids in complex geometries.

## Abstract

We study the asymptotic behavior of micropolar fluid flows in a thin domain of thickness $\eta_\varepsilon$ with a periodic oscillating boundary with wavelength $\varepsilon$. We consider the limit when $\varepsilon$ tends to zero and, depending on the limit of the ratio of $\eta_\varepsilon/\varepsilon$, we prove the existence of three different regimes. In each regime, we derive a generalized Reynolds equation taking into account the microstructure of the roughness.