Modeling of a micropolar thin film flow with rapidly varying thickness and non-standard boundary conditions

TL;DR

This paper derives a generalized Reynolds equation for micropolar fluid flow in a thin, rough domain, revealing how roughness influences pressure, velocity, and microrotation under specific boundary conditions.

Contribution

It introduces a rigorous derivation of a generalized Reynolds equation accounting for roughness effects in micropolar thin film flows with non-standard boundary conditions.

Findings

Derived a generalized Reynolds equation incorporating roughness effects.

Provided explicit expressions for average velocity and microrotation.

Analyzed the asymptotic behavior of micropolar fluids in thin, rough domains.

Abstract

In this paper, we study the asymptotic behavior of the micropolar fluid flow through a thin domain assuming zero Dirichlet boundary condition on the top boundary, which is rapidly oscillating, and non-standard boundary conditions on the flat bottom. Assuming ``Reynolds roughness regime", in which the thickness of the domain is very small compared to the wavelenth of the roughness (i.e. a very slight roughness), we rigorously derive a generalized Reynolds equation for pressure clearly showing the roughness-induced effects. Moreover, we give expressions for the average velocity and microrotation.