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

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 wavelength 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.