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arXiv · 2512.15202

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

María Anguiano·Francisco J. Suárez-Grau
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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.

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María Anguiano, Francisco J. Suárez-Grau. 2025-12-17. Modeling of a micropolar thin film flow with rapidly varying thickness and non-standard boundary conditions. https://doi.org/10.1007/s10473-026-0113-6

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