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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • María Anguiano,
  • Francisco Javier Suárez-Grau

摘要

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.