Acta mathematica scientia,Series B ›› 2026, Vol. 46 ›› Issue (1): 209-242.doi: 10.1007/s10473-026-0113-6

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MODELING OF A MICROPOLAR THIN FILM FLOW WITH RAPIDLY VARYING THICKNESS AND NON-STANDARD BOUNDARY CONDITIONS

María ANGUIANO1, Francisco Javier SUÁREZ-GRAU2,*   

  1. 1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41012-Sevilla, Spain;
    2. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, 41012-Sevilla, Spain
  • Received:2024-09-23 Revised:2024-12-17 Online:2026-01-25 Published:2026-05-22
  • Contact: * Francisco Javier SUÁREZ-GRAU, E-mail: fjsgrau@us.es
  • About author:María ANGUIANO, E-mail: anguiano@us.es

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.

Key words: micropolar fluid, thin-film flow, rapidly oscillating boundary, nonzero boundary conditions, homogenization

CLC Number: 

  • 35B27
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