Modeling of a micropolar thin film flow with rapidly varying thickness and non-standard boundary conditions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914205417865216 |
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| author | Anguiano, María Suárez-Grau, Francisco J. |
| author_facet | Anguiano, María Suárez-Grau, Francisco J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15202 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modeling of a micropolar thin film flow with rapidly varying thickness and non-standard boundary conditions Anguiano, María Suárez-Grau, Francisco J. Analysis of PDEs 35B27, 35Q35, 76A05, 76M50, 76A20 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. |
| title | Modeling of a micropolar thin film flow with rapidly varying thickness and non-standard boundary conditions |
| topic | Analysis of PDEs 35B27, 35Q35, 76A05, 76M50, 76A20 |
| url | https://arxiv.org/abs/2512.15202 |