Modeling of a non-Newtonian thin film passing a thin porous medium
This theoretical study deals with asymptotic behavior of a coupling between a thin film of fluid and an adjacent thin porous medium. We assume that the size of the microstructure of the porous medium is given by a small parameter 0 < ε ≪ 1, the thickness of the thin porous medium is defined by a...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/177373 |
| Acceso en línea: | https://hdl.handle.net/11441/177373 https://doi.org/10.1051/mmnp/2025020 |
| Access Level: | acceso abierto |
| Palabra clave: | Homogenization non-Newtonian fluid thin film thin porous medium Reynolds equation |
| Sumario: | This theoretical study deals with asymptotic behavior of a coupling between a thin film of fluid and an adjacent thin porous medium. We assume that the size of the microstructure of the porous medium is given by a small parameter 0 < ε ≪ 1, the thickness of the thin porous medium is defined by a parameter 0 < hε ≪ 1, and the thickness of the thin film is defined by a small parameter 0 < ηε ≪ 1, where hε and ηε are devoted to tend to zero when ε → 0. In this paper, we consider the case of a non-Newtonian fluid governed by the incompressible Stokes equations with power law viscosity of flow index r ∈ (1, +∞), and we prove that there exists a critical regime, which depends on r, between ε, ηε and hε. More precisely, in this critical regime given by hε ≈ ηε^{(2r-1)/r-1} ε^{-r/(r−1)}, we prove that the effective flow when ε → 0 is described by a 1D Darcy law coupled with a 1D Reynolds law. |
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