Theoretical derivation of Darcy's law for fluid flow in thin porous media
In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated $3D$ domain confined between two parallel plates. The description of the domain includes two small parameters: $\varepsilon$ representing the distance b...
| Autor: | |
|---|---|
| Formato: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/162350 |
| Acesso em linha: | https://hdl.handle.net/11441/162350 https://doi.org/10.1002/mana.202000184 |
| Access Level: | acceso abierto |
| Palavra-chave: | Homogenization Stokes equations Darcy's law thin porous media thin film fluids |
| Resumo: | In this paper we study stationary incompressible Newtonian fluid flow in a thin porous media. The media under consideration is a bounded perforated $3D$ domain confined between two parallel plates. The description of the domain includes two small parameters: $\varepsilon$ representing the distance between pates and $a_\ep$ connected to the microstructure of the domain such that $a_\ep\ll \ep$. We consider the classical setting of perforated media, i.e. $a_\ep$-periodically distributed solid (not connected) obstacles of size $a_\varepsilon$. The goal of this paper is to introduce a version of the unfolding method, depending on both parameters $\varepsilon$ and $a_\varepsilon$, and then to derive the corresponding 2D Darcy's law. |
|---|