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...

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Detalles Bibliográficos
Autor: Suárez Grau, Francisco Javier
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2022
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/162350
Acceso en línea:https://hdl.handle.net/11441/162350
https://doi.org/10.1002/mana.202000184
Access Level:acceso abierto
Palabra clave:Homogenization
Stokes equations
Darcy's law
thin porous media
thin film fluids
Descripción
Sumario: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.