Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure

We consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ε and containing a thin fissure of width ηε. The viscosity is supposed to obey the power law with flow index 5/3 ≤ q ≤ 2. The limit when size of the pores tends to zero gi...

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Detalhes bibliográficos
Autor: Anguiano Moreno, María
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/157559
Acesso em linha:https://hdl.handle.net/11441/157559
https://doi.org/10.1017/S0956792518000049
Access Level:acceso abierto
Palavra-chave:Non-Newtonian flow
Non-stationary Stokes equation
Darcy’s law
porous medium
fissure.
Descrição
Resumo:We consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ε and containing a thin fissure of width ηε. The viscosity is supposed to obey the power law with flow index 5/3 ≤ q ≤ 2. The limit when size of the pores tends to zero gives the homogenized behavior of the flow. We obtain three different models depending on the magnitude ηε with respect to ε: if ηε ≪ ε^{q/(2q−1)} the homogenized fluid flow is governed by a time-dependent nonlinear Darcy law, while if ηε ≫ ε^{q/(2q−1)} is governed by a time-dependent nonlinear Reynolds problem. In the critical case, ηε ≈ ε^{q/(2q−1)} , the flow is described by a time-dependent nonlinear Darcy law coupled with a time-dependent nonlinear Reynolds problem.