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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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/157559 |
| Acceso en línea: | https://hdl.handle.net/11441/157559 https://doi.org/10.1017/S0956792518000049 |
| Access Level: | acceso abierto |
| Palabra clave: | Non-Newtonian flow Non-stationary Stokes equation Darcy’s law porous medium fissure. |
| Sumario: | 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. |
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