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

Published online by Cambridge University Press:  05 February 2018

MARÍA ANGUIANO
MARÍA ANGUIANO*
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, P. O. Box 1160, 41080-Sevilla, Spain email: anguiano@us.es
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Abstract

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 $\frac{5}{3}\leq q\leq 2$. The limit when size of the pores tends to zero gives the homogenized behaviour of the flow. We obtain three different models depending on the magnitude ηϵ with respect to ϵ: if ηϵ ≪ $\varepsilon^{q\over 2q-1}$ the homogenized fluid flow is governed by a time-dependent non-linear Darcy law, while if ηϵ ≫ $\varepsilon^{q\over 2q-1}$ is governed by a time-dependent non-linear Reynolds problem. In the critical case, ηϵ ≈ $\varepsilon^{q\over 2q-1}$, the flow is described by a time-dependent non-linear Darcy law coupled with a time-dependent non-linear Reynolds problem.

Keywords

Non-Newtonian flowNon-stationary Stokes equationDarcy–Reynolds equationporous mediumfissure

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Type
Papers
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European Journal of Applied Mathematics , Volume 30 , Issue 2 , April 2019 , pp. 248 - 277
Copyright
Copyright © Cambridge University Press 2018 

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