Communications in Mathematical Sciences

Volume 16 (2018)

Number 1

Analysis of the effects of a fissure for a non-Newtonian fluid flow in a porous medium

Pages: 273 – 292

DOI: https://dx.doi.org/10.4310/CMS.2018.v16.n1.a13

Authors

María Anguiano (Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Spain)

Francisco Javier Suárez-Grau (Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Spain)

Abstract

We study the solution of a non-Newtonian flow in a porous medium which characteristic size of the pores $\varepsilon$ and containing a fissure of width $\eta_\varepsilon$. The flow is described by the incompressible Stokes system with a nonlinear viscosity, being a power of the shear rate (power law) of flow index $1 \lt r \lt + \infty$. We consider the limit when size of the pores tends to zero and we obtain different models depending on the magnitude $\eta_\varepsilon$ with respect to $\varepsilon$.

Keywords

non-Newtonian flow, Stokes equation, Darcy’s law, porous medium, fissure

2010 Mathematics Subject Classification

35B27, 76M50

Full Text (PDF format)

María Anguiano has been supported by Junta de Andalucía (Spain), Proyecto de Excelencia P12-FQM-2466. Francisco Javier Suárez-Grau has been supported by Ministerio de Economía y Competitividad (Spain), Proyecto Excelencia MTM2014-53309-P.

Received 23 April 2017

Accepted 22 November 2017

Published 29 March 2018