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

Abstract

We study the solution of a non-Newtonian flow in a porous medium which characteristic size of the pores ε and containing a fissure of width ηε. 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 < r < +∞. We consider the limit when size of the pores tends to zero and we obtain different models depending on the magnitude ηε with respect to ε.