Filtration Law for Polymer Flow Through Porous Media

In this paper we study the filtration laws for the polymeric flow in a porous medium. We use the quasi-Newtonian models with share dependent viscosity obeying the power-law and the Carreau’s law. Using the method of homogenization in [5] the coupled micro-macro homogenized law, governing the quasi-newtonian flow in a periodic model of a porous medium, was found. We decouple that law separating the micro from the macro scale. We write the macroscopic filtration law in the form of non-linear Darcy’s law and we prove that the obtained law is well posed. We give the analytical as well as the numerical study of our model.