Mathematical modelling and numerical simulation of a non-Newtonian viscous flow through a thin filter

We consider non-Newtonian flows, like polymer in fusion or in solution, pushed through a thin periodic filter with period and thickness epsilon << 1. Starting from the Stokes system with a nonlinear viscosity obeying Carreau's law ( with a high rate viscosity or without it), we study the asymptotic behavior of the flow as epsilon --> 0. We obtain the global convergence of the pressure in the whole domain and not separately in the upper part and in the lower part. Numerical tests for various fluids and various filter shapes are comparing results given by the homogenized model with the ones given by the microscopic Carreau-Stokes model.