ABSTRACT
We investigate the filtration law of an incompressible viscous Newtonian fluid through a rigid non-inertial porous medium or when submitted to a magnetic field. The filtration law is obtained by upscaling the flow at the pore scale. We use the method of multiple scale expansions which rigorously gives the macroscopic behaviour without any prerequisite on the form of the macroscopic equations. The filtration laws are shown to resemble Darcy’s laws, but with a permeability tensor which depends on the angular velocity of the porous matrix or on the magnetic field, respectively. In both cases Hall – Onsager relations are verified.
