Non-linear diffusion in porous media

The investigations of solute diffusion in porous medium are commonly carried out for weak concentrations, when the molecular diffusion coefficient D is considered as a concentration-independent constant. In such cases, the homogenization method can be applied to derive the macroscopic equivalent behaviour and the diffusion tensor in the form D-eff = D tau, where tau is the tortuosity tensor introduced by Bear and Bachmat (Bear; 1972). Strong concentrations make D = D(c) concentration-dependent, there fore the problem becomes non-lineal: In this paper the two-scale method is applied to determine the macroscopic equivalent behaviour in the case of strong concentration. It is shown that the macroscopic diffusion is governed by the classical diffusion equation, with D-eff = D(c) tau. Extension of the results to the transient case as well as dispersion is also addressed.