Effective medium equation for fractional Cattaneo's diffusion and heterogeneous reaction in disordered porous media

This paper focuses on the reaction-diffusion problem in a disordered porous medium. The objective is to obtain an effective medium description of the concentration dynamics having a fractional Cattaneo's law equation as the flux constitutive equation. The methodology is based on a volume averaging procedure, and simplifications are made on the basis of an order of magnitude analysis with physical grounds. Sufficient conditions to obtain pseudo-homogeneous models are given. The closure problem associated with the effective diffusivity definition results to be the same that the one corresponding to Fickian diffusion. (c) 2006 Elsevier B.V. All rights reserved.