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.