Method of homogenization applied to dispersion in porous media

The theory of homogenization which is a rigorous method of averaging by multiple scale expansions, is applied here to the transport of a solute in a porous medium. The main assumption is that the matrix has a periodic pore structure on the local scale. Starting from the pores with the Navier-Stokes equations for the fluid motion and the usual convective-diffusion equation for the solute, we give an alternative derivation of the three-dimensional macroscale dispersion tensor for solute concentration. The original result was first found by Brenner by extending Brownian motion theory. The method of homogenization is an expedient approach based on conventional continuum equations and the technique of multiple-scale expansions, and can be extended to more complex media involving three or more contrasting scales with periodicity in every but the largest scale.