Abstract
We review and discuss diffusion and hydrodynamic dispersion in a heterogeneous porous medium. Two types of heterogeneities are considered. One is percolation disorder in which a fraction of the pores do not allow transport to take place at all. In the other type, the permeabilities of various regions of the pore space are fractally distributed with long-range correlations. Both systems give rise to unusual transport in which the mean square displacement <r 2(t)> of a particle grows nonlinearly with time. Depending on the heterogeneities and the mechanism of diffusion and disperison, we may havefractal transport in which <r 2> growsslower than linearly with time, orsuperdiffusive transport in which <r 2> growsfaster than linearly with time. We show that percolation models can give rise to both types of transport with scale-dependent transport coefficients such as diffusivity and dispersion coefficients, which are consistent with many experimental observations.
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