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We propose a unified physical framework for transport in variably saturatedporous media. This approach allows fluid flow and solute migration to betreated as ensemble averages of fluid and solute particles, respectively. Weconsider the cases of homogeneous and heterogeneous porous materials. Within afractal mobile-immobile (MIM) continuous time random walk framework, theheterogeneity will be characterized by algebraically decaying particleretention-times. We derive the corresponding (nonlinear) continuum limitpartial differential equations and we compare their solutions to Monte Carlosimulation results. The proposed methodology is fairly general and can be usedto track fluid and solutes particles trajectories, for a variety of initial andboundary conditions.

A continuous time random walk model of transport in variably saturated heterogeneous porous media