We propose a unified physical framework for transport in variably saturated
porous media. This approach allows fluid flow and solute migration to be
treated as ensemble averages of fluid and solute particles, respectively. We
consider the cases of homogeneous and heterogeneous porous materials. Within a
fractal mobile-immobile (MIM) continuous time random walk framework, the
heterogeneity will be characterized by algebraically decaying particle
retention-times. We derive the corresponding (nonlinear) continuum limit
partial differential equations and we compare their solutions to Monte Carlo
simulation results. The proposed methodology is fairly general and can be used
to track fluid and solutes particles trajectories, for a variety of initial and
boundary conditions.Comment: 12 pages, 9 figure