A nonlinear random walk approach to concentration-dependent contaminant   transport in porous media
  We propose a nonlinear random walk model to describe the dynamics of dense contaminant plumes in porous media. A coupling between concentration and velocity fields is found, so that transport displays non-Fickian features. The qualitative behavior of the pollutant spatial profiles and moments is explored with the help of Monte Carlo simulation, within a Continuous Time Random Walk approach. Model outcomes are then compared with experimental measurements of variable-density contaminant transport in homogeneous and saturated vertical columns. 
Andrea Zoia, Christelle Latrille, Alain Cartalade