Transport phenomena in sharply contrasting media with a diffusion   barrier
  Using the advection-diffusion equation, we analytically study contaminant transport in a sharply contrasting medium with a diffusion barrier due to localization of a contaminant source in a low-permeability medium. Anomalous diffusion behavior and crossover between different transport regimes are observed. The diffusion barrier results in exponential attenuation of the source power, retardation of the contaminant plume growth, and modification of the concentration distribution at large distances. 
O. A. Dvoretskaya and P. S. Kondratenko
cond-mat.other cond-mat.soft