Anomalous transport in fractal media with randomly inhomogeneous diffusion barrier

We investigate a contaminant transport in fractal media with randomly inhomogeneous diffusion barrier. The diffusion barrier is a low permeable matrix with extremely rare high permeability pathways (punctures). At times, less than a characteristic matrix diffusion time, the problem is effectively barrier-free with an effective source acting during the time t<<teff. The punctures result in a precursor contaminant concentration at short times and additional stage of the asymptotic concentration distribution at long times. If the size of the source surface area is large enough, the barrier can be considered as statistical homogeneous medium; otherwise, strong fluctuations occur.