Anomalous infiltration

Infiltration of anomalously diffusing particles from one material to another through a biased interface is studied using continuous time random walk and Lévy walk approaches. Subdiffusion in both systems may lead to a net drift from one material to another (e.g. 〈x(t)〉 > 0) even if particles eventually flow in the opposite direction (e.g.the number of particles in x > 0 approaches zero). A weaker paradox is found for a symmetric interface: a flow of particles is observed while the net drift is zero. For a subdiffusive sample coupled to a superdiffusive system we calculate the average occupation fractions and the scaling of the particle distribution. We find a net drift in this system, which is always directed to the superdiffusive material, while the particles flow to the material with smaller sub-or superdiffusion exponent. We report the exponents of the first passage times distribution of Lévy walks, which are needed for the calculation of anomalous infiltration.