Anomalous Infiltration

TL;DR

This paper investigates anomalous particle infiltration across biased interfaces using continuous time random walk and Levy walk models, revealing paradoxical flows and drifts in subdiffusive and superdiffusive systems.

Contribution

It introduces a detailed analysis of anomalous infiltration phenomena, including paradoxical flows and the effects of coupling subdiffusive and superdiffusive systems.

Findings

Subdiffusion can cause a net drift opposite to the flow direction.

Symmetric interfaces can exhibit particle flow with zero net drift.

Net drift always directed towards superdiffusive material.

Abstract

Infiltration of anomalously diffusing particles from one material to another through a biased interface is studied using continuous time random walk and Levy 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. 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 particles 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 Levy walks, which are needed for the calculation of anomalous infiltration