Paradoxes of Subdiffusive Infiltration in Disordered Systems

TL;DR

This paper investigates paradoxical infiltration behaviors in disordered systems with anomalous diffusion, revealing counterintuitive drift phenomena and providing a unified model based on continuous time random walks.

Contribution

It introduces a comprehensive model for anomalous infiltration, demonstrating that paradoxical drift behaviors are a general feature of disordered systems.

Findings

Diffusion can cause net drift opposite to flow direction.

Flow can occur without any net drift.

Similar behaviors are observed in the quenched trap model.

Abstract

Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead to an averaged net drift <x> from one material to another even if all particles eventually flow in the opposite direction, or may lead to a flow without drift. Starting with an underlying continuous time random walk model we solve diffusion equations describing this problem. Similar drift against flow is found in the quenched trap model. We argue that such a behavior is a general feature of diffusion in disordered systems.