Anomalous transport regimes and asymptotic concentration distributions in the presence of advection and diffusion on a comb structure

TL;DR

This paper investigates various anomalous transport regimes of impurity particles on a comb structure with advection, revealing seven distinct regimes and complex concentration tail structures, including the unique quasidiffusion regime.

Contribution

It identifies and characterizes seven different transport regimes on a comb structure with finite teeth, highlighting the unique quasidiffusion regime and its properties.

Findings

Seven transport regimes identified, including quasidiffusion.

Quasidiffusion exhibits linear mean squared displacement growth.

Concentration tails have a cascade structure.

Abstract

We study a transport of impurity particles on a comb structure in the presence of advection. The main body concentration and asymptotic concentration distributions are obtained. Seven different transport regimes occur on the comb structure with finite teeth: classical diffusion, advection, quasidiffusion, subdiffusion, slow classical diffusion and two kinds of slow advection. Quasidiffusion deserves special attention. It is characterized by a linear growth of the mean squared displacement. However, quasidiffusion is an anomalous transport regime. We established that a change of transport regimes in time leads to a change of regimes in the space. Concentration tails have a cascade structure, namely consisting of several parts.