Diffusion through a network of compartments separated by partially-transmitting boundaries

TL;DR

This paper analyzes particle diffusion in compartmentalized environments with partially-transmitting boundaries, revealing how disorder and heterogeneity influence anomalous diffusion and providing a mesoscale analytical framework.

Contribution

It introduces a mesoscale analytical description that captures microscale dynamics and explores the effects of disorder and heterogeneity on anomalous diffusion in compartmentalized systems.

Findings

Disorder in transmittances induces anomalous diffusion.

Spatial heterogeneity can reduce or compensate for subdiffusion.

The mesoscale description matches long-term microscale behavior.

Abstract

We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two relevant spatio-temporal scales that provide alternative descriptions of the dynamics: i) the microscale, in which the particle position is monitored at constant time intervals; and ii) the mesoscale, in which it is monitored only when the particle crosses a boundary between compartments. Both descriptions provide --by construction-- the same long time behavior. The analytical description obtained at the proposed mesoscale allows for a complete characterization of the complex movement at the microscale, thus representing a fruitful approach for this kind of systems. We show that the presence of disorder in the transmittances is a necessary condition to induce anomalous diffusion, whereas the spatial heterogeneity reduces the degree of subdiffusion and, in some cases, can even compensate for the disorder induced by the stochastic transmittance.