Time-dependent diffusion in one-dimensional disordered media decorated by permeable membranes: Theoretical findings backed by simulations and a new disorder class

TL;DR

This paper studies how fluid diffusion is affected by permeable membranes, using theory and simulations to predict diffusion behavior over time.

Contribution

A new disorder class is introduced, generalizing hyperuniform and short-range disorders in membrane arrangements.

Findings

Theoretical predictions of long-time diffusivity match numerical simulations closely.

A new disorder family was introduced to model membrane arrangements.

The methods provide a new approach for studying time-dependent diffusion processes.

Abstract

As the diffusion of fluids is hindered by semipermeable membranes, the long-time behavior of the diffusion coefficient is influenced by the arrangement of the membranes. We develop methods that predict this long-time instantaneous diffusivity from bulk diffusivity, the membranes' locations, and their permeabilities. We studied this problem theoretically and expressed the instantaneous diffusivity analytically as an infinite sum. An independent numerical scheme was employed. Several types of disorder in the membranes' positions were considered including a new disorder family that generalizes hyperuniform and short-range disorders. Our theoretical and numerical findings are in excellent agreement. Our methods provide an alternative means for studying time-dependent diffusion processes.

Figures