Scaling form of concentration profiles in a subdiffusive membrane system

TL;DR

This paper derives a universal scaling form for concentration profiles in subdiffusive membrane systems and provides a relation to determine subdiffusion parameters from experimental data.

Contribution

It introduces a general scaling form for concentration profiles in subdiffusive systems with membranes and relates the scaling parameters to subdiffusion properties.

Findings

Scaling form $C o t^0; F(\u03b4/t^1)$ derived

Relation between subdiffusion parameters and scaling parameters established

Method to extract subdiffusion parameters from experiments proposed

Abstract

We show that the concentration profiles in the subdiffusive system with a membrane, which separates a homogeneous solution from a pure solvent at an initial moment, has a general scaling form in the long time limit $C\sim t^\lambda F(\delta/t^{\rho})$, where $\delta$ is a distance from the membrane surface. There is also derived the relation involving the subdiffusion parameters of the medium and the membrane with the scaling parameters $\lambda$ and $\rho$, which are measured experimentally. The relation allows one to extract the subdiffusion parameters of the system from experimental data.