Scaling form of concentration profiles in a subdiffusive membrane system

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.