How to Measure Subdiffusion Parameters

Abstract

We propose a method to measure the subdiffusion parameter $α$ and subdiffusion coefficient $D_α$ which are defined by means of the relation $<x^2> =\frac{2D_α} {Γ(1+α)} t^α$ where $<x^2>$ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. We experimentally study a diffusion of glucose and sucrose in a gel solvent, and we precisely determine the parameters $α$ and $D_α$, using a fully analytic solution of the fractional subdiffusion equation.