How to Measure Subdiffusion Parameters

TL;DR

This paper introduces an experimental method to accurately measure subdiffusion parameters using a membrane system and applies it to glucose and sucrose diffusion in gel solvents, utilizing an analytic solution of the fractional subdiffusion equation.

Contribution

The paper presents a novel experimental approach combined with an analytic solution to determine subdiffusion parameters in a membrane system.

Findings

Successfully measured subdiffusion parameters for glucose and sucrose

Validated the method with experimental data and analytic solutions

Provided precise estimates of $\alpha$ and $D_\alpha$

Abstract

We propose a method to measure the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_{\alpha}$ which are defined by means of the relation $<x^2> =\frac{2D_\alpha} {\Gamma(1+\alpha)} t^\alpha$ 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 $\alpha$ and $D_{\alpha}$, using a fully analytic solution of the fractional subdiffusion equation.