Measuring subdiffusion parameters

We propose a method to extract from experimental data the subdiffusion parameter alpha and subdiffusion coefficient D(alpha) which are defined by means of the relation x(2) = [2 D(alpha) /Gamma (1+alpha) ] t(alpha) where x(2) denotes the 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. Using such a system, we experimentally study the diffusion of glucose and sucrose in a gel solvent. We find a fully analytic solution of the fractional subdiffusion equation with the initial and boundary conditions representing the system under study. Confronting the experimental data with the derived formulas, we show the subdiffusive character of sugar transport in a gel solvent. We precisely determine the parameter alpha , which is smaller than 1, and the subdiffusion coefficient D(alpha) .