How to measure subdiffusion parameters -: art. no. 170602

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)] = 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.