Subdiffusive model of substance releasing from a thick membrane

TL;DR

This paper develops a theoretical and experimental framework for modeling subdiffusive substance release from thick membranes, providing analytical solutions and estimating subdiffusion coefficients in hydrogels.

Contribution

It introduces an analytical model for subdiffusive release from membranes and validates it with experimental data, estimating key parameters.

Findings

Analytical formulas accurately describe concentration profiles.

Experimental data fit yields subdiffusion coefficient for PEG 2000 in agarose.

Model captures the time evolution of substance release.

Abstract

We study both theoretically and experimentally the process of subdiffusive substance releasing from a thick membrane. The theoretical model uses the subdiffusion equation with fractional time derivative and specific boundary conditions at the membrane surfaces. Using a special \textit{ansatz} we find analytical formulas describing the time evolution of concentration profiles and an amount of the substance remains in the membrane. Fitting the theoretical functions to the experimental results, we estimate the subdiffusion coefficient of polyethylene glycol 2000 in agarose hydrogel.