How to determine a boundary condition at a thin membrane for diffusion from experimental data

Abstract

We present a new method of deriving a boundary condition at a thin membrane for diffusion from experimental data. Based on experimental results obtained for normal diffusion of ethanol in water, we show that the derived boundary condition at a membrane contains a term with the Riemann--Liouville fractional time derivative of the $1/2$ order. Such a form of the boundary condition shows that a transfer of particles through a thin membrane is a `long memory process'. Presented method is an example that an important part of mathematical model of physical process may be derived directly from experimental data.

4 pages, 4 figures

References in corpus (1)

• Random walk model of subdiffusion in a system with a thin membrane

Cited by in corpus (5)

• Model of anomalous diffusion--absorption process in a system consisting of two different media separated by a thin membrane
• Diffusion through a network of compartments separated by partially-transmitting boundaries
• Subdiffusion equation with Caputo fractional derivative with respect to another function in modelling diffusion in a complex system consisting of matrix and channels
• Boundary conditions at a thin membrane for normal diffusion equation which generate subdiffusion
• Boundary conditions at a thin membrane that generate non--Markovian normal diffusion