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arXiv · 1704.02662

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

Tadeusz Kosztołowicz·Sławomir Wąsik·Katarzyna D. Lewandowska
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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.

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Tadeusz Kosztołowicz, Sławomir Wąsik, Katarzyna D. Lewandowska. 2017-04-09. How to determine a boundary condition at a thin membrane for diffusion from experimental data. https://doi.org/10.1103/physreve.96.010101

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