Exact mean exit time for surface-mediated diffusion

TL;DR

This paper derives an exact analytical expression for the mean exit time of particles diffusing on a surface and in the bulk within a sphere, revealing how to optimize this time by adjusting the desorption rate.

Contribution

It provides the first exact integral equation solution for mean exit time in surface-mediated diffusion, enabling optimization of desorption rates.

Findings

Mean exit time can be optimized by tuning desorption rate.

Exact integral expression for mean exit time derived.

Optimization criteria are analytically determined.

Abstract

We present an exact expression for the mean exit time through the cap of a confining sphere for particles alternating phases of surface and of bulk diffusion. The present approach is based on an integral equation which can be solved analytically. In contrast to the statement of Berezhkovskii and Barzykin [J. Chem. Phys. 136, 54115 (2012)], we show that the mean exit time can be optimized with respect to the desorption rate, under analytically determined criteria.