Mean first-passage time of surface-mediated diffusion in spherical domains

TL;DR

This paper provides an exact analytical method to compute the mean first-passage time for molecules diffusing on a spherical surface with bulk diffusion, revealing how reaction times can be optimized by adjusting desorption rates.

Contribution

It introduces an exact integral equation approach for calculating mean first-passage times in surface-mediated diffusion on spheres, including validated approximation schemes.

Findings

Mean reaction time can be minimized by tuning desorption rates.

Analytical solutions for 2D and 3D spherical domains.

Validated approximation schemes for practical calculations.

Abstract

We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. The presented approach is based on an integral equation which can be solved analytically. Numerically validated approximation schemes, which provide more tractable expressions of the mean first-passage time are also proposed. In the framework of this minimal model of surface-mediated reactions, we show analytically that the mean reaction time can be minimized as a function of the desorption rate from the surface.