Narrow-escape times for diffusion in microdomains with a particle-surface affinity: Mean-field results

TL;DR

This paper derives a mean-field analytical expression for the average escape time of a diffusing particle in a sphere with a small escape window, considering bulk and surface diffusion with weak surface affinity.

Contribution

It introduces a mean-field model to analytically compute escape times accounting for particle-surface interactions and diffusion dynamics.

Findings

Derived an explicit formula for escape time as a function of diffusion coefficients.

Quantified the impact of surface affinity on escape times.

Provided insights into particle behavior in confined microdomains.

Abstract

We analyze the mean time t_{app} that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches the surface of the domain where it becomes weakly adsorbed, and then wanders diffusively along the boundary for a random time until it desorbs back to the bulk, and etc. Using a mean-field approximation, we define t_{app} analytically as a function of the bulk and surface diffusion coefficients, the mean time it spends in the bulk between two consecutive arrivals to the surface and the mean time it wanders on the surface within a single round of the surface diffusion.