General flux to a trap in one and three dimensions

TL;DR

This paper analytically solves the flux to a spherical trap for diffusing particles with discrete jumps in one and three dimensions, confirming the effective trap radius reduction described by the Milne extrapolation length.

Contribution

It provides a general solution for flux to a trap with discrete jumps, validating the Smoluchowski-like approximation involving the Milne extrapolation length.

Findings

The effective trap radius is reduced by an amount proportional to the jump length.

The solution applies to both one and three-dimensional diffusion.

The results confirm the validity of the Smoluchowski approximation with the Milne length.

Abstract

The problem of the flux to a spherical trap in one and three dimensions, for diffusing particles undergoing discrete-time jumps with a given radial probability distribution, is solved in general, verifying the Smoluchowski-like solution in which the effective trap radius is reduced by an amount proportional to the jump length. This reduction in the effective trap radius corresponds to the Milne extrapolation length.