Mean joint residence time of two Brownian particles in a sphere

TL;DR

This paper derives the mean joint residence time of two Brownian particles within a sphere, considering various initial conditions and diffusion coefficients, with implications for bimolecular reaction kinetics.

Contribution

It provides a general analytical calculation of joint residence time for two Brownian particles, extending understanding of diffusion-controlled reactions.

Findings

Residence time depends on diffusion coefficients

Results applicable to catalytic reaction kinetics

Provides formulas for various initial conditions

Abstract

We calculate the mean joint residence time of two Brownian particles in a sphere, for very general initial conditions. In particular, we focus on the dependence of this residence time as a function of the diffusion coefficients of the two particles. Our results can be useful for describing kinetics of bimolecular diffusion controlled reactions activated by catalytic sites.