Electrolyte friction and the Langevin equation for charged Brownian particles

Abstract

A Langevin equation for a charged spherical Brownian particle, diffusing in an ionic solution, is derived as a contraction of a description based on the fluctuating diffusion equation for the local concentrations of the electrolyte ions of the supporting solution. A fluctuation-dissipation relation is demonstrated between the electrostatic friction and its corresponding fluctuating force. Expressions are derived for the electrolyte contribution to the friction coefficient in terms of the equilibrium interionic correlation functions. The results previously found by Schurr are shown to follow in the Debye-H\"uckel limit.