Mean first passage times of ions between charged surfaces

Abstract

Analytic expressions for the mean first passage times of ions diffusing in the electric double layer between two planar charged surfaces have been derived. The theory is based on the Smoluchowski–Poisson–Boltzmann model in which the diffusing ion is assumed to move in the potential field given by the non-linear Poisson–Boltzmann equation. Numerical results for the mean first passage times of co-ions and counter-ions calculated under the non-linear Poisson–Boltzmann model are given for a range of surface separations, surface potentials and ionic concentrations. Two simple analytic methods for calculating the mean first passage times are also presented.