Dynamic Interactions of Two Electrical Double Layers

Abstract

The unsteady-state electrical potential and the concentrations of ions between two identical, negatively-charged particles immersed in an a:b electrolyte solution are investigated. In particular, the effects of ionic strength,I, the geometric mean of the diffusivities of counterionsDconand coionsDco,D, the separation distance between two particles,H, and the surface charge density, σ0, on these distributions are examined. We conclude that under the following conditions a system needs a longer time for ions to reach equilibrium distributions: (a) smallI, (b) smallD, (c) largeH, and (d) large σ0. The rate of approach of two particles is faster if both surfaces are maintained at constant potential than if both surfaces are at constant charge density. The dynamic behavior of the relaxation of ions in the double layers has the effect of retarding the motion of particles. The deviation in the contact time between two particles predicted by an equilibrium model, which assumes that the distributions of ions in a double layer reach the Boltzmann distribution instantly, from that estimated by the corresponding dynamic model is on the order of 10%.