ment in the computing facilities makes numerical solution of
The unsteady-state electrical potential and the concentrations a complicated problem feasible, and approximate analytical of ions between two identical, negatively-charged particles imsolutions to PBE becomes convenient in the estimation of mersed in an a:b electrolyte solution are investigated. In particuthe thermodynamic properties of an electrical double layer lar, the effects of ionic strength, I , the geometric mean of the . Previous efforts on the relevant problems, however, diffusivities of counterions D con and coions D co , D , the separaalmost always assume that the electrical condition near a tion distance between two particles, H , and the surface charge charged surface is at equilibrium. In particular, the space density, s 0 , on these distributions are examined. We conclude charges are assumed to establish Boltzmann distribution inthat under the following conditions a system needs a longer time for ions to reach equilibrium distributions: ( a ) small I , ( b ) stantaneously, regardless of the variable condition at the small D , ( c ) large H , and ( d ) large s 0 . The rate of approach surface (5, 6). In a study of the stability of a colloidal of two particles is faster if both surfaces are maintained at system, Overbeek (7) pointed out that the relaxation time constant potential than if both surfaces are at constant charge for surface charges (about 10 06 to 10 4 s) can be comparable density. The dynamic behavior of the relaxation of ions in the to the time scale for Brownian coagulation (about 10 07 to double layers has the effect of retarding the motion of particles. 10 05 s). In other words, aggregation of colloidal particles The deviation in the contact time between two particles premay occur before the electrical condition near a surface dicted by an equilibrium model, which assumes that the distrireaches equilibrium. Kijlstra and van Leeuwen (5) conbutions of ions in a double layer reach the Boltzmann distribucluded that the temporal variation in the surface charge dention instantly, from that estimated by the corresponding dysity has a significant effect on the stability ratio of a colloidal namic model is on the order of 10%.