Solution of the Non-Linear Poisson Boltzmann Theory for the General Case of Dissimilar Double Layers

Abstract

Calculation of the surface potentials, surface charges or electrostatic pressure for interacting colloidal particles is exceedingly important in mineral processing, environmental engineering, ceramic sciences, etc. Such calculations require solving the non-linear Poisson-Boltzmann theory at each plate separation. Though approximate analytical solutions of this theory are available for simplified cases, a general, but compact analytical solution is yet to be developed. A solution with no restrictions on surface potentials or charges is developed in this paper. The expressions developed are straightforward and require as input only the surface potentials at infinite separations.