Analytical solutions of nonlinear Poisson–Boltzmann equation for colloidal particles immersed in a general electrolyte solution by homotopy perturbation technique

Abstract

We present the first application of the homotopy perturbation technique to analytically solve the nonlinear PB equation describing spherical and planar colloidal particles immersed in an arbitrary valence and mixed electrolyte solution. Analytical expressions for electrical potential distribution and surface charge density/surface potential relationship are acquired. Our analytical solutions contrast sharply with previous ones by two striking features: (1) the present ones apply irrespective of the types of electrolyte considered or whether single electrolyte or mixed electrolytes are being considered, and (2) the valid application scopes of present solutions are in small κa domain and thus are complementary with those of previous ones. Our expressions are considered to provide the constituents whose combinations with previous solutions may end up global valid expressions.