Perturbation Expansions for the Potential of a Small Radius, Charged Dielectric Sphere in 1-1 Electrolytes

Abstract

Regular and singular perturbation expansions are given for the electrostatic potential of a uniformly charged dielectric sphere in a 1-1 electrolyte for distances the order of the sphere radius and for much larger distances the order of a Debye length. Since the regular perturbation expansion valid near the sphere diverges as R and the comparable singular perturbation expansion as In R, we match the regular perturbation expansions at small and large distances. The matched perturbation expansions hold for potentials somewhat greater than 25 mv and are a nonlinear generalization of the expansion of Gronwall et al.