The Solution of Some Potential Problems in the Theory of Electrolytes

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Abstract
The Poisson-Boltzmann equation for the potential in an electrolyte is solved for the following cases: (a) Electrolyte bordered by a uniformly charged plane; (b) two semi-infinite electrolytes of different composition separated by a plane boundary; (c) electrolyte confined between parallel charged planes; (d) uniformly charged cylinder immersed in an electrolyte; (e) electrolyte in a cylinder with charged walls; (f) electrolyte between two concentric charged cylinders; (g) solid charged sphere in an electrolyte; and (h) sphere of electrolyte immersed in another electrolyte extending to infinity, and of different composition. All the problems discussed are of interest in the theory of colloids or emulsions. In each case a series solution in powers of a parameter involving the charge or charges on relevant surfaces is given. The first term of each series is the solution of the Poisson-Boltzmann equation when the so-called Debye-Hückel approximation is applied to the equation. The additional terms are built up from the first by an iterative method. No restrictions on the compositions of the electrolytes are required.

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