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Analytic expressions for electrical energy and electrical force of two spheres.

Analytical expressions for the electrical force and the electrical energy of two spheres immersed in a symmetric electrolyte solution are derived under conditions of constant surface potential and constant surface charge. Previous analysis under Debye-Huckel condition (linear case) is extended to the corresponding nonlinear case; because the level of the surface potential is arbitrary the results obtained have much wider applications. In general, the performance of the analytical formulas derived is satisfactory, and better than that of the available results in literature. For the case of constant surface potential, the analytic formulas obtained are most accurate for large particles, and for the case of constant surface charge, they are most accurate for small particles.