Double-layer interactions of unequal spheres. Part 1.—The effect of electrostatic attraction with particles of like sign of potential

Abstract

The Poisson–Boltzmann equation for two unequal spheres with fixed surface potentials is analysed. When both potentials are of the same sign but of different magnitude it is shown that the electrostatic energy decreases owing to the fact that a portion of the surfaces may be attractive even though the rest of the surfaces may be repulsive. This effect depends on the separation, as well as on the difference in the potentials and the sizes of the two spheres.