Abstract
The superposition formula for the electrical double-layer interaction between two uniformly charged spherical particles immersed in an unbounded electrolyte has been used extensively since its formulation some 50 years ago. However, the corresponding result for two heterogeneously charged spherical particles has to date remained elusive. In this paper, we present such analytical results and also consider the special case of a heterogeneously charged spherical particle interacting with a uniformly charged plate. In the sphere–plate case we suggest a simple modification to the superposition result, based on the incorporation of image effects, that can dramatically improve its regime of validity. We assess the validity and accuracy of the superposition formulae by comparison with results of a rigorous boundary element calculation of the electrostatic interaction.
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