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Electrostatic polarization is important in many nano-/micro-scale physicalsystems such as colloidal suspensions, biopolymers, and nanomaterials assembly.The calculation of polarization potential requires an efficient algorithm forsolving 3D Poisson's equation. We have developed a useful image charge methodto rapid evaluation of the Green's function of the Poisson's equation in thepresence of spherical dielectric discontinuities. This paper presents anextensive study of this method by giving an convergence analysis and developinga coarse-graining algorithm. The use of the coarse graining could reduce thenumber of image charges to around a dozen, by 1-2 orders of magnitude. We usethe algorithm to investigate the interaction force between likely chargedspheres in different dielectric environments. We find the size and chargeasymmetry leads to an attraction between like charges, in agreement withexisting results. Furthermore, we study three-body interaction and find in thepresence of an external interface, the interaction force depends on thecurvature of the interface, and behavior a non-monotonic electrostatic force.

Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction