A fast algorithm for treating dielectric discontinuities in charged spherical colloids.

Electrostatic interactions between multiple colloids in ionic fluids are attracting much attention in studies of biological and soft matter systems. The evaluation of the polarization surface charges due to the spherical dielectric discontinuities poses a challenging problem to highly efficient computer simulations. In this paper, we propose a new method for fast calculating the electric field of spaced spheres using the multiple reflection expansion. The method uses a technique of recursive reflections among the spherical interfaces based on a formula of the multiple image representation, resulting in a simple, accurate and close-form expression of the surface polarization charges. Numerical calculations of the electric potential energies of charged spheres demonstrate the method is highly accurate with small number of reflections, and thus attractive for the use in practical simulations of related problems such as colloid suspension and macromolecular interactions.