Theory is developed to address a significant problem of how two charged dielectric particles interact in the presence of a polarizable medium that is a dilute solution of a strong electrolyte. The electrostatic force is defined by characteristic parameters for the interacting particles (charge, radius, and dielectric constant) and for the medium (permittivity and Debye length), and is expressed in the form of a converging infinite series. The limiting case of weak screening and large inter-particle separation is considered, which corresponds to small (macro)ions that carry constant charge. The theory yields a solution in the limit of monopole and dipole terms that agrees exactly with existing analytical expressions, which are generally used to describe ion-ion and ion-molecular interactions in a medium. Results from the theory are compared with DLVO theory and with experimental measurements for the electrostatic force between two PMMA particles contained in a nonpolar solvent (hexadecane) with an added charge control agent.

The problem of electrostatic interactions between colloidal particles in an electrolyte solution has been solved within the Debye-Hückel approximation using the boundary condition of constant potential. The model has been validated in two independent ways - by considering the limiting cases obtained from DLVO theory and comparison with the available experimental data. The presented methodology provides the final part of a complete theory of pairwise electrostatic interactions between spherical colloidal particles; one that embraces all possible chemical scenarios within the boundary conditions of constant potential and constant charge.