Electrostatic Attraction between Like-Charged Particles

A point charge Coulomb force model provides an inadequate description of the interaction between finite-sized particles. Experiments find that dielectric particles of like charge can polarize one another, causing effective attractive forces between them that lead to clumping. To more accurately model the origin of these attractive forces, we study the effective interaction between two dielectric spherical shells with like charge as a function of their size and charge ratios, and the dielectric constant of each. We base our work on a model developed by Bichoutskaia et. al. [1] in which the authors map a phase diagram of attractive interactions between like-charged spheres at touching. We extend the phase diagram to finite separations between the particles, determining the boundary at which the force becomes repulsive. Though a closed form expression for the force between particles does not exist, we find an effective force in certain parameter regimes that can be used as an input in simulations of charged granular particles. The form of this force is found to vary depending on whether we are in the small size ratio or the small charge ratio regime.
[1] Bichoutskaia et al, J. Chem Phys 133, 024105, (2010) https://doi.org/10.1063/1.3457157.