Electrostatic interaction between two charged dielectric spheres in contact

Of fundamental importance in numerous industrial and natural processes, the problem of two electrified spheres has been studied by many authors. However, the problem of particular importance for understanding electrostatic effects on powder or granular behavior, such as two dielectric spheres both carrying arbitrary amounts of charge, is still open for investigation. In the present work, two touching dielectric spheres of equal size and permittivity but arbitrary amounts of charge are studied by computational means of the Galerkin finite-element method. The effects of permittivity and the ratio of charge on the spheres are the main focus here. Because of the electric polarization, the electrostatic force can become attractive even when the two spheres carry charges of the same sign, due to positive dielectric effects, or to become repulsive for spheres with charges of the opposite sign, due to negative dielectric effects. In the presence of dielectrophoretic effect, whether the electrostatic force between the two spheres is attractive or repulsive is found to be determined by the ratio of charge on the two spheres.