Electrostatic interactions between anisotropic particles

Abstract: We investigate the electrostatic interactions between two charged anisotropic conductors using a combination of asymptotic and numerical methods. For widely separated particles, we employ the method of reflections to analyze the interactions. Although the formulation applies to conductors of arbitrary shapes, it is specifically implemented for spheroid-sphere systems to capture anisotropy effects in a simple configuration. In near-contact cases with axisymmetric configurations, the lubrication approximation is used to extend the analysis. Additionally, we develop a Boundary Integral Method (BIM) to study particle interactions at arbitrary separations, validating the results with asymptotic solutions for both near and far fields. We derive analytical expressions for the electrostatic force and torque on a spheroid due to another spheroid in the far-field regime. When combined with hydrodynamic effects, the electrostatic torque competes with the hydrodynamically favourable alignments of a pair of settling spheroids in certain regions while reinforcing them in others. Consequently, the inclusion of electrostatic effects may influence the instability observed in dilute suspensions of spheroids.