Pair trajectories of uncharged conducting spheres in an electric field

Abstract

In this paper, we study the role of electrostatic forces on pair trajectories of two uncharged conducting spheres subject to an external electric field. We consider the hydrodynamic interactions between the spheres as they move relative to one another. Previous studies have shown that electric-field-induced forces on a two spheres system are always attractive, except for the configuration when the line joining the centers is perpendicular to the external electric field. In the current study, we derive the asymptotic form of the interparticle force induced by the electric field in the lubrication limit for arbitrary size ratios. The attractive electric force diverges as the separation approaches zero. Thus, our calculation shows that the electric-field-induced forces can overcome the continuum lubrication resistance and allow finite time contact between the surfaces of two spherical conductors. We calculate the asymptotic variation of interparticle separation using the near-field asymptotic expressions for the electric-field-induced forces, exploring the role hydrodynamic interactions play for interparticle motion parallel and perpendicular to the electric field.

Collision efficiency of like-charged spheres settling in a quiescent environment

“…Experiments in a cloud chamber by Wang et al (2020) demonstrated that a strong electric field can dominate the collision process. Recently, Thiruvenkadam et al (2023) theoretically analysed the effects of an external electric on relative trajectories of a pair of uncharged conducting spheres, and they showed that electric-field-induced forces allow surface-to-surface contact in a finite time by overcoming continuum lubrication resistance. We plan to study the combined effects of gravity, non-continuum interactions, van der Waals forces and electric-field-induced forces on the collision dynamics of uncharged micron-sized droplets.…”