Collision efficiency of poly-dispersed charged spheres settling in a quiescent environment

We study the gravity-induced collisions of charged spheres of dielectric materials dispersed in a gaseous medium. When the gap thickness between the surfaces of two spheres is shorter than the mean free path of the surrounding fluid medium, continuum assumptions for the hydrodynamics interactions are no longer valid, and the non-continuum lubrication interactions result in surface-to-surface contact in finite time. Two like-charged dielectric spheres attract each other at close separations for a wide range of size and charge ratio values. We use trajectory analysis to calculate the collision rate and, thus, explore the role of electrostatic interactions on the collision dynamics of a pair of like-charged dielectric spheres. We present the modifications of pair trajectories due to electrostatic forces and show how collision efficiencies vary with the non-dimensional parameter capturing the relative strength of the electrostatic force to gravity as well as the charge ratio and size ratio.