Gravity-induced collisions of uncharged cloud droplets in an electric field

We theoretically study the collision dynamics of uncharged, conducting droplets settling under the influence of gravity in the presence of an external electric field. Our study demonstrates that the attractive forces induced by an external electric field can overcome lubrication resistance, facilitating surface-to-surface contact between two spherical conductors within a finite time. For water droplets moving in air, continuum lubrication theory fails when the gap between droplets becomes less than the mean free path of air molecules. To account for this, we incorporate non-continuum lubrication effects in the collision calculations. By numerically computing the relative trajectories of the droplets, we assess how collision efficiency depends on the droplet size ratio, non-continuum lubrication effects, the angle between the electric field and gravity, electric field strength, and van der Waals forces. Our findings reveal that electric-field-induced forces significantly enhance collision efficiency, highlighting their critical role in droplet collision dynamics.