Gravity-Induced Collisions of Cloud Droplets under External Electric Fields

We theoretically investigate the collision dynamics of uncharged, conducting droplets settling under gravity in the presence of an external electric field. Our analysis shows that electric-field-induced attractive forces can overcome the lubrication resistance and lead to droplet coalescence within a finite time. However, for water droplets moving through air, the assumptions of continuum lubrication theory break down when the inter-droplet gap becomes comparable to the mean free path of air molecules. To address this, we incorporate non-continuum corrections into the hydrodynamic interaction model. Using numerical simulations of droplet pair trajectories, we evaluate collision efficiencies and explore their dependence on droplet size ratio, non-continuum effects, electric field strength, the angle between the electric field and gravity, and van der Waals forces. The results demonstrate that even modest electric fields can substantially enhance collision efficiencies, underscoring the important role of electrostatic interactions in droplet growth and coalescence dynamics in atmospheric environments.