The droplet collision rate in electrified clouds

Differential gravitational sedimentation and the intensity of the local turbulence are known to influence the cloud droplet collision rate, which results in the formation of drizzle and rain droplets in warm clouds. In electrified clouds, such as occur in thunderstorms, the presence of charge can also modify the droplet collision rate, and we address that problem here. We have derived an approximate analytical expression for the charged cloud droplet collision rate in turbulent flow, valid for conditions typical for small (weakly inertial) droplets in clouds. To verify it, we have made laboratory measurements of the charged droplets in isotropic turbulence and have performed a direct numerical simulation (DNS) of charged, inertial droplets in a turbulent flow. The analytical expression shows acceptable agreement with experiments and the DNS. With this expression, we have simulated the growth of a population of cloud droplets in a closed parcel model and showed that typical thunderstorm charge levels can suppress collisions and therefore the broadening of the size distribution that eventually leads to rain formation.