  Water droplets coalesce into larger ones in atmospheric clouds to form rain.
But droplets on collision courses do not always coalesce due to the cushioning
effects of the air between them. The extent to which these so-called
hydrodynamic interactions reduce coalescence rates is embodied in the collision
efficiency, which is often small and is not generally known. In order to
characterize the mechanisms that determine the collision efficiency, we
exploited new time-resolved three-dimensional droplet tracking techniques to
measure the positions of cloud droplet pairs settling through quiescent air. We
did so with an unprecedented precision that enabled us to calculate the
relative positions, velocities, and accelerations of the droplets at droplet
surface-to-surface separations as small as about one-tenth of a droplet
diameter. We show that relative accelerations clearly distinguish coalescing
from non-coalescing droplet trajectories, the former being associated with
relative accelerations that exceeded a threshold value. We outline how relative
accelerations relate to hydrodynamic interactions, and present scaling
arguments that predict the threshold relative acceleration. We speculate that
the relative acceleration distribution of droplets in turbulent clouds can
parameterize the collision efficiency, and that this distribution together with
the well-known relative position and velocity distributions can generate a
physical description of both the collision and coalescence rates of cloud
droplets.
