Theory of Droplet Growth in Clouds: II. Diffusional Interaction Between Two Growing Droplets

Abstract

The interaction of two growing droplets in a supersaturated atmosphere has been examined, and the temperature and vapor density profiles have been determined. It is found that the smaller droplet tends to “catch up” with the larger at a slower rate than predicted by conventional diffusion theory. Consideration of droplet fallspeeds leads to the conclusion that, under atmospheric conditions, growth interaction becomes significant only for droplet “pairs” having equal or nearly equal radii. The number of such pairs is generally small enough so that the effect on the size distribution is quite small. Of a much greater importance is the possibility of a resulting attractive diffusio-phoretic force between two growing drops which, in turn, gives rise to a net velocity of one drop toward the other. If this diffusion force of attraction becomes sufficiently strong to overcome the hydrodynamic and thermo-phoretic forces acting in the opposite direction, both collision efficiencies and coagulation of small droplets could be further enhanced, thus accounting for departures from monodispersity in actual atmospheric clouds.