Growth and equilibrium size of water droplets in air

A model is presented to describe the growth in time of the average water drop in supersaturated air, and predict their radius at equilibrium. Many previous works consider the growth of an isolated drop, whereas in the present work the effect of the presence of a large number of drops, with the ensuing depletion in water content in the surrounding air, is considered: it is shown that the effect of depletion is crucial to obtain the equilibrium radius. Preliminary results, obtained under some simplifying assumptions, are presented: expressions accounting for this depletion effect are given for the time evolution of the liquid-water temperature and of the number of water molecules in the drop and drop radius near equilibrium, and for their asymptotic equilibrium values.