The size distribution of liquid droplets during their growth from a vapor

Abstract

We consider a collection of droplets growing from a supersaturated vapor or from a gas mixture containing such a vapor. The evolution of the distribution function of their radii is calculated in a simple mean field approximation for the time regime starting well after nucleation and continuing well into the Ostwald ripening regime. Between the diffusion controlled regime and the Ostwald ripening regime one often observes a long “waiting period” during which the typical droplet size appears to grow slower than any power of the time (or at most with a very small power). The waiting period increases with decreasing initial width of the distribution and with a decreasing volume ratio of liquid and vapor in the ultimate equilibrium state. The waiting period is shown to be connected with the existence of an unstable fixed point in the evolution equation for the droplet size distribution, corresponding to equal size of all droplets. The dependence of the length of the waiting period on the parameters of the problem and its sensitivity to changes in the model are also discussed.