Kinetics of droplet growth processes: Simulations, theory, and experiments

The formation of a distribution of various size droplets is a characteristic feature of many systems from thin films and breath figures to fog and clouds. In this paper we present the results of our investigations of the kinetics of droplet growth and coalescence. In general, droplet formation occurs either by spontaneous nucleation or by growth from heterogeneously distributed nucleation centers, such as impurities. We have introduced two models to describe these two types of processes. In the homogeneous nucleation model droplets can form and grow anywhere in the system. The results of the simulations of the model are presented and it is shown that the droplet size distribution has a bimodal structure consisting of a monodispersed distribution of large droplets superimposed on a polydispersed distribution of smaller droplets. A scaling description for the evolution of the time-dependent droplet size distribution and its moments is presented and it is found that the scaling predictions are in excellent agreement with the simulations. A rate-equation similar to the Smoluchowski equation is also introduced for describing the kinetics of homogeneous droplet growth. The results of the simulations of the homogeneous nucleation model are also compared with the experiments on droplet growth in thin films obtained by vapor deposition of tin on sapphire substrate. It appears that this model captures the essential features of the distribution of droplets in the vapor deposition experiments. We also introduce a heterogeneous nucleation model for studying processes in which droplets only form and grow at certain nucleation centers which are initially chosen at random. Simulations, scaling theory, and a kinetic equation approach for describing the heterogeneously nucleated droplet growth model are also presented. The theoretical predictions are found to be in excellent agreement with the simulations.