Gibbs-Thomson Effect on Droplet Condensation

Abstract

The present study is primarily aimed at theoretically investigating the growth of a single spherical droplet due to condensation. The droplet is either at the center of a large spherical container or in an infinite domain. The effect on the droplet growth due, respectively, to the subcooling, the Gibbs-Thomson condition, and the density-difference-induced convection will be analyzed and discussed systematically. Dimensional analysis indicates that three different time scales exist during the droplet growth due to condensation. The first and second small time scales describe, respectively, the transient temperature distributions of the gas phase and droplet, while the largest time scale describes the droplet growth. With the aid of multiple time-scale analysis, the analytic solutions for the droplet growth and the temperature distribution are obtained. The results indicate that, with a large Stefan number, the subcooling effect is stronger and the droplet grows faster. The Gibbs-Thomson effect, on the contrary, suppresses the droplet growth. However, the effect becomes smaller as time proceeds. Moreover, if the density difference between the liquid and the gas phases becomes larger, the induced convection will be stronger, which is conducive to the droplet growth.