Theoretical analysis of crystallization by homogeneous nucleation of water droplets

We propose a novel method for analyzing the crystallization process from supercooled water droplets. The method, which is based on nucleation theory, simultaneously evolves homogeneous ice nucleation and crystal growth in the cooling process and obtains the crystallization temperature and the number of crystal nuclei in the droplets. The model can reproduce not only the crystallization of water but also the vitrification process. The model well replicated the results of previous laboratory experiments, especially, the different responses of the crystallization temperatures of the micrometer- and nanometer-sized particles as a function of cooling rates. For particle sizes ranging from 1 to 1000 μm and cooling rates below 104 K s-1, the crystallization temperature was 230-240 K. At cooling rates above 104 K s-1, the crystallization temperature decreased rapidly. On the other hand, the crystallization temperature of 10 nm particles was 200-230 K at cooling rates below 104 K s-1. When describing the interfacial tension by σ = 29.1 + 0.1(T - 273.15) erg cm-2 (where T is the water droplet temperature in K), the analyses explained well the previously reported crystallization temperatures of droplets sized from a few nm to 100 μm under various cooling conditions. Our model also predicts the critical cooling rate for vitrification of the liquid water droplets. The critical cooling rate of vitrification is predicted to be 107-108 K s-1, consistent with the experimental rates. These analyses are useful not only for comprehensively understanding the ice nucleation process but also for predicting the crystallization processes in various environments such as cirrus clouds, which are difficult to reproduce in experiments.