Critical Radius of Supercooled Water Droplets: On the Transition toward Dendritic Freezing

The freezing of freely suspended supercooled water droplets with a diameter of bigger than a few micrometers splits into two rather different freezing stages. Within the first very fast dendritic freezing stage a spongy network ice with an ice portion of less than one-third forms and more than two-thirds of liquid water remain. In the present work the distribution of the ice portion in the droplet directly after the dendritic freezing phase as well as the evolution of the ice and temperature distribution has been investigated in dependence of the most relevant parameters as droplet diameter, dendritic freezing velocity (which correlates with the supercooling) and heat transfer coefficient to the surroundings (which correlates with the relative droplet velocity compared to the ambient air and with the droplet size). For this purpose on the experimental side acoustically levitated droplets in climate chambers have been investigated in combination with high-speed cameras. The obtained results have been used for finite element method (FEM) simulations of the dendritic freezing phase under consideration of the beginning second, much slower heat-transfer dominated freezing phase. A theoretical model covering 30 layers and 5 shells of the droplet has been developed which allows one to describe the evolution of both freezing phases at the same time. The simulated results are in good agreement with experimental as well as with calculated results exploiting the heat balance equation. The most striking result of this work is the critical radius of the droplet which describes the transition of one-stage freezing of the supercooled water droplet toward the thermodynamically forced dendritical two-stage freezing in which the droplet cannot sufficiently get rid of the formation heat anymore. Depending on the parameters named above this critical radius was found to be in the range of 0.1 to 1 μm by FEM simulation.