An analytical framework for predicting the total freezing delay time of water droplet impact on hydrophobic solid surfaces

Abstract

An analytical framework is developed to investigate the impact and freezing delay of a water droplet on solid surfaces, particularly hydrophobic ones, at subfreezing temperatures. Submodules for droplet dynamics, supercooling, nucleation and recalescence, and equilibrium solidification are developed for different droplet impact and freezing stages. These submodules are then integrated to estimate the total freezing delay time per unit mass of the water droplet. It is found that the nucleation time depends on the impact height, surface temperature, droplet impact temperature, and the droplet-substrate contact angle, while the solidification time depends on the droplet size, the nucleation temperature, and the droplet final contact diameter, which is related to the initial droplet diameter, the Weber number, the Reynolds number, and contact angle. The analytical model is validated with results from droplet freezing experiments in a subfreezing environment. By simplifying the complex droplet dynamics, nucleation, and freezing processes, the new analytical framework provides a useful way to estimate the total freezing time of impacting water droplets on hydrophobic surfaces. Its accuracy needs to be improved for practical engineering applications.