Modelling of sessile water droplet shape evolution during freezing with consideration of supercooling effect

The freezing process of a supercooled water droplet on a cold plate is studied theoretically and experimentally. A novel model that considers both the supercooling effect on the physical properties and the gravity effect on the droplet shape is developed to simulate the droplet freezing behaviors. The model introduces a dynamic contact angle coupled with a slipping velocity to describe the tip singularity formation. Experiments are conducted on 10, 20 and 30 μL supercooled water droplets and the droplet freezing behaviors including the freezing front movements and droplet profile evolutions are observed and analyzed using the image recognition technology. The freezing rates and times and the droplet profiles calculated by the model agree well with the experimental observations. The model can better predict the freezing characteristics especially the freezing rate and time than the traditional model that ignores the supercooling effect, with the deviation in freezing time decreasing from over 40% to about 10% for droplets with different volumes at different temperatures and a larger supercooling degree causing a more obvious difference between the new and traditional models. The calculation results suggest that the final droplet profile is less dependent on the supercooling degree because it is less affected by the freezing rate. As the cold plate temperature goes down, the freezing rate increases and the freezing time decreases.