A new freezing model of sessile droplets considering ice fraction and ice distribution after recalescence

In this work, a new three-dimensional sessile droplet freezing model, involving the ice fraction and ice distribution after the droplet recalescence, is established based on the many-body dissipative particle dynamics with the energy conservation method for the first time. The proposed model is verified by comparing it with experimental results, and the accuracy of this model increases as the ice distribution becomes more non-uniform after recalescence. Furthermore, the effects of surface contact angle, droplet volume, surface temperature, and droplet supercooling degree on the freezing process are investigated in detail. The numerical results demonstrate that the angle of ice tips maintains a constant under various conditions. The upper and lower limits of solidification time under specific conditions are derived, and the droplet solidification time decreases linearly with the increase in supercooling. In addition, the average droplet solidification rate decreases with the increase in droplet volume, contact angle, and surface temperature, and the surface temperature is demonstrated to have the greatest influence on the solidification rate. Emphatically, we put forward an empirical formula, as a function of droplet volume, contact angle, droplet supercooling degree, and surface temperature, to predict the freezing time of a sessile supercooled droplet.