On the dynamics of freezing sessile droplets: Frost halo formation

The freezing of a supercooled sessile droplet unveils fascinating physics, characterized by the progression of the liquid-ice interface, the formation of a cusp-like morphology at the tip of the droplet and often by the emergence of a frost halo on the underlying substrate. Here, we focus on the latter which has been verified experimentally but has not been theoretically explored. We consider the freezing of a thin volatile sessile droplet on a sub-cooled substrate and develop a comprehensive model based on lubrication theory. It is demonstrated that the vapor that is present in the atmosphere comes into contact with the sub-cooled substrate resulting to considerable condensation near the contact line at early stages of the freezing process, forming a frost halo in the droplet periphery. Liquid volatility also influences the shape of the liquid-ice interface and aspect ratio of the droplet, as it affects the total remaining mass of ice and the thermal profile inside the droplet. The latter is determined by the conductivity of the droplet, the thermal resistance of the substrate, convection to the atmosphere and, crucially, evaporative cooling. We conduct a detailed parametric study and discuss about the effects of ambient conditions, the latent heat of vaporization and melting, and the thermal properties of liquid, ice and the substrate on the frost halo formation and the dynamics of the freezing process in general.