Unified icing theory based on phase transition of supercooled water on a substrate

Lack of knowledge on substrate icing hinders us from predicting the effects of typical substrate properties in icing and anti-icing research. The pattern formation and tip shape of icing on a substrate must be explored to understanding the physics of icing on a substrate. In this paper, the pattern, velocity and tip shape of ice on substrates with different thermal conductivities and surface energies are evaluated in a series of experiments. Experimental results show that as supercooling and thermal conductivity increase, the ice on substrate evolves from a single-needle dendrite to a smooth ice film. In contrast, for free icing the same evolution process can be completed at a higher supercooling than substrate icing. Experimental results on hydrophilic and Plexiglas surfaces demonstrate an abruptly decrease of velocity and Peclet number of ice occurs at approximately 271.6 K, whereas the tip shape of ice does not change obviously; while for free icing this phenomenon is not found. Furthermore, a theoretical analysis on phase transition of substrate icing is performed. It shows that the surface energy of substrates can increase the size of metastable cubic ice and reduce the temperature on the ice tip by 1.5 K compared to free ice, thereby causing the decrease in the velocity and Peclet number of ice. Also the heat conduction of substrates decrease the heat flux in ice growth direction and lead to absolute stability of substrate icing in lower supercooling compared to free icing. In terms of the comparison between free icing and substrate icing, a unified icing theory is proposed to describe the equilibrium icing mode, the non-equilibrium growth state, and the corresponding growth equations. Using this theory, the velocity and pattern of substrate icing with different supercooling, thermal conductivity, and surface energy can be predicted well, as well as these results of free icing.