Effect of Latent Heat Released by Freezing Droplets during Frost Wave Propagation

Frost spreads on nonwetting surfaces during condensation frosting via an interdroplet frost wave. When a supercooled condensate water droplet freezes on a hydrophobic or superhydrophobic surface, neighboring droplets still in the liquid phase begin to evaporate. Two possible mechanisms govern the evaporation of neighboring water droplets: (1) The difference in saturation pressure of the water vapor surrounding the liquid and frozen droplets induces a vapor pressure gradient, and (2) the latent heat released by freezing droplets locally heats the substrate, leading to evaporation of nearby droplets. The relative significance of these two mechanisms is still not understood. Here, we study the significance of the latent heat released into the substrate by freezing droplets, and its effect on adjacent droplet evaporation, by studying the dynamics of individual water droplet freezing on aluminum-, copper-, and glass-based hydrophobic and superhydrophobic surfaces. The latent heat flux released into the substrate was calculated from the measured droplet sizes and the respective freezing times (t_f), defined as the time from initial ice nucleation within the droplet to complete droplet freezing. To probe the effect of latent heat release, we performed three-dimensional transient finite element simulations showing that the transfer of latent heat to neighboring droplets is insignificant and accounts for a negligible fraction of evaporation during microscale frost wave propagation. Furthermore, we studied the effect of substrate thermal conductivity on the transfer of latent heat transfer to neighboring droplets by investigating the velocity of ice bridge formation. The velocity of the ice bridge was independent of the substrate thermal conductivity, indicating that adjacent droplet evaporation during condensation frosting is governed solely by vapor pressure gradients. This study not only provides key insights into the individual droplet freezing process but also elucidates the negligible role of latent heat released into the substrate during frost wave propagation.