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

Abstract

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), 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.

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“…As mentioned by Chavan et al [98], the role of latent heat is negligible and the ice bridging is primarily governed by vapor pressure gradients, whose physics is explicitly illustrated by Nath and Boreyko [97]. They explain the in-plane exchange of vapor molecules between an ice droplet and a supercooled liquid droplet with similar dimensions at constant temperature with the higher equilibrium vapor pressure of the liquefied droplet compared to the ice [97].…”

“…Since freezing on solid surfaces occurs very frequently in nature, it is of great interest to elucidate the mechanisms of ice crystallization in a variety of practical situations, including isolated droplets [52,94], groups of droplets [95] and condensation icing [96][97][98] with direct benefits to the future fabrication of intrinsically icephobic materials.…”

“…This spectacular physical mechanism, labelled as "self-dislodging", allows inherent impediment of the ice adhesion and preservation of the surface free of ice. Nonetheless, from practical point-of-view, the water droplets always appear collectively rather than isolated and this is especially true during condensation icing, whither often the water vapor condenses into supercooled liquid droplets at multiple places across the surface [97,98]. Then, the freezing of an individual supercooled droplet may inflict further solidification of neighboring condensates via the mechanism of released latent heat, as shown in Figure 3.…”

“…Then, the freezing of an individual supercooled droplet may inflict further solidification of neighboring condensates via the mechanism of released latent heat, as shown in Figure 3. Accordingly, the icing of a single droplet is accompanied by the generation of a latent heat flux that warms the surface and the adjacent liquid droplets begin to evaporate instantly [98]. Here, the scientific community considers two major hypotheses for the pathway of icing.…”

“…In turn, heterogeneous nucleation of the surrounding liquid condensates occurs via physical contact with the airborne crystals resulting in a cascade freezing [95]. Second, the water vapor attach to the frozen droplet and start the growth of ice bridges directed to the vaporizing droplet, which freezes once the bridge connects to it [98]. Interestingly, the velocity of ice bridging seems to be independent of the substrate's thermal conductivity (i.e., heat transfer rate) [98], hinting for the ascendancy of distinct freezing mechanism.…”