The role of shadowed droplets in condensation heat transfer

Abstract

Dropwise condensation (DWC) is a phenomenon of common occurrence and significant utility in nature and technology. In energy applications, sustenance of DWC and avoidance of transition to film formation is directly related to efficient heat removal, ensuring high performance of related devices and processes. The efficiency of heat transfer in DWC depends on the heat transfer rates of individual droplets and the droplet size distribution. While the former can be summarily captured in engineering analysis through thermal resistance modeling, the theoretical analysis of the droplet size distribution involves assumptions often oversimplifying the complexity of droplet interactions, especially in the important sub–10 μm regime. Here, a modeling framework based on the thermal resistance approach is coupled with a dynamic model of droplet interactions: Droplet growth, coalescence, jumping, and removal of condensate due to gravity are all present during the unfolding of the phenomenon to accurately predict the droplet size distribution. The motivation is condensation experiments on superhydrophobic surfaces, namely rough aluminum substrates with a hydrophobic coating. Through the “interaction” of computations with measurements, the experimental findings are explained and critical parameters for condensation heat transfer on superhydrophobic surfaces are illuminated. Although larger droplets can be easily observed in experiments, it is shown that large droplets do not significantly affect heat transfer after reaching such state of growth. Instead, it is the small (with radius < 10 μm) and what we term “shadowed” droplets, i.e., the droplets grown in the shadow of the vertical projection area of the larger droplets, that play an important role in the heat transfer process. Due to the growth of these droplets and their concomitant shadowed coalescence and ensuing re-nucleation, the shift in the droplet size distribution towards smaller sizes is significant-enough to render the heat transfer rate rather insensitive to the presence of large droplets. In this regime, the effect of contact angle hysteresis on heat transfer is not crucial. Through the comparison with measurements, the dominant role of the density of nucleation sites on heat transfer is revealed and an estimation of the density of sites (∼105 mm−2) as a function of subcooling is extracted. Finally, the distribution of sites is found critical for heat transfer; an ordered distribution of sites outperforms random and clustered distributions.