Dropwise Condensation Modeling Suitable for Superhydrophobic Surfaces

TLDR

A mathematical model is developed to predict dropwise condensation on nonwetting surfaces with hydrophobic or superhydrophobic (contact angle >150°) features. The model combines single‑droplet heat transfer—including interfacial, conductive, coating, and curvature resistances—with a population balance for small droplets and an empirical distribution for large droplets, thereby linking heat transfer to drop size distribution. Results show that higher contact angles enhance condensation heat transfer, reduce the size of droplets at detachment, increase the number of small droplets, and agree well with previously reported experimental data.

Abstract

A mathematical model is developed to represent and predict the dropwise condensation phenomenon on nonwetting surfaces having hydrophobic or superhydrophobic (contact angle greater than 150 deg) features. The model is established by synthesizing the heat transfer through a single droplet with the drop size distribution. The single droplet heat transfer is analyzed as a combination of the vapor-liquid interfacial resistance, the resistance due to the conduction through the drop itself, the resistance from the coating layer, and the resistance due to the curvature of the drop. A population balance model is adapted to develop a drop distribution function for the small drops that grow by direct condensation. Drop size distribution for large drops that grow mainly by coalescence is obtained from a well-known empirical equation. The evidence obtained suggests that both the single droplet heat transfer and drop distribution are significantly affected by the contact angle. More specifically, the model results indicate that a high drop-contact angle leads to enhancing condensation heat transfer. Intense hydrophobicity, which produces high contact angles, causes a reduction in the size of drops on the verge of falling due to gravity, thus allowing space for more small drops. The simulation results are compared with experimental data, which were previously reported.