Modeling and Optimization of Superhydrophobic Condensation

Superhydrophobic micro/nanostructured surfaces for dropwise condensation have recently received significant attention due to their potential to enhance heat transfer performance by shedding water droplets via coalescence-induced droplet jumping at length scales below the capillary length. However, achieving optimal surface designs for such behavior requires capturing the details of transport processes that is currently lacking. While comprehensive models have been developed for flat hydrophobic surfaces, they cannot be directly applied for condensation on micro/nanostructured surfaces due to the dynamic droplet-structure interactions. In this work, we developed a unified model for dropwise condensation on superhydrophobic structured surfaces by incorporating individual droplet heat transfer, size distribution, and wetting morphology. Two droplet size distributions were developed, which are valid for droplets undergoing coalescence-induced droplet jumping, and exhibiting either a constant or variable contact angle droplet growth. Distinct emergent droplet wetting morphologies, Cassie jumping, Cassie nonjumping, or Wenzel, were determined by coupling of the structure geometry with the nucleation density and considering local energy barriers to wetting. The model results suggest a specific range of geometries (0.5-2 mu m) allowing for the formation of coalescence-induced jumping droplets with a 190% overall surface heat flux enhancement over conventional flat dropwise condensing surfaces. Subsequently, the effects of four typical self-assembled monolayer promoter coatings on overall heat flux were investigated. Surfaces exhibiting coalescence-induced droplet jumping were not sensitive (< 5%) to the coating wetting characteristics (contact angle hysteresis), which was in contrast to surfaces relying on gravitational droplet removal. Furthermore, flat surfaces with low promoter coating contact angle hysteresis (< 2 deg) outperformed structured superhydrophobic surfaces when the length scale of the structures was above a certain size (> 2 mu m). This work provides a unified model for dropwise condensation on micro/nanostructured superhydrophobic surfaces and offers guidelines for the design of structured surfaces to maximize heat transfer.