Dropwise condensation on superhydrophobic nanostructure surface, part II: Mathematical model

Abstract

Inspired by our finding that nano-grass-surface (NGS) with smaller droplets has poorer condensation heat transfer performance than smooth-single-molecule-layer surface (SSML) and the long-term operation of NGS deteriorates heat transfer to approach limit values, the secrets of droplets interacting with nano-pillars structure are explored. A comprehensive dropwise condensation model is developed. The contact angles are treated to show correct trend with respect to Cassie, partial Wenzel and Wenzel morphologies. A mixed droplet detachment model is developed to consider the coalescence-induced-jumping, rolling and sliding modes simultaneously. The maximum drop radius is rmax = min(rmax,jump, rmax,roll, rmax,slide), where rmax,jump, rmax,roll and rmax,slide are maximum drop radii in jumping, rolling and sliding modes, respectively. The number of drop nucleation sites on NGS is f times of that on SSML, where f is the surface roughness. Our model predictions match the measured heat transfer data well. It is concluded that the dropwise condensation is the outcome of a series of positive and negative effects by introducing the nanostructure. The increased droplet population density and number of drop nucleation sites are the positive contributions, while the decreased single drop heat transfer rate and additional nano-porous thermal resistance are the negative contributions. The densely populated nano-pillars structure has the largest capability to enhance heat transfer. The Heterogeneous hydrophilicity/hydrophobicity surface limits droplet sweeping distance within neighboring hydrophilic dots, to avoid that stone rolls on the lawn to spoil the grasses, the heterogeneous surface is recommended to resist nanostructure failure for long-term operation.