Droplet Growth and Drop Size Distribution Model for Dropwise Condensation on Hydrophobic Tubular Surfaces

Condensation over a tubular surface has a wide range of applications. A steady-state mathematical model for droplet condensation of saturated water vapor on the outer surface of a hydrophobic tube is proposed. The tube curvature effect on a single drop heat transfer as well as on the drop size distributions has been incorporated. A single droplet growth model utilizing heat conducted through the droplet population to the condensing surface is established. Thermal resistances that include curvature, interfacial, drop and the hydrophobic promoter layer have been considered for model development. The tube curvature effect on a single droplet heat transfer is considered based on condensation over a concave substrate (Zhang and Zhang in ACS Omega 5:22,560–22,567, 2020). The surface wetting phenomena and their characteristics are defined on the basis of an equilibrium contact angle and hysteresis. The developed model is built on the definition of an apparent contact angle. A general transcendental equation for the apparent contact angle via droplet and the tube radius to the intrinsic contact angle is utilized. Population balance theory is used for the droplet number density distribution. The droplet number densities for gravity-driven drop removal and drainage have been iteratively determined. The numerically obtained drop size distribution is integrated with the single droplet heat flux for obtaining the overall heat transfer rate during droplet condensation outside a vertical tube.