A point sink superposition method for predicting droplet interaction effects during vapor-diffusion-driven dropwise condensation in humid air

Abstract

During dropwise condensation from the ambient environment, water vapor present in air must diffuse to the surface of each droplet. The spatial distribution of water vapor in the local surroundings of each individual droplet determines the total condensation rate. However, available models for dropwise condensation in humid air assume that such systems of droplets grow either as an equivalent film or that the growth of each droplet is completely isolated; the interactions between droplets are poorly described and, consequently, predictions of total condensation rates may mismatch experimental observations. This paper presents a reduced-order analytical method to calculate the condensation rate of each individual droplet within a group of droplets on a surface by resolving the vapor concentration field in the surrounding air. A point sink superposition method is used to account for the interaction between droplets without requiring solution of the diffusion equation for a full three-dimensional domain containing all of the droplets. For a simplified scenario containing two neighboring condensing droplets, the rates of growth are studied as a function of the inter-droplet distance and the relative droplet size. For representative systems of condensing droplets on a surface, the total condensation rates predicted by the reduced-order model match numerical simulations to within 15%. The results show that assuming droplets grow as an equivalent film or in a completely isolated manner can severely overpredict condensation rates.