Modeling Dropwise Condensation: From Atomic Scale to Drop Instability

Abstract

The large body of literature available on the subject suggests the following three independent mechanisms of dropwise condensation: (1) The vapor condenses primarily between the droplets, i.e., the droplet-free area. This condensate layer gets transported to the droplets in their vicinity by surface diffusion. According to this model, the thin film between the droplets and the free surface of the droplets contribute to overall heat transfer. (2) While vapor condensation begins in a filmwise mode, the film reaches a critical thickness and ruptures due to surface tension-driven instability forming droplets. It is postulated that major part of the heat transfer takes place at this very thin condensate film, while the droplets mainly act as liquid collectors. (3) Droplets are only formed at individual nucleation sites, while the area between the droplets is regarded to be inactive with respect to condensation. In this model, heat transfer occurs only through the droplets and is primarily limited by their heat conduction resistance. Majority of the studies support this mechanism, in which the condensate is in the form of discrete drops located at the nucleation sites on or underneath a lyophobic substrate. A mathematical model based on the third mechanism is developed in this chapter. A comprehensive mathematical model of dropwise condensation underneath an inclined substrate, with and without a wettability gradient, is presented. The dropwise condensation process is hierarchical because it starts from the atomic scale and progresses on to the macroscale. The mathematical models of various sub-processes in dropwise condensation are described and correlated to experimental observations. Individual models of atomic level condensation, nucleation of a drop of minimum radius, growth by direct condensation, coalescence, instability, and fresh nucleation leading to a condensation cycle, are described. The model is then presented in the form of a numerical algorithm.