Instability Analysis of the Drop Growth Mechanism on Condensation of a Water-Ethanol Binary Mixture

Abstract

When a water-ethanol binary mixture condenses, one observes dropwise condensation on the liquid film even though either substance is completely soluble in the other. The phenomenon is not well understood. This paper discusses liquid film instability using perturbation theory as the drop growth mechanism. The results show that in drop growth, the Marangoni number (Ma, i.e., the concentration dependence of the surface tension) plays a more important role than the absolute value of the surface tension. When a pure, single-component vapor condenses, dropwise condensation does not occur because Ma of a pure substance is always negative ; however, in a binary mixture, the surface tension may be different, and therefore the possibility exists that Ma is positive. If so, the mode of condensation may become dropwise. However, this will depend on the diffusive resistance which, if lowered, makes dropwise condensation more difficult.