Thermodynamics of heterogeneous binary condensation on insoluble nuclei

We consider heterogeneous binary condensation as the formation of wetting films of arbitrary thickness on insoluble nuclei. Using this approach, we show that the concurrence of the capillary and disjoining pressures in thin films plays a key role in the thermodynamics of the whole process. The limiting partial supersaturations necessary for barrierless condensation are obtained as functions of the droplet composition and an explicit expression for the formation free energy of a binary droplet on an insoluble nucleus is derived. The surface describing the formation free energy as a function of film thickness and composition has a minimum and a saddle point whose coordinates correspond to droplets in stable and unstable equilibria, respectively, with the vapor mixture. Equations for determining the coordinates of the well and saddle points are presented. The theoretical results are illustrated with numerical calculations for the butanol-hexanol and butanol-water droplets formation on quartz particles.