In the last chapter, we discussed the thermodynamic equilibrium among different phases of water substance and derived the Clausius–Clapeyron equation to describe the equilibrium quantitatively. We found that, while this equation is useful in many respects, it has problems when predicting certain phenomena related to phase change due to its omission of surface effects in the system. In actual clouds, especially in the initial stage of cloud formation, particles often have high curvatures and hence strong curvature effects, which cannot be neglected. In this chapter, we will study the surface effects and then use that knowledge to study the equilibrium behavior of cloud and precipitation particles in a more realistic way.

The interface as a phase

The interface between two bulk phases is a very special “system” that sometimes is more complicated than a bulk system. Conceptually we often simplify the interface as a geometrical surface (i.e. no thickness but has area), but in reality it must be a layer of finite thickness (albeit very, very thin). Fig. 5.1 shows a conceptual model of the interface between liquid water and water vapor for a water drop of radius a.