On the thermodynamic stability of small droplets at positive line tension

Abstract

The thermodynamic formalism with the Ω potential is applied for finding the conditions of mechanical equilibrium (Laplace's law and Young's equation) in the case of small liquid droplets attached at a plane surface. The conditions of stability of the equilibrium drops are examined. It is shown that at positive values of the line tension of the contact perimeter there exists a supersaturation above which no heterogeneous nucleation occurs. Below this maximum value of the supersaturation two equilibrium cap-shaped drops could coexist. They are both in unstable equilibrium with their surroundings. No range of supersaturations exists where the smaller equilibrium drop would be in stable equilibrium with the surroundings. Such a conclusion has been proposed (V.C. Noninski, Colloids Surfaces, 42 (1989) 205; J. Colloid Interface Sci., 143 (1991) 374) on the basis of the incorrect assumption that the stability of the equilibrium could be referred to the slope of the Thomson—Gibbs dependence of vapour pressure on drop size. Positive slopes of this dependence imply stability equilibrium in the case of free drops only. For the case of cap-shaped drops where the Ω potential is a function of two (or more) geometrical variables, the determination of the stability conditions follows another procedure shown in the present paper.