Curvature Dependency of Surface Tension in Multicomponent Systems

The effect of curvature on the surface tension of droplets and bubbles in both single and multicomponent systems is modeled using the basic equations from classical thermodynamics. The three expressions used in our work are the Gibbs adsorption equation for multicomponent systems, the relation between the surface tension at the surface of tension and the distance parameter , and the Macleod–Sugden equation for surface tension and its extension to multicomponent systems. The Peng–Robinson equation of state is used to describe the bulk phases. We also assume that the surface tension expression remains valid in terms of the properties of the bulk phases for both flat and curved interfaces. For a flat surface we have developed a rigorous thermodynamics approach for the calculation of the Tolman distance parameter. For curved surfaces, the results from our model reveal a decrease in surface tension with curvature in bubbles and a nonmonotonic behavior in droplets for single-component systems. Our predictions are in good agreement with the literature results when the interface is described using the framework of the density functional theory by three different groups. For multicomponent systems, the results show that the surface tension in a bubble, although monotonic with curvature, can increase or decrease in a large bubble depending on the temperature and composition of the mixture. In a droplet, the surface tension can have a nonmonotonic behavior similar to that of single-component systems. © 2005 American Institute of Chemical Engineers AIChE J, 52: 311–322, 2006