Abstract
We revisit the theory of condensation of a droplet in a vapour with the aim of finding the effect that the surface tension has on the phase diagram of a binary mixture. For that purpose we consider condensation under volume control and rederive the Gibbs phase rule. The Gibbs phase rule is equivalent to the ‘common tangent construction’ for two free enthalpies corresponding to different pressures: in this case, the pressure in the vapour and the pressure in the droplet. Explicit results are calculated for a droplet mixed from incompressible liquids and for a vapour that is an ideal gas mixture. It turns out that in a certain range of volumes the equilibrium state of droplet and vapour has a higher free energy than the vapour alone. At the lower bound of that range of volumes a stable droplet of finite size will nucleate and consequently the vapour pressure will drop. The usual condensation line in a (p, X 1)-phase diagram without surface tension is thus replaced by two lines: One for the incipient condensation and one for its completion; both lie above the condensation line without surface tension.
Similar content being viewed by others
References
Laplace, P.S., Traité de Méchanique Céleste, Vol. 4, Courcier, Paris, 1806.
Thomson, W., Proc. Roy. Soc. Edinburgh 7 (1870) 63.
Cahn, J.W. and Larché, F., ‘A simple model for coherent equilibrium’, Acta Metall. 32(11) (1984).
Müller, I., ‘Boiling and condensation with interfacial energy’, Meccanica 31 (1996).
Müller, I. and Ansorg, J., ‘Phase diagrams, heat of mixing and interfacial energy’, in: P. Argoul (ed.), Proc. IUTAM Symp. Variations de Domaines et Frontières Libres en Méchanique des Solides, Kluwer, 1999.
Ansorg, J., Einführung der Grenzflächenenergie in die Darstellung von Phasenübergängen binärer Mischungen, Dissertation, TU Berlin, 2001.
Truskinovsky, L. and Zanzotto, G., ‘Ericksen's bar revisited: energy wiggles’, J. Mech. Phys. Solids 8 (1966).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Huo, Y., Mueller, I. Nucleation of Droplets in a Binary Mixture. Meccanica 38, 493–504 (2003). https://doi.org/10.1023/A:1024779230999
Issue Date:
DOI: https://doi.org/10.1023/A:1024779230999