Homogeneous nucleation and growth of droplets in vapours

Abstract

The theory of homogeneous nucleation of liquid drops in supersaturated vapours is reviewed. A new kinetic treatment which accounts for the heating of the growing clusters due to the latent heat of condensation is presented, and the irreversible thermodynamics of non-isothermal nucleation discussed. It is found that growing clusters are generally colder than the surrounding vapour during their sub-critical growth period. Time dependent nucleation is discussed and a simple estimate for the time-lag in establishing the steady state is given. The nucleation in cloud chambers expanding with constant speed is discussed in detail, and the number of droplets formed and their final mean size is calculated as a function of the terminal expansion ratio. Re-evaporation of nucleated clusters is discussed. Numerical results are given for a number of typical situations in experiments on water-vapour. These results for the nucleation rate as corrected by Lothe and Pound predict much lower ‘critical’ expansion ratios than indicated by the limited experimental data available, even when the non-isothermal theory is used. To restore agreement between theory and experiments the surface tension for small droplets (≃100 molecules) could be increased some 15% above that of the bulk liquid, or the pre-exponential in the nucleation rate could be decreased by some 10⁻¹⁵. This latter expedient roughly corresponds to use of the ‘classical’ instead of the Lothe-Pound nucleation rate. These two alterations would, however, affect the theoretical curves in different manners and careful experiments could possibly distinguish between them.