Nucleation in Very Rapid Vapor Expansions

In the Volmer theory, sub-critical droplets (embryos), with vapor pressure greater than their surroundings, nevertheless, grow statistically, because they exist in sufficiently greater numbers than neighboring larger droplets. Thus the formation of nuclei against the thermodynamic barrier presupposes the presence of very large numbers of embryos of all sizes. An approximate lower bound for the time (nucleation time) required for the formation of this system of embryos can be calculated readily by (1) neglecting the thermodynamic barrier which impedes their formation; (2) assuming that when droplets contain a certain supercritical number, Γ, of molecules they grow very rapidly because their vapor pressure is considerably lower than their surroundings; (3) assuming that the formation of the embryo system begins when the vapor first becomes saturated. The equation for the rate of formation of embryos then reduces to the heat conduction equation yielding a simple solution. The lower bound sought is found to be inversely proportional to the fourth power of the degree of supercooling. Comparison with the experiments of Wegener and Smelt indicates that in some nozzle expansions the occurrence of nucleation is determined by this process. On this theory the thermal accommodation coefficient which determines the heat transfer and especially the accommodation coefficient for growth, which determines the probability of a molecule sticking to the surface, play a much more prominent role than they do in the Volmer steady-state theory. Comparison with experimental time lags for the condensation of H2O in air at −30 to −60°C gives the order of magnitude of the accommodation coefficient for growth as 5×10−4.