Time-dependent nucleation theory

The theory of time-dependent homogeneous nucleation in a supersaturated cooling gas is investigated both analytically and numerically. The character of the nucleation process (e.g., the critical supercooling when the nucleation rate peaks, and the final cluster size) depends almost entirely on just two dimensionless quantities: the ratio ϑ/T (where T is the temperature, and kϑ is essentially the surface free energy per surface site) and a dimensionless parameter η which measures the number of times monomers collide with a single surface site during one supersaturation ratio e-folding time. Within the framework of classical nucleation theory (assuming the nucleating vapor to be in a carrier gas) an approximate analytical treatment of the regime η≫1 (which includes nearly all terrestrial nucleation experiments) is given, resulting in simple formulas for the critical supersaturation ratio, the mean final cluster size, and the relative dispersion in final cluster sizes. To test the accuracy of the approximations the analytic results are compared with more exact numerical calculations for a number of values of ϑ/T and η; good agreement is found in the limit η≫1. Validity criteria for the use of the results are obtained.