Comparison between solutions of the general dynamic equation and the kinetic equation for nucleation and droplet growth

A comparison is made between two models of homogeneous nucleation and droplet growth. The first is a kinetic model yielding the master equations for the concentrations of molecular clusters. Such a model does not make an explicit distinction between nucleation and droplet growth. The second model treats nucleation and growth separately, fully ignoring stochastic effects, and leads to the continuous general dynamic equation (GDE). Problems in applying the GDE model are discussed. A numerical solution of the kinetic equation is compared with an analytic solution of the GDE for two different cases: (1) the onset of nucleation and (2) the nucleation pulse. The kinetic model yields the thickness of the condensation front in size space as a function of supersaturation and dimensionless surface tension. If the GDE is applied properly, solutions of the GDE and the kinetic equation agree, with the exception of very small clusters, near-critical clusters, and the condensation front