Comparison among various approaches to the calculation of the nucleation rate

Abstract

The discrete, finite difference equations for cluster distribution are transformed into partial differential equations using various expansions. The rate of nucleation is calculated by combining each of these expansions with the kinetic theory of nucleation in liquids developed recently by the authors [Ruckenstein, E., and Nowakowski, B., J. Colloid Interface Sci. 137, 583 (1990)] . Rates of nucleation calculated using expansions compatible with the discrete equilibrium distribution are compared with those obtained using the conventional expansion of finite difference equations to differential equation, and to the classical theory. The results obtained on the basis of the kinetic approach are very different from those based on the classical theory, regardless of the expansion employed. The comparison between the different expressions demonstrates that the rate of nucleation can be very sensitive to the expansion employed for the transformation of the discrete equations for cluster distribution into the continuous equation. Since the expansions compatible with the equilibrium distribution of clusters are expected to be closer to the finite difference equations for cluster distribution, they should be preferred to the other kind of expansions.