Time-dependent cluster distribution in nucleation

Abstract

The time-dependent size distribution function of clusters, as well as the relaxation and lag times, are calculated numerically in the framework of the recently developed kinetic theories of nucleation in liquids (E. Ruckenstein and B. Nowakowski, J. Colloid Interface Sci. 137, 583 (1990)), and gases (B. Nowakowski and E. Ruckenstein, J. Chem. Phys. 94, 1397 (1991)). The basic approach used in the calculation is the same as that employed for the classical theory. Differences in the treatment occur as a result of the fact that, in contrast to the classical theory, the rates of condensation and evaporation are calculated independently. The size distribution function of clusters approaches monotonically the steadystate distribution. The nucleation rate relaxes monotonically to the steady-state value for clusters greater than the critical cluster x ∗ ; for x < x ∗ the nucleation rate exhibits an initial overshoot that exceeds the stationary value and then tapers to the steady-state rate from above. The relaxation times calculated for typical systems are of the order of 1 μs both in liquids and gases. The time lags were found to be of the order of, but larger than, the relaxation time and were found to increase with the size of the cluster. In contrast to the steady-state nucleation rates, which differ by orders of magnitude, the relaxation and lag times calculated in the framework of the kinetic theories are comparable to those obtained on the basis of the classical theory.