Non-Steady-State Nucleation

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Abstract
The non‐steady‐state nucleation of water vapor is examined by an exact mathematical approach which solves on a computer the 100 or so simultaneous differential equations which describe nucleation. This approach avoids the numerous mathematical approximations of Kantrowitz, Probstein, and Collins. The customary kinetic and thermodynamic assumptions of the classical liquid‐drop theory of steady‐state nucleation were used. The times for the concentration of the nucleus of liquid water to reach 95% of steady state at —10°, —40°, and —60°C are 1.4, 19, and 27 μsec with supersaturations of 5, 10, and 20, respectively, and are only 10% longer than the ``time lags'' estimated by the approximate methods. Since the surface tensions of small clusters and the accommodations coefficients are unknown, the approximate methods, although incorrect by greater than 100%, are sufficiently accurate for most purposes. The results of Frisch are shown to be incorrect. The steady‐state concentrations of water clusters are equal to their equilibrium concentrations for clusters which contain up to about 15 and 5 molecules less than the nucleus at —10° and —60°, respectively. Contrary to general opinion, the equilibrium concentrations of liquid‐drop clusters do not decrease sharply in the vicinity of the nucleus.

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