Kinetics of Condensation of Water Vapor

Abstract

The condensation of water vapor via steady-state nucleation is examined by an exact mathematical approach which solves the kinetic equations on a computer. This approach avoids the usual assumption that nucleation abruptly stops when the parent phase becomes slightly depleted. The corrected classical theory of steady-state liquid-drop homogeneous nucleation and the growth law used in the classical nucleation theory were assumed. Results gave no indication of a ``critical'' supersaturation for condensation and showed that condensation via classical homogeneous nucleation would be much slower than experimentally observed in cloud chambers. Condensation in 50 msec via homogeneous nucleation theoretically requires 13 particles/cc and an initial supersaturation of 5.2 at —5°C and 3.3×104 particles/cc and an initial supersaturation of 35 at —60°. Nucleation rates are sensitive to supersaturation but at —60° one-third of the particles are formed after a 4% decrease in supersaturation, contrary to the usual interpretation of condensation kinetics in a cloud chamber. The rapid condensation rates experimentally observed in a cloud chamber may be due either to heterogeneous nucleation or to homogeneous nucleation with the surface energy of an 80- or 90-molecule cluster being smaller than the macroscopic value, e.g., about 3 and 30% smaller at —5 and —60°, respectively. However, the liquid-drop theory of homogeneous nucleation as classically formulated in terms of the macroscopic surface energy apparently cannot explain the experimental results in a cloud chamber and thus remains to be verified.