Time Lag in the Self-Nucleation of a Supersaturated Vapor

Abstract

Recent experiments have indicated that the quasi‐equilibrium Volmer theory of self‐nucleation fails in some cases to predict when the condensation of water vapor or the components of air will occur in the very rapid vapor expansions in a supersonic wind tunnel. By the obtaining of an approximate solution to the non‐steady Becker‐Döring equation for the self‐nucleation of a super‐saturated vapor, an attempt has been made to determine whether the time lag associated with the approach to the steady state rate of formation of condensation nuclei could account for the discrepancies between theory and experiment. A similar calculation, where the work required to form embryos of the condensing phase was neglected, has been carried out by Kantrowitz. In the present paper the work term has been taken into account to a first approximation. Also considered is the time lag arising from the heating of the nuclei due to bombardment by molecules of the condensing phase as well as the time lag resulting from an accommodation coefficient for the liquid nuclei different from unity. Calculations of the self‐nucleation of water vapor in air and nitrogen in air have been carried out. From the results it appears that the build‐up time is not appreciably lengthened by inclusion of the work term to a first approximation. The results also indicate that, unless the accommodation coefficient should have a value much lower than what appears to be reasonable from meager experimental evidence, the time lag alone could not account for the existing discrepancies between theory and experiment.