Abstract

Kirkaldy (1958) has raised objections to the usual quasi-stationary analysis (QS) of evaporation and condensation processes. Fuchs’ (1959) attempt to study the validity of QS is marred by a number of errors (which are identified in the present work). This paper presents a critical examination of QS, largely based on mathematical methods capable of establishing the accuracy of QS in cases where the exact solution is unavailable.

Exact similarity solutions for n-dimensional condensation (zero initial radius) are presented. These, and an exact solution for diffusion about a spherical body of constant radius, provide points of departure for the development of two simple and powerful approximate methods, a perturbation method and a continuity-preserving quasi-stationary analysis (CPQS). The perturbation method provides an apparently highly accurate means of using the relevant known exact solutions; but it is less versatile than CPQS. Under a wide range of circumstances, CPQS, which satisfies the diffusion equation in the Pohlhausen sense, correctly indicates the order of magnitude of the errors of QS. Where both methods apply, they give mutually consistent results.

The study indicates, that, despite the fundamental objections to QS, it is sufficiently accurate for many meteorological purposes. The success of QS arises from the particular circumstances of the three-dimensionality of the processes and of the very small ratio of vapor density differences to the density of the condensed phase. Further study is needed of the psychrometric aspects of certain problems, and of processes where conditions at the droplet surface are radius-dependent.

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