Droplet growth in a dilute vapor

Abstract
When the mass flux Γ to a liquid droplet is expanded in terms of a parameter α which is the ratio of the droplet size to the mean free path (inverse Knudsen number), one obtains a series of the form Γ=Γ(0)(1)α + Γ(2)a2lna + ···. As shown in a previous paper, the coefficients in this series are determined by integrals associated with sequences of successive collisions among a number of vapor molecules and the droplet. For a droplet surrounded by its pure vapor, we have calculated the coefficient Γ(1) of the first inverse Knudsen number correction to the free molecular growth rate Γ(0) assuming that the vapor molecules can be treated as hard spheres. For most nonequilibrium conditions, the ratio Γ(1)(0) turns out to be positive, rather than negative, as heretofore was assumed in the literature. This result implies that the reduced growth rate Γ/Γ(0) will pass through a maximum as a function of the Knudsen number.

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