The failure of theory to predict the density distribution of gas flowing through a tube under free molecular conditions

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Abstract
The equations describing the density distribution of molecules flowing through a tube have been solved numerically for the practical case of uniform temperature and negligible density beyond the tube exit. The shape of the radial density profile is found to be symmetrical about the transverse mid-plane of the tube. The axial density, normalised with respect to the source density, is approximately equal to the Clausing function for the rate of impingement of molecules on the walls of the tube. Several approximations have been proposed for the entrance and exit densities for use in molecular beam formation calculations and that of Ivanov and Troitskii (1963) comes closest to the authors' results. These are not, however, in good agreement with the measurements of Kurepa and Lucas (1981). It is suggested that the usual assumption, that molecules leave a surface with a cosine distribution and without surface diffusion, requires modification.

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