| Abstrakt: |
In a number of experiments (see [1], in which experimental papers are listed), diffusion has been observed in the radial direction in the process of flow of a mixture along tubes at low pressures. The heavier molecules accumulate near the tube axis. The attempt made in [1] to explain this phenomenon by the influence of the Burnett contribution to the diffusion did not lead to success, and the Burnett terms in the radial diffusion velocity indicate a motion of heavy molecules away from the tube axis. In the present paper, a complete analysis is given of this phenomenon. We consider the problem of the flow of a mixture along a cylindrical tube of finite length for given pressure difference ?p between its ends. On the basis of the hydrodynamic equations of the Burnett and super-Burnett approximations, a consistent asymptotic (with respect to the small parameter ?) solution is given; ? = (?p/p)R/L is the relative change in the pressure along the tube at a distance of order R (R and L are the radii and length of the tube). Radial diffusion occurs in the quadratic approximation in ?. It is shown that the radial diffusion velocity contains new terms not present in [1]; these are due to the inhomogeneity of the temperature and the pressure over the tube section, the expansion of the gas, and the super-Burnett correction to the diffusion velocity. The most important is the thermodiffusion term, which is determined by the hydrodynamic equations of the Navier-Stokes approximation. The remaining terms have order relative to it of Kn2 (Kn = < 1 >/R is the Knudsen number, and < 1 > is the mean free path of the molecules). The expression obtained for the diffusion velocity agrees in sign with the experiment. |
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