The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen [Ann. Phys. 4, 75 (1909)]. Previously, the phenomenon has been studied with models of the Boltzmann equation, but results for the Boltzmann equation itself have not been reported. In the present paper, proceeding from recent studies, first the SN numerical algorithm for solving the linearized Boltzmann equation for the cylindircal geometry is outlined. Then, explicit numerical results for a rigid sphere gas and the boundary condition of diffuse specular reflection are obtained. The results show a minimum of the flow rate, and generally, provide a good description of the experimental data.
The problem of isothermal condensation onto a spherical particle for a vapor diffusing through a background gas is considered. Accurate numerical results for the condensation rate and density profile in the Knudsen layer, for arbitrary mass ratio (background/vapor) and Knudsen number, are obtained by use of the SN method and the resulting theoretical values are compared with recent experimental data. The present theoretical results correspond to an assumption of rigid sphere molecular interactions, but the development is sufficiently general that results for other molecular force laws could also be obtained.
The half-space problem of isothermal condensation of a vapor diffusing through a background gas is considered. Accurate numerical results for the jump distance and density profile in the Knudsen layer for arbitrary mass ratio (background/vapor) are obtained via the use of the SN method. The results correspond to the assumption of rigid sphere molecular interaction, but the development is sufficiently general that results for other molecular force laws could also be obtained. Finally, a correlation for the jump coefficient as a function of the mass ratio is given.
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