О бародиффузии при медленных течениях газовой смеси

Barodiffusion in slow flows of a gas mixture is studied with an approximation using hydrodynamic equations of motion for the individual mixture components. It is shown that consideration of the viscous momentum transfer and the contribution of Knudsen layers for the mixture flowing in a channel has a considerable effect on the value of the barodiffusion factor. The relations are obtained for the mean diffusion fluxes of components and for the total flux of the mixture in a circular cylindrical capillary; these relations are valid for moderately small Knudsen numbers used for calculation of the diffusion baroeffect and separation effect when the gas mixture flows in a set of capillaries connecting two volumes. The modification of the relations for the barodiffusion factor (and for the diffusion slip coefficient cross-linked with it) allows interpreting the sign alteration of these effects observed experimentally for some gas mixtures at intermediate Knudsen numbers.

A force acting on an oblate spheroid with discontinuous surface temperature in a slightly rarefied gas

An oblate spheroid, the respective hemispheroids of which are kept at different uniform temperatures, placed in a rarefied gas at rest is considered. The explicit formula for the force acting on the spheroid (radiometric force) is obtained for small Knudsen numbers. This is a model of a vane of the Crookes radiometer. The analysis is performed for a general axisymmetric distribution of the surface temperature of the spheroid, allowing abrupt changes. Although the generalized slip flow theory, established by Sone (Rarefied Gas Dynamics, vol. 1, 1969, pp. 243–253), is available for general rarefied gas flows at small Knudsen numbers, it cannot be applied to the present problem because of the abrupt temperature changes. However, if it is combined with the symmetry relations for the linearized Boltzmann equation developed recently by Takata (J. Stat. Phys., vol. 136, 2009, pp. 751–784), one can bypass the difficulty. To be more specific, the force acting on the spheroid in the present problem can be generated from the solution of the adjoint problem to which the generalized slip flow theory can be applied, i.e. the problem in which the same spheroid with a uniform surface temperature is placed in a uniform flow of a rarefied gas. The analysis of the present paper follows this strategy.

Analyse du flux de Poiseuille bidimensionnel via l'équation de Boltzmann

The two-dimensional Poiseuille flow induced by an external force is analysed in the framework of Boltzmann–Maxwell kinetic theory. In the limit of small Knudsen numbers (Kn [Formula: see text] 0.1), Boltzmann's nonlinear equation, written in terms of moments, is solved using perturbation theory. In our results, the hydrodynamic variable profiles are determined up to the fourth order in the perturbation parameter. Nonetheless, the method of solution remains valid to obtain all physical quantities of a gas undergoing Poiseuille flow. The major conclusion of our analysis has two elements. First, the profiles of hydrodynamic variables in two dimensions differ quantitatively (and sometimes qualitatively) from those in plane geometry. Thus, the Poiseuille flow representation in a cylindrical pipe is more accurate than in a canal between two parallel planes. Second, a critical comparaison between the theoretical predictions of the kinetic theory and those of Navier–Stokes shows that the two theories agree only up to the first order of perturbation. Starting at the second order, the difference between the two increases. Thus, within the limit of validity of the present study, the description by Navier–Stokes remains insufficient to predict the correct profiles for the hydrodynamic variables in the Poisseuille flow. [Journal translation]