Drag on a sphere in a slow flow of a binary mixture of rarefied gases

Abstract

The drag force on a sphere in an isothermal binary mixture of rarefied gases is calculated on the basis of the McCormack model for the linearized Boltzmann equation. The diffuse scattering of the gas–surface interaction law is assumed as the boundary condition. The rigid-spheres model of interatomic interaction potential is used as well as ab initio potentials for helium, argon, and krypton gases. The force is obtained in a wide range of the gas rarefaction, which covers the free molecular, transition, and slip regimes of the gas flow. In the free molecular and slip flow regimes, the problem is solved analytically, while in the transition regime, the system of kinetic equations is solved numerically via the discrete velocity method optimized to overcome the problem of discontinuity of the distribution function of molecular velocities on the convex surface. The calculations are carried out for the mixtures helium–argon and helium–krypton at 300 K. In the slip flow regime, the data available in the literature for the viscous slip coefficient of the helium–argon mixture are used, while for the mixture helium–krypton, it is calculated. The influence of the interatomic interaction potential, molar fraction, and ratio of atomic mass of species in the mixture on the drag force is analyzed.