The critical accommodation coefficient for velocity inversion in rarefied cylindrical Couette flow in the slip and near free-molecular regimes

This paper investigates velocity inversion in rarefied cylindrical Couette flow at the two extremes of the Knudsen number regime. For low Knudsen numbers, velocity inversion is independent of the accommodation coefficient of the inner cylinder and will only occur when the accommodation coefficient of the outer cylinder lies below a critical value. It is shown that this critical value depends upon the Knudsen number and the ratio of the outer and inner cylinders. In addition, velocity inversion is also investigated in the free-molecular and near free-molecular regimes. For the specific case of specular reflection at the outer cylinder, the present study has identified two distinct categories of molecules within the flow. The first category consists of particles that collide alternately with the inner and outer cylinders whilst the second consists of particles that never collide with the inner cylinder. It is shown that recognizing these different categories of particles is the key to understanding the velocity inversion process in the near free-molecular flow regime. Finally, for large but finite Knudsen numbers, our DSMC simulations demonstrate that velocity inversion does occur provided the accommodation coefficient of the outer cylinder is sufficiently small.