Effect of a boundary condition on the cylindrical Couette flow of a rarefied gas

The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated on the basis of kinetic theory. We perform a numerical analysis of the (BGK model) Boltzmann equation for a wide range of the Knudsen number and an asymptotic analysis for small Knudsen numbers employing two kinds of kinetic boundary conditions on the cylinders. One is the modified Maxwell-type boundary condition (proposed by S. K. Dadzie and J. G. Méolans) and the other is the Cercignani–Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. Our main interest is in the effect of those boundary conditions on the inverted velocity profile. The results show that the onset of the inversion is practically controlled by the tangential accommodation only.