Nonplanar oscillatory shear flow: From the continuum to the free-molecular regime

The case of oscillatory cylindrical Couette gas flow has been used to investigate the effects of curvature and rarefaction on the dynamic velocity and shear stress profiles. In addition, Stokes’ second problem for a curved surface has been extended to include the effects of slip. It is shown that curvature plays a more important role than slip in determining the penetration depth, but the effects of slip are enhanced if the surface is nonplanar. The current analysis for the oscillatory cylindrical Couette problem presents new analytical solutions in the slip-flow regime and the free-molecular regime. For both cases, direct simulation Monte Carlo data are in good agreement with the analytical solutions. To complete the study throughout the entire Knudsen regime, the direct simulation Monte Carlo method was used to predict the velocity and shear stress in the transition regime. There are marked differences between the solutions obtained for the inner and outer cylinders oscillating, especially at low frequencies. It is shown that if the Knudsen number is large ( > 1.0 ) , the shear stress tends to the solution for the planar Couette case in the free-molecular regime and is essentially independent of the oscillatory frequency. Moreover, we show that the phenomenon of velocity inversion can occur for oscillatory flow provided the accommodation coefficient of the outer cylinder is small and the frequency is not too high.