Cylindrical Couette gas flow in the noncontinuum regime has been investigated using the boundary treatment derived from Maxwell's slip-flow model. It is shown that the tangential momentum accommodation coefficient plays an important role in determining the predicted velocity profile. The present analysis is in close agreement with previous analytical studies and shows good qualitative agreement with available direct simulation Monte Carlo data. The results predict the presence of an inverted velocity profile for the case where the inner cylinder rotates and the outer cylinder is stationary. However, our analysis further shows that the phenomenon of velocity inversion is only dependent on the accommodation coefficient of the outer cylinder. From the analysis, we derive specific criteria for the accommodation coefficient of the outer cylinder under which ͑i͒ no velocity inversion will take place, ͑ii͒ a partially inverted velocity profile will be observed, and ͑iii͒ a fully inverted velocity profile will be present. In contrast, when the outer cylinder rotates and the inner cylinder is stationary, it is shown that velocity inversion does not occur.

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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 ͑Ͼ1.0͒, 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.

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In this paper we present analytical investigations of the slip flow in a hard disk drive where the flying head is approximately 25 nm above the rotating disk. A new slip velocity model is developed, incorporating molecular dynamics to take into account the impact of molecular collisions which play an important role in the interactions between molecules and the solid surface. A modified Reynolds equation is derived based on the modified slip model. Analytical solutions for velocity distribution and flow rate, using the modified Reynolds equation are obtained. Non-dimensional flow rate for plane Poiseuille flow, pressure distributions and load-carrying capacities for slope flow are compared with those available in the literature. Comparison with first-order, second-order and 1.5-order slip models shows that the new model agrees reasonably well with the solution obtained from the linearized Boltzmann equation.

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