Analytical modeling of ultra-thin-film bearings

We develop an analytical model based on kinetic theory of gases and we apply this to thin-film bearings that are frequently encountered in data storage systems. This model incorporates the effects of the higher-order stress tensor and temperature gradient in the governing equations and it can be used for a wide range of Knudsen numbers covering the complete slip regimes. The corresponding modified Reynolds equation is obtained and the flow rate is plotted versus the inverse Knudsen number. Pressure distributions along the air bearing at various Knudsen numbers, bearing numbers, Mach numbers and pitching angles are presented and the load carrying capacities are also obtained. The results are compared with the first-order and second-order slip models. It is observed that the current work is in very good agreement with solutions obtained from the linearized Boltzmann equation and direct simulation Monte Carlo results.