New models that describe gas flow behaviour in microtubes are presented. To avoid time-consuming calculations in solving the integral equation which is obtained from the microscopic point of view, the high-order slip-flow boundary condition is utilized to correct the gas flow in such a micron or submicron spacing. The proposed model can be applied to arbitrary Knudsen number conditions under the assumption that the bulk flow velocity is negligible compared with the sonic velocity of the gas. The analytical solution of the pressure distribution for the first-order slip-flow model is obtained. The results show that the first-order slip-flow model is in good agreement with this model. The nonlinear pressure distribution is due to gas compressibility. The dominant mechanism influencing the nonlinear pressure distribution comes from the rarefaction of gas and the inlet pressure. The rarefaction effect increases the pressure drop at the inlet region of the channel and decreases the pressure drop at the exit region of the channel. The decrease of inverse Knudsen number changes the pressure distribution from concave to almost linear and increases the mass flow.

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In this paper, the relations expressing the effects of roughness orientations and molecular mean free path on the roughness-induced flow factors are derived. Such consideration of the effects of roughness orientation on bearing performance is necessary when rotary actuators are used in magnetic recording systems. Using the perturbation approach and the coordinate transformation, the flow factors are derived and expressed as functions of the roughness orientations, the Peklenik numbers, the standard deviations of roughness heights of each surfaces, the inverse Knudsen number and the film thickness ratio of the lubrication film, where h/ sigma is the ratio of average film thickness to standard deviation of the composite roughness. Two orientation coefficients are proposed to reveal the combined effects of Peklenik number and orientation angle and the change of flow factors is analysed as the orientation coefficients vary. Finally, the static performance of a magnetic recording head flying above a rotating disc under the ultra-thin-spacing condition is analysed with roughness and rarefaction effects taken into account. The effects of surface characteristics of the moving surface on load capacity are more significant than those of the stationary surface.

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