The air-bearing shear force in the head-disk interface (HDI) of hard disk drives is a dominant factor determining the motion and instability of the lubricant layer, which plays an important role in drive reliability. In this communication, an analytical formula, which is applicable to the flow of an arbitrarily rarefied gas in the HDI and is more general than that based on the first-order slip theory, is presented based on the Boltzmann equation. When a hard sphere model is used for the air molecules, the formula reduces to that based on the first-order slip theory, and it thus validates previous studies based on the latter formula.Keywords Air bearings Á Head-disk interface Á Shear force Á HDD reliabilityThe head-disk interface (HDI), as shown in Fig. 1, is the region between a slider and a disk in hard disk drives. The slider, carrying a read-write transducer at the trailing edge, flies over the disk which rotates and has a local speed U around 10-30 m/s. A specifically designed pattern called the air-bearing surface (ABS) exists on the slider's surface facing the disk. In the HDI, the flow of air, setup by the moving disk and compressed by the ABS, creates pressure that balances the suspension load on the slider, and it serves as a cushion layer to stabilize the motion of the slider and reduce contact between the slider and the disk. To further reduce the possibility of the slider's impact on the disk, and mitigate its effect when contact occurs, a layer of lubricant, with thickness of about 1 nm, is coated on the disk. In modern hard disk drives, the minimum flying height of the slider has been reduced to less than 5 nm. This leads to strong interactions between the slider, the air flow, and the lubricant. Experiments have shown that the lubricant, due to its mobility, deforms and creates specific patterns due to these interactions [1,2]. It has also been experimentally observed that the lubricant in some cases transfers from the disk to the slider [3], which decreases the effect of the lubricant as a protecting layer for the disk and may alter the performance of the slider. Thus, despite its very small thickness, the lubricant layer plays an important role in the reliability of hard disk drives [4].Although the thickness of the lubricant layer is often less than 1 nm, experiments have shown that it can still be modeled using continuum theory with a modification to its viscosity [5]. Inspired by this finding, many papers, mostly numerical analyses, have been published on the deformation and instability of the lubricant layer in the framework of continuum theory [3,4,[6][7][8][9][10]. It is generally agreed [4,8,10] that the shear force induced by the air flow is a dominant factor determining the lubricant dynamics. However, in all of these studies, the shear force was represented by either an oversimplified model [4,6] that contains only the Couette flow component or a model based on the first-order slip theory [8]. Wu [8] compared results based on these two models and showed that the approach to mo...