Rarefaction cloaking: Influence of the fractal rough surface in gas slider bearings

Abstract

For ultra-thin gas lubrication, the surface-to-volume ratio increases dramatically when the flow geometry is scaled down to the micro/nano-meter scale, where surface roughness, albeit small, may play an important role in gas slider bearings. However, the effect of surface roughness on the pressure and load capacity (force) in gas slider bearings has been overlooked. In this paper, on the basis of the generalized Reynolds equation, we investigate the behavior of a gas slider bearing, where the roughness of the slider surface is characterized by the Weierstrass-Mandelbrot fractal function, and the mass flow rates of Couette and Poiseuille flows are obtained by deterministic solutions to the linearized Bhatnager-Gross-Krook equation. Our results show that the surface roughness reduces the local mass flow rate as compared to the smooth channel, but the amount of reduction varies for Couette and Poiseuille flows of different Knudsen numbers. As a consequence, the pressure rise and load capacity in the rough bearing become larger than the ones in the smooth bearing in the slip and early transition flow regimes, e.g., a 6% roughness could lead to an increase of 20% more bearing load capacity. However, this situation is reversed in the free-molecular flow regime, as the ratio of the mass flow rates between Couette and Poiseuille flows is smaller than that in the smooth channel. Interestingly, between the two extremes, we have found a novel "rarefaction cloaking" effect, where the load capacity of a rough bearing equals to that of a smooth bearing at a certain range of Knudsen numbers, as if the roughness does not exist.