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 be...

中文翻译：

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稀薄掩蔽：分形粗糙表面对气体滑块轴承的影响

对于超薄气体润滑，当流动几何结构按比例缩小到微米/纳米级时，表面积与体积比会急剧增加，尽管表面粗糙度很小，但可能在气体滑块轴承中发挥重要作用。然而，表面粗糙度对气体滑块轴承压力和负载能力（力）的影响却被忽视了。在本文中，基于广义雷诺方程，我们研究了气体滑块轴承的行为，其中滑块表面的粗糙度由 Weierstrass-Mandelbrot 分形函数以及 Couette 和 Poiseuille 流的质量流量表征是通过线性化的 Bhatnager-Gross-Krook 方程的确定性解获得的。我们的结果表明，与光滑通道相比，表面粗糙度降低了局部质量流量，但不同克努森数的库埃特流和泊肃叶流的减少量不同。结果，粗糙的压力上升和负载能力...