Chapter 6: Gas Lubrication in Nano-Gap
Authors: Yonggang Meng 
Published: October 2009

IN COMPARISON WITH OTHER LUBRICATION TECHnologies, gas lubrication has the advantages of extremely low friction, no lubricant leakage, capabilities of withstanding high or low temperatures, and severe radiation. In 1897, Kingsbury [1] successfully developed the first air journal bearing. In the 1930s, air bearings were applied to gyroscope systems for navigation of missiles [2]. Air bearings were also successfully used in the man-made satellite launched by NASA in 1959. Today, gas lubrication has become a technology widely applied to precision instruments, the aerospace industry, and magnetic recording systems. Since the first hard disk drive, IBM350RAMAC, was invented in 1956 as a major external data storage element for computers, hard disk technology has continuously rapidly developed for five decades. When a hard disk drive works, a read/write magnetic head, also referred to as a slider, floats above a rotating platen medium disk with a small spacing, which was 20 μm at the time of IBM350RAMAC. The position of the slider relative to the rotating disk in the vertical direction is determined by the balance of the force of a flexible suspension spring with the resultant of the air pressure generated due to the hydrodynamic effect within the headdisk clearance. With a continuous increase of the areal recording density of hard disks, the head-disk physical gap, also called flying height, has been demanded to reduce substantially, from 20 [m in the first hard disk drive down to 10 nm in the latest products at present, keeping the headdisk interface be noncontacted. It is expected that the flying height may drop down to 3 nm approximately when the areal density of recording approaches to 1,000 Gb/in. in the near future [3]. Because air pressure within the head-disk working area is a decisive factor to ensure a steady and proper flying height, gas lubrication theory has been a foundation of the engineering design of a head-disk system. Meanwhile, study on ultra-thin film gas lubrication problems has become one of the most attractive subjects in the field of tribology during the past three decades. Historically, gas lubrication theory was developed from the classical liquid lubrication equation—Reynolds equation [4]. The first gas lubrication equation was derived by Harrison [5] in 1913, taking the compressibility of gases into account. Because the classical gas lubrication equation is based on the Navier-Stokes equation, it does not incorporate some gas flow characteristics rooted in the rarefaction effects of dilute gases. As early as 1959, Brunner's experiment [6] showed that the classical gas lubrication equation was not applicable to the situation where gas film thickness was less than 10 μm. One of the gas flow characteristics is the discontinuities in velocity and temperature on walls. The velocity discontinuity is referred to as velocity slip, which was recognized and predicted by Maxwell [7] in 1867. According to Maxwell theory, velocity slip is related to Knudsen number, Kn, which is a dimensionless characteristic parameter defined as the ratio of the mean free path of gas molecules to a characteristic length in a problem. By accounting for the effect of velocity slip into gas flow, Burgdorfer [8] derived a modified Reynolds equation for thin film gas lubrication in the small Knudsen number conditions in 1959. His theory is commonly known as the first-order slip-flow model because he used the linear model proposed by Maxwell to deal with flow slippage. Later, two other modified Reynolds equations based on second-order slip-flow and 1.5-order slip-flow models were respectively proposed for higher Knudsen number conditions [9,10]. However, the applicability of these slip-flow models at ultra-thin gas film conditions is questionable from the viewpoints of physical background and experiment verification. To deal with the ultra-thin film gas lubrication problem for arbitrary Knudsen numbers, Fukui and Kaneko [11] treated it in a different approach in their derivation. Instead of the fundamental momentum equilibrium equations of continuum mechanics, the linearized Boltzmann equation of the kinetic theory was solved to obtain the flow rates of fundamental Couette flow and Poiseuille flow. By applying the mass flow conservation law, they subsequently reached a generalized Reynolds equation, also called the F-K model. The F-K model is a refinement of Gans's work [12], and is widely accepted for analyzing the ultra-thin film gas lubrication problem in magnetic storage systems. Because the model is originated from the kinetic theory of dilute gases, it is also referred to as the molecular gas film lubrication (MGL) theory.