The precise knowledge of the force and moment generated by the air squeezed under the read-write slider by the rotating disc is an engineering necessity in designing the air bearing surface slider. This paper reviews methods addressing the thin gas film bearings problem. It firstly reviews briefly the relatively well-known two methods of calculations of the microgas flows under flying head sliders, the generalized Reynolds equation, having given a number of useful results of slider design, and the DSMC method, which is precise and appropriate for the flow of complex configurations but is restricted to miniature (~micrometer) size sliders. The main purpose of the paper is to introduce to the reader an alternative method, the information preservation (IP) method, for use in simulation of the flows under air bearing surfaces. Some recent results of IP simulation of slider flows published on conference proceedings are introduced here.

The problem of thin gas film bearings in the gap between the flying head slider and the magnetic disc now has an increasing interest among scientists concerning computation of actual problems of micro gas flows. To calculate precisely the force and moment generated by the air squeezed by the rotating disc is essential in the design of the head slider. The typical slider length in disk drives is about 1 mm and the width is the same order of the length. The size of the clearances between the slider and the disc is much smaller and is constantly decreasing to increase the recording density. The flying height in the early stage of the disc recording head was of the order of 8^{2} and 1 Tbit/in^{2} in consideration require sliders to have a flying height of 5

The thin film air flow between the slider air bearing surface and the disc is most appropriately described by the Reynolds equation which is a differential equation relating the pressure

The Reynolds equation was first used in the continuum regime, the derivation is enlightening and with its essential assumption clearly revealed, and its framework can be easily used in the slip flow and transitional flow cases; so we give a simplified version of derivation of it. For simplicity the two-dimensional case is considered (see Figure

A schematic model of the thin film air bearing flow.

Writing the continuity equation

In [

Velocity profiles and the flow rates of the slip-less and slip Couette flows (the transitional case also is symmetric relative to the central line but is not shown here).

Fukui and Kaneko [

showed good agreement of the generalized Reynolds equation with the results of DSMC simulation; this just confirms that the generalized Reynolds equation is a mass conservation equation in form (although some framework of the N-S equation has been used) but in fact it balances the flow rates of Poiseuille flow and Couette flow calculated from the kinetic theory; so it has the kinetic theoretical merit and can be used to solve the air bearing problem in the entire transitional flow regime.

By analogy with the above derivation of Reynolds equation for the two-dimensional case, it is a simple matter to derive the unsteady and three-dimensional Reynolds equation in the following form (cf., e.g., the 3D Reynolds equation shown in [

Fukui and Kaneko [

In deriving the Reynolds equation in the form of (

In applying the generalized Reynolds equation to the modern authentic sliders having rails on the peripheries (sometimes with thin terraces on them) and on the center part of the slider and fully recessed regions (see, e.g., the NSIC (National Storage Industry Consortium) slider cited in [

The direct simulation Monte-Carlo (DSMC) method [

The information preservation (IP) method is proposed in [

Omitting description of IP simulation of many different flow fields we give here only some detailed simulation of micro channels, for the geometrical forms and flow patterns of two cases of channel and disc flow are similar. Besides there have been two means to test the calculation of the channel flow to show the validity of the IP method. Firstly abundant experimental results of pressure distribution and flow rated through the channel for Knudsen numbers in the transitional regime. And the degenerated Reynolds equation suited for channel flows has been suggested to be derived easily for the generalized Reynolds equation originally derived for the flows under flying sliders and has the merit of kinetic theoretical test stone. So we use both the experimental data and strict theoretical computations to show the validity of the IP method for calculation of the microflows.

The channel flow of fluids has a long history beginning with the famous Poiseuiulle flow, that is, the fluid flow driven by constant pressure gradient. But for gas because of the global mass conservation the pressure distribution along the channel could not be linear and the gas Poiseuille flow with constant pressure gradient is only a hypothetic flow. With the emergence of the MEMS (micro-electromechanical systems) and the technique of manufacture of them, LIGA (abbreviation of German words Lithographie Galvanoformung Abformung) and EDM (electrodischarge machining), fine experiments were carried in new micromachined channels (see, e. g., [

The generalized Reynolds equation originally is derived for application in the thin film air bearing problem with the lower plate moving with a velocity

We emphasize here, that as the assumption

The microchannel flow problem was solved by IP method in [

Comparison of streamwise pressure distributions of helium flow given by IP [

Comparison of the pressure distribution in a

Comparison of the mass flow rate obtained from global mass conservation, transitional flow, (

As shown in the above comparisons the IP method gives pressure and mass flow results of microchannels in excellent agreement with the degenerated Reynolds equation and also experimental data; so it can be considered as a reliable tool in dealing with the microscale slow gas flows including the micro flows under flying sliders. The detailed IP method simulation of internal rarefied gas flows can be found in [

The IP method was applied to simulate the 2D flat slider problem [

The pressure distribution of the slider bearing for

In [

The contours of

Note that the DSMC sample process starts and lasts 0.2 million time steps but for IP sample only 200 time steps are used. The total computation time (the time of convergence process plus the time of sampling process) of the DSMC method is about 100 times longer than the IP method. When the slider surface speed is lower, for example, when

The contours of

The 3D slider with complex configuration simulated by IP method in [

Configuration of a slider used in simulation in [

The simulated results of the pressure distribution by both IP method and DSMC method are shown in Figure

The contours of

(1) The precise calculation of the thin gas film bearings characteristics is an engineering necessity in designing the air bearing surface slider. Various calculation methods are desirable to meet the need of design.

(2) The generalized Reynolds equation is now successfully been used to calculate the air bearing parameters in sliders with complicated air bearing surfaces and accomplished a number of design purposes. As the calculation of complex configuration, slider flows by both DSMC and IP method shows the modern complex configuration sliders may violate the condition

(3) The DSMC method is appropriate for simulation of thin film flows under sliders. But the computational process is very time-consuming and only simulation results of sliders of miniature (micrometer, not millimeter, i.e., authentic) sizes are available. The merit of DSMC in the microflows under flying slider is in that its results can be compared with other methods for small size and complicated configurations to check the other methods’ feasibility.

(4) The IP method has been tested in the problem of micro channel flows by DSMC, experimental and kinetic theoretical results. It was used to calculate the 2D and 3D flows under flat sliders. The result of simulation of flow under an authentic complex configuration slider of small size is in good agreement with the DSMC method. It is a promising alternative method in simulating the microflow field under authentic size, authentic configuration air bearing surfaces.

Numerical constant

Numerical constant

Molecular thermal velocity

The width of the slider along

Height of the gap between the head slider and the magnetic disc

Minimum height of the gap between the head slider and the magnetic disc

Dimensionless height

The length of the slider along

Pressure

Pressure at the front edge of the slider

Flow rate

Flow rate of the Poiseuiulle flow

Flow rate of the Poiseuiulle flow for continuum flow case

Flow rate of the Poiseuiulle flow for slip flow case

Flow rate of the Poiseuiulle flow for transitional flow case

Dimensionless flow rate of the Poiseuiulle flow for transitional flow case

Time

Dimensionless time

Gas velocity along

Molecular information velocity in IP method

Boundary velocity of the magnetic plate along

Information velocity of cells in IP method

Gas velocity along

Gas velocity along

Boundary velocity of the magnetic plate along

Length direction along the moving disc surface

Dimensionless coordinate

Direction vertical to the moving disc surface

Width direction along the moving disc surface

Dimensionless coordinate

Density of the gas

Viscosity of the gas

Reflection coefficient

Mean free path of the gas

Bearing number

Bearing number calculated by

Bearing number calculated by

Factor proportional to

Angular velocity of the rotating disc.

Direct simulation Monte Carlo

Electrodischarge machining

Information preservation

Lithographie Galvanoformung Abformung

Micro-electromechanical systems

National Storage Industry Consortium.

The author would like to express his appreciation for the support of Natural Science Foundation of China through Grants 10621202 and 90205024. He also thanks Mr. Jun Li for his help in formulating this manuscript.