A Database for Couette Flow Rate Considering the Effects of Non-Symmetric Molecular Interactions

2002 ◽  
Vol 124 (4) ◽  
pp. 869-873 ◽  
Author(s):  
Wang-Long Li
Keyword(s):  
Couette Flow ◽  
Molecular Interactions ◽  
Flow Rate ◽  
Molecular Gas ◽  
Mems Devices ◽  
Magnetic Head ◽  
Linearized Boltzmann Equation ◽  
Accommodation Coefficients ◽  
Molecular Gas Film Lubrication ◽  
Film Lubrication

A complete database for Couette flow rate (QCD,α1,α2,0.1⩽α1,α2⩽1.0,0.01⩽D⩽100, where D=inverse Knudsen number) for ultra-thin gas film lubrication problems is advanced. When the accommodation coefficients (AC) of the two lubricating surfaces are different α1≠α2, the Couette flow rate in the modified molecular gas film lubrication (MMGL) equation should be corrected. The linearized Boltzmann equation (under small Mach number conditions) is solved numerically for the case of non-symmetric molecular interactions α1≠α2. The Couette flow rate is then calculated, and the database is constructed. The present database can be easily implemented in the MMGL equation. In addition, the present database extends the previously published results for 0.1⩽α1,α2⩽0.7. The database for low ACs is valuable in the analysis and applications of MEMS devices (bushings of electrostatic micro motors, micro bearings, magnetic head/disk interfaces, etc.), and their future development.

Thermo-Molecular Gas-Film Lubrication (t-MGL) Considering Temperature Distributions and Accommodation Coefficients: Analyses by Quasi-Free-Molecular t-MGL Equation

2018 ◽  
Author(s):  
Shigehisa Fukui ◽  
Fumiya Shinohara ◽  
Ryota Asada ◽  
Hiroshige Matsuoka
Keyword(s):  
Specular Reflection ◽  
Flow Region ◽  
Molecular Flow ◽  
Molecular Gas ◽  
Gas Temperature ◽  
Accommodation Coefficients ◽  
Ambient Gas ◽  
Molecular Gas Film Lubrication ◽  
Local Temperature Distribution ◽  
Film Lubrication

In the present paper, the flying characteristics of a step slider flying in either air or He with a local temperature distribution of the disk are analyzed using the thermo-molecular gas-film lubrication (t-MGL) equation in the quasi-free-molecular flow region (quasi-free-molecular t-MGL equation: t-MGLqfm eq.). The gas temperature in the t-MGLqfm equation, τG, is assumed to be that in the free molecular limit, τGfm, defined by temperatures and accommodation coefficients at the disk, τW0, α0, and those at the slider, τW1, α1, respectively. The decreases in static spacing for the slider flying in He are significant. Moreover, the spacing decreases as the accommodation coefficients of the disk, α0, decreases, that is, as the ratio of specular reflection increases. The spacing fluctuation caused by a running wavy disk varies according to both the ambient gas (air/He) and the boundary accommodation coefficients.

Asymptotic Analysis of Ultra-Thin Gas Squeeze Film Lubrication for Infinitely Large Squeeze Number (Extension of Pan’s Theory to the Molecular Gas Film Lubrication Equation)

1995 ◽  
Vol 117 (1) ◽  
pp. 9-15 ◽  
Author(s):  
R. Matsuda ◽  
S. Fukui
Keyword(s):  
Film Thickness ◽  
Squeeze Film ◽  
Molecular Gas ◽  
Lubrication Equation ◽  
Linearized Boltzmann Equation ◽  
Flow Rate Coefficient ◽  
Load Carrying ◽  
Molecular Gas Film Lubrication ◽  
Squeeze Number ◽  
Film Lubrication

Ultra-thin gas squeeze film characteristics are analyzed by extending Pan’s asymptotic theory for infinite squeeze number to the molecular gas film lubrication equation which was derived from the linearized Boltzmann equation and is valid for arbitrary Knudsen numbers. The generalized asymptotic method is shown to solve the boundary value equation which contains the flow rate coefficient as a function of the product of pressure P and film thickness H. Numerical results are obtained for a circular squeeze film. The PH ratio and the load carrying capacity ratio to those of continuum flow both decrease when the average film thickness is less than several microns because of molecular gas effects.

On the Physical Meanings of Λ/Q˜p0 and σ/Q˜p0 in Molecular Gas Film Lubrication Problems

1996 ◽  
Vol 118 (2) ◽  
pp. 364-369 ◽  
Author(s):  
S. Fukui ◽  
R. Matsuda ◽  
R. Kaneko
Keyword(s):  
Flow Rate ◽  
Squeeze Film ◽  
Molecular Gas ◽  
Thrust Bearings ◽  
Molecular Gas Film Lubrication ◽  
Lubrication Characteristics ◽  
Bearing Number ◽  
Squeeze Number ◽  
Film Lubrication ◽  
The Continuum

To estimate molecular gas film lubrication (MGL) characteristics, we propose a modified bearing number Λ′ and a modified squeeze number σ′, which are, respectively, the conventional bearing Λ and squeeze number σ divided by the relative Poiseuille flow rate Q˜p0. Using Λ′ and σ′, the linearized MGL problem can be reduced to the continuum gas film lubrication problem and the MGL characteristics can be exactly estimated, if the characteristic flow rate corresponding to the spacing, Q˜p0, is known. For nonlinear MGL problems, the lubrication characteristics can be verified to be roughly estimated by Λ′ and σ′ both in rectangular slider bearings and in circular squeeze-film thrust bearings.

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