On The Reynolds Equation For Linearized Models Of The Boltzmann Operator

Rarefied gas flows in ultra‐thin film slider bearings are studied in a wide range of Knudsen numbers. The generalized Reynolds equation, first derived by Fukui and Kaneko (1987, 1988, 1990) on the basis of the linearized Bhatnagar‐Gross‐Krook (BGK) Boltzmann equation (Bhatnagar et al. 1954), has been extended by considering a more refined kinetic model of the collisional Boltzmann operator, i.e., the linearized ellipsoidal statistical (ES) model, which allows the Prandtl number to assume its proper value (Cercignani and Tironi 1966). Since the generalized Reynolds equation is a flow rate–based model and is obtained by calculating the fundamental flows in the lubrication film (i.e., the Poiseuille and Couette flows), the plane Poiseuille‐Couette flow problem between parallel plates has been preliminarily investigated by means of the linearized ES model. General boundary conditions of Maxwell's type have been considered by allowing for bounding surfaces with different physical properties.

[1]  Francis J. Alexander,et al.  Direct simulation Monte Carlo for thin‐film bearings , 1994 .

[2]  Carlo Cercignani,et al.  Mathematical Methods in Kinetic Theory , 1970 .

[3]  C. Shen,et al.  Statistical Simulation of Thin-Film Bearings , 2005 .

[4]  Carlo Cercignani,et al.  Variational approach to gas flows in microchannels , 2004 .

[5]  S. A. Schaaf.  Rarefied Gas Dynamics , 1969 .

[6]  C. Cercignani,et al.  Flow of a Rarefied Gas between Parallel and Almost Parallel Plates , 2005 .

[7]  M. N. Kogan,et al.  Flow of rarefied gas between two parallel plates , 1975 .

[8]  C. Cercignani,et al.  Plane Poiseuille Flow with Symmetric and Nonsymmetric Gas‐Wall Interactions , 2004 .

[9]  Mikhail Naumovich Kogan,et al.  Rarefied Gas Dynamics , 1969 .

[10]  Robert M. Crone,et al.  A new molecular gas lubrication theory suitable for head-disk interface modeling , 1999 .

[11]  K. L. Deckert.  Computer-aided design of silder bearings in magnetic disk files , 1990 .

[12]  C. Cercignani.  Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations , 2000 .

[13]  C. Cercignani.  The Boltzmann equation and its applications , 1988 .

[14]  Carlo Cercignani,et al.  Plane Poiseuille-Couette problem in micro-electro-mechanical systems applications with gas-rarefaction effects , 2006 .

[15]  Norio Tagawa.  State of the art for nanospacing flying head slider mechanisms in magnetic recording disk storage , 1993 .

[16]  Weidong Huang,et al.  The Effect of the Accommodation Coefficient on Slider Air Bearing Simulation , 2000 .

[17]  S. Fukui,et al.  Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report—Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow , 1988 .

[18]  Some applications of a linearized kinetic model with correct prandtl number , 1966 .

[19]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[20]  Carlo Cercignani,et al.  Slow rarefied flows : theory and application to micro-electro-mechanical systems , 2006 .

[21]  Shigehisa Fukui,et al.  Analysis of Ultra-thin Gas Film Lubrication Based on the Linearized Boltzmann Equation : Influence of Accommodation Coefficient , 1987 .

[22]  Shigehisa Fukui,et al.  A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems , 1990 .