A NEW SLIP MODEL FOR GAS LUBRICATION Sheng Shen Mechanical Engineering Department Massachusetts Institute of Technology, Cambridge, MA 02139, USA sshen1@mit.edu Gang Chen Mechanical Engineering Department Massachusetts Institute of Technology, Cambridge, MA 02139, USA gchen2@mit.edu Robert M Crone Seagate Technology, Minneapolis, MN, 55417, USA Robert.M.Crone@seagate.com Manuel Anaya-Dufresne Seagate Technology, Minneapolis, MN, 55417, USA Manuel.AnayaDufresne@seagate.com ABSTRACT In this paper, a new slip boundary condition is derived using the solution of the Boltzmann equation. The physical mechanisms of velocity slip in rarefied gas flow are discussed and emphasized. The Poiseuille flow rates predicted by the new slip model show better agreements with those calculated from the existing slip models such as 1st, 2nd, and 1.5th slip order. Based on the new slip model, a new modified Reynolds equation is also proposed to predict the pressure field in gas lubrication problem. INTRODUCTION In the current hard drive design, molecular rarefaction effects are incorporated into the generalized Reynolds lubrication equation via correction of the Poiseuille flow rate. Two approaches have been proposed to calculate the Poiseuille flow rate. One is based on a slip model, using Navier-Stokes equation with various velocity slip boundary conditions. The other approach utilizes a molecular-based model. The most typical molecular-based model is Fukui-Kaneko (FK) model [1] based on solving the linear Boltzmann equation [2], which is believed to give the most accurate results for arbitrary Knudsen numbers among the existing compressible lubrication equations. Huang [3] used the direct simulation Monte Carlo (DSMC model) to solve the three-dimensional nanoscale gas film lubrication problem and compared to the solution of FK model. Overall, the two solutions agree well with each other. Compared with molecular-based models, slip models are simpler and more efficient because they allow solving gas film lubrication problems using the continuum description. The first expression of slip velocity can be traced back to the work of Maxwell [4]. Burgdorfer [5] first applied the Maxwell result for the lubrication problem, which was subsequently called the first order slip velocity boundary condition, to derive a modified Reynolds equation. However, the first order velocity-slip boundary condition cannot explain the existence of the Knudsen minimum [2]. Hsia and Domoto [6] expanded the velocity slip at the boundaries to second order directly and proposed the corresponding Reynolds equation. Although the second order slip model does predict the existence of the Knudsen minimum, it significantly overpredicts the flow rates at large Knudsen numbers. Mitsuya [7] thereby corrected the second-order slip coefficient and presented the 1.5 order slip model. Hajicontantinou [8] modified Cercignani’s second-order slip model [9] to propose a new two-second order slip model for hard sphere gases. However, his model just extends the applicability of the Navier-Stokes Copyright©2006 by ASME 1 Proceedings of IMECE2006 2006 ASME International Mechanical Engineering Congress and Exposition November 5-10, 2006, Chicago, Illinois, USA IMECE2006-16275 Downloaded from https://asmedigitalcollection.asme.org/IMECE/proceedings-pdf/IMECE2006/47829/71/2782922/71_1.pdf by Seagate Technology, Robert Crone on 28 May 2020