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New Development In The Study Of Micro Flows
Date：2005-08-16Source：
The paper “Use of the Degenerated Reynolds Equation in Solving the Microchannel Flow Problem”of Professor C. Shen concerning the research in micro flows has been recently published in Physics of Fluids, 17:0460101-06(2005).
Reynolds as early as in 1886 proposed to use the global mass conservation across the cross section of the gas flow to solve the gas film lubrication problem and obtained the Reynolds equation (Reynolds ,1886). This is an appropriate method for solving the gas film bearing problem in the write-read head of the hard disk drive. The method has been developed by Burgdorfer(1959) and Fukui & Kaneko(1988) to treat the air bearing problem in slip and transitional regimes. In this paper Professor C. Shen proposes that the generalized Reynolds equation employed in the gas film lubrication problems, where the flow rate of the Poiseuille flow are calculated from the Boltzmann equation, be degenerated for solving the microchannel flow problem in the transitional regime. Thus the strict kinetic solution of the pressure distribution and the mass flow rate of rarefied gas in microchannel is obtained. Using this approach, the calculated results of pressure distribution in long microchannels show excellent agreement with the experimental data and the result of the information preservation (IP) method. The results in short microchannels show excellent agreement with the direct simulation Monte Carlo (DSMC) method and the IP method. Thus the IP method in the two-dimensional case (C. Shen, J. Fan, C. Xie, 2003) now is verified by the strict kinetic theoretical results. The lattice Boltzmann method (LBM, Nie, G. D. Doolen, S. Chen, 2002) has been shown as unfeasible for solving the microchannel flow in transitional regime by Shen and Tian ((Shen C, Tian DB, Xie C, Fan J, 2004) by comparison with the DSMC calculations. In this paper LBM is reexamined by comparison with the degenerated Reynolds equation calculations and the disagreement in the pressure distribution reconfirms that the lattice Boltzmann method is unsuitable for the solution of the MEMS flows in transitional regime. For microchannel flows, the degenerated Reynolds equation can serve as a criterion having the merits of kinetic theory for testing various methods intending to solve rarefied gas flow problems in MEMS devices in the transitional flow regime.
Reynolds as early as in 1886 proposed to use the global mass conservation across the cross section of the gas flow to solve the gas film lubrication problem and obtained the Reynolds equation (Reynolds ,1886). This is an appropriate method for solving the gas film bearing problem in the write-read head of the hard disk drive. The method has been developed by Burgdorfer(1959) and Fukui & Kaneko(1988) to treat the air bearing problem in slip and transitional regimes. In this paper Professor C. Shen proposes that the generalized Reynolds equation employed in the gas film lubrication problems, where the flow rate of the Poiseuille flow are calculated from the Boltzmann equation, be degenerated for solving the microchannel flow problem in the transitional regime. Thus the strict kinetic solution of the pressure distribution and the mass flow rate of rarefied gas in microchannel is obtained. Using this approach, the calculated results of pressure distribution in long microchannels show excellent agreement with the experimental data and the result of the information preservation (IP) method. The results in short microchannels show excellent agreement with the direct simulation Monte Carlo (DSMC) method and the IP method. Thus the IP method in the two-dimensional case (C. Shen, J. Fan, C. Xie, 2003) now is verified by the strict kinetic theoretical results. The lattice Boltzmann method (LBM, Nie, G. D. Doolen, S. Chen, 2002) has been shown as unfeasible for solving the microchannel flow in transitional regime by Shen and Tian ((Shen C, Tian DB, Xie C, Fan J, 2004) by comparison with the DSMC calculations. In this paper LBM is reexamined by comparison with the degenerated Reynolds equation calculations and the disagreement in the pressure distribution reconfirms that the lattice Boltzmann method is unsuitable for the solution of the MEMS flows in transitional regime. For microchannel flows, the degenerated Reynolds equation can serve as a criterion having the merits of kinetic theory for testing various methods intending to solve rarefied gas flow problems in MEMS devices in the transitional flow regime.