Use of the degenerated Reynolds equation in solving the microchannel flow problem

Abstract

In this paper, the author proposes that the generalized Reynolds equation employed in the gas film lubrication problems, where the flow rates of the Poiseuille flow are calculated from the Boltzmann equation, can be degenerated for solving the microchannel flow problem in the transitional regime. 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 method and the IP method. The lattice Boltzmann method solution of the microchannel flow is examined by comparison with the degenerated Reynolds equation calculations and the disagreement in the pressure distribution confirms that the lattice Boltzmann method is unsuitable for the solution of the microelectromechanical systems (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.