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Abstract

Gas lubrication theory is used widely in microelectromechanical systems such as microbearings, micropumps and microvalves. Because of microsize or even nanosize geometries, rarefaction and compressible effects will have an impact on the viscosity on flow in these devices. In this paper, the concept of effective viscosity is taken into account for non-continuum flows. The influence of the effective viscosity is incorporated in the analytical solutions of plane Poiseuille flow and flow in inclined channels. The results obtained in the slip, transition and free molecular regimes are compared with the existing first-order and second-order slip models and the linearized Boltzmann equation. It was found that the first-order model underestimates the slip effect while the second-order model overestimates the slip effect. The results obtained from the proposed slip model provide a more accurate approximation to the linearized Boltzmann equation.

Keywords

effective viscosity Knudsen number mean free path slip velocity microelectromechanical systems (MEMS)

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A slip model for gas lubrication based on an effective viscosity concept

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