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A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations

Lockerby, Duncan A. and Reese, Jason and Gallis, Michael A. (2004) A wall-function approach to incorporating Knudsen-layer effects in gas micro flow simulations. In: Rarefied Gas Dynamics. AIP Conference Proceedings, 762 . American Institute of Physics, pp. 731-736. ISBN 0-7354-0247-7

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For gas flows in microfluidic configurations, the Knudsen layer close to the wall can comprise a substantial part of the entire flow field and has a major effect on quantities such as the mass flow rate through micro devices. The Knudsen layer itself is characterized by a highly nonlinear relationship between the viscous stress and the strain rate of the gas, so even if the Navier-Stokes equations can be used to describe the core gas flow they are certainly inappropriate for the Knudsen layer itself. In this paper we propose a "wall-function" model for the stress/strain rate relations in the Knudsen layer. The constitutive structure of the Knudsen layer has been derived from results from kinetic theory for isothermal shear flow over a planar surface. We investigate the ability of this simplified model to predict Knudsen-layer effects in a variety of configurations. We further propose a semi-empirical Knudsen-number correction to this wall function, based on high-accuracy DSMC results, to extend the predictive capabilities of the model to greater degrees of rarefaction.