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.
|Name||AIP Conference Proceedings|
|Publisher||American Institute of Physics|
|Conference||24th International Symposium on Rarefied Gas Dynamics, Bari, Italy|
|Period||1/01/00 → …|
- knudsen layer
- gas microflows