Integrating multiple physical properties of microchannel gas flow to extend the Navier–Stokes equations over a wide Knudsen number range

Abstract

Gas flow in microchannels can be predicted by the Navier–Stokes equations with slip boundary conditions, but only limited to a slightly rarefied flow regime. To improve that, the considerations of the effective mean free path and the volume diffusion phenomena were introduced to the non-kinetic model by previous studies separately. In this study, these two effects, along with the newly proposed wall-to-wall-collision effect, are integrated to extend the Navier–Stokes equations for the planar Poiseuille flows over a wide Knudsen number (Kn) range. The dimensionless mass flow rates calculated by the proposed model can be consistent among different working fluids or flow conditions and mostly agree with the experimental data with Kn≅0.03−57. This analysis facilitates an understanding of the mutual effects on the physical properties of microchannel gas flows and shows a promising prospect for developing a non-kinetic model for highly rarefied flows.