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

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 ( K n) 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 K n approximately equal to 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.

Automated summary

This study integrates the effects of effective mean free path, volume diffusion, and wall-to-wall collisions into the Navier-Stokes equations, extending its applicability to a wide range of Knudsen numbers. The dimensionless mass flow rates calculated by the proposed model are consistent across different conditions and largely agree with experimental data.