Rarefied Gas Flows in Long Circular and Square Microchannels

Comprehensive reviews of rarefied gas flows in circular and square microchannels over wide ranges of rarefaction show large differences in Poiseuille numbers and reduced flow rates when identical length scales are used. The continuum Poiseuille numbers differ by 12.5%, and the free molecule reduced flow rates differ by 11%. This work demonstrates that the product of reduced flow rate and continuum Poiseuille number differs by a maximum of 1.6% over wide ranges of Knudsen numbers, and maximum differences occur at and near the Knudsen minimum, which occurs at the same rarefaction when identical length scales are used. A novel definition of dimensionless mass flow rate shows that it is related to the product of the reduced flow rate and continuum Poiseuille number, and accurate correlations are proposed for two ranges of the rarefaction from the free molecule regime to the Knudsen minimum and from the Knudsen minimum to the hydraulic regime. Models are proposed for Poiseuille–Knudsen number relations for the slip flow regime and the transition from the Knudsen minimum to the hydraulic regime. This work demonstrates that rarefied gas flows in circle and square microchannels are equivalent over wide ranges of rarefaction. The circle–square models can be used to model rarefied gas flows in regular polygonal microchannels and selected trapezoid microchannels having flow characteristics similar to flow in square microchannels.