Slip Flow Models for Gas Flows in Rectangular, Trapezoidal, and Hexagonal Microchannels

What is it about?

Since the original experimental work of Knudsen over 100 years ago, many analytical, experimental and numerical works dealing with rarefied gas flows in Rectangular, Trapezoidal and Hexagonal Microchannels reveal significant apparent discrepancies. The differences occur because there are two different approaches to this important problem. For slip flow one model gives reduced flow rates in terms of rarefactions while the second model gives Poiseuille numbers in terms of Knudsen numbers for appropriate ranges of rarefaction and Knudsen numbers. The numerical works are based on reduced flow rates in terms of rarefaction for different ranges of rarefaction from free molecule to near continuum flows. Because different length scales are employed, the numerical results are significantly different. This paper shows that dimensionless mass flow rates of rarefied gas flows in Rectangular, Trapezoidal and Hexagonal Microchannelsare almost identical over very wide ranges of rarefaction or Knudsen number when the same length scale such as the radius of the inscribed circle is employed. Thus all apparent discrepanies are eliminated.

Featured Image