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The gas flow diode effect: theoretical and experimental analysis of moderately rarefied gas flows through a microchannel with varying cross section

An Erratum to this article was published on 19 April 2015

Abstract

Moderately rarefied gas flows are clearly distinguished from viscous flow in the continuum regime and from free molecular flow at high rarefaction. Being of relevance for various technical applications, the understanding of such flow processes is crucial for considerable enhancement in micro electromechanical systems (MEMS) and vacuum techniques. In this work, we focus on the isothermal rarefied gas flow through long channels with longitudinally varying cross section. We apply two approaches, an analytical one and a numerical one that is based on the solution of the linearized S-model, both allowing us to predict the mass flow rate in diverging and converging flow directions for arbitrary pressure gradients. Both approaches are validated by CO2, N2 and Ar permeation experiments on tapered microchannels manufactured by means of micromilling. The local Knudsen numbers ranged from 0.0471 to 0.2263. All the numerical and analytical results are in good agreement to the experimental data and show that the mass flow rate is significantly higher when the duct is perfused in converging direction. The understanding of the physical phenomenon of this gas flow diode effect might pave the way for novel components in MEMS such as static one-way valves.

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Acknowledgments

Some of the presented results are based on a project funded by German Federal Ministry of Economics and Technology (BMWi) according to a decision of the German Federal Parliament; funding code 0327512A. One of the authors (Thomas Veltzke) wants to thank Georg Grathwohl for his support.

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Correspondence to T. Veltzke.

Appendix

Appendix

See Tables 2, 3, 4, 5, 6, 7, 8, 9 and 10.

Table 2 Experimental results obtained in diffusor direction on the tapered channel according to Fig. 2 with CO2 as working gas, analytical solution, numerical solution
Table 3 Experimental results obtained in nozzle direction on the tapered channel according to Fig. 2 with CO2 as working gas, analytical solution, numerical solution
Table 4 Experimental results obtained in diffusor direction on the tapered channel according to Fig. 2 with N2 as working gas and the analytical solution
Table 5 Experimental results obtained in nozzle direction on the tapered channel according to Fig. 2 with N2 as working gas and the analytical solution
Table 6 Experimental results obtained in diffusor direction on the tapered channel according to Fig. 2 with argon as working gas and the analytical solution
Table 7 Experimental results obtained in nozzle direction on the tapered channel according to Fig. 2 with argon as working gas and the analytical solution
Table 8 Knudsen number and experimental and numerically calculated diodicity of carbon dioxide
Table 9 Knudsen number and experimental and numerically calculated diodicity of nitrogen
Table 10 Knudsen number and experimental and numerically calculated diodicity of argon

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Graur, I., Veltzke, T., Méolans, J.G. et al. The gas flow diode effect: theoretical and experimental analysis of moderately rarefied gas flows through a microchannel with varying cross section. Microfluid Nanofluid 18, 391–402 (2015). https://doi.org/10.1007/s10404-014-1445-4

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Keywords

  • Rarefied gas
  • Long tapered channel
  • Gas flow diode effect
  • Microchannel production
  • Mass flow rate measurement