Skip to main content
SpringerLink
Log in

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

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Albertoni S, Cercignani C, Gotusso L (1963) Numerical evaluation of the slip coefficient. Phys Fluids 6:993

    Article  Google Scholar 

  • Aubert C, Colin S (2001) High-order boundary conditions for gaseous flows in rectangular microducts. Microscale Therm Eng 5:41–54

    Article  Google Scholar 

  • Aubert C, Colin S, Caen R (1998) Unsteady gaseous flows in tapered microchannels. In: Technical proceedings of the 1998 international conference on modeling and simulation of microsystems, volume chapter 11: applications: microfluidics, pp 486–491

  • Bird GA (1994) Molecular gas dynamics and the direct simulation of gas flows. Oxford Science Publications, Oxford University Press Inc., New York

    Google Scholar 

  • Colin S, Lalonde P, Caen R (2004) Validation of a second-order slip flow model in a rectangular microchannel. Heat Transf Eng 25:23–30

    Article  Google Scholar 

  • de Silva LR, Deschamps CJ (2012) Modeling of gas leakage through compressor valves. In: International compressor engineering conference, paper 2105

  • Ewart T, Perrier P, Graur IA, Méolans JG (2007) Mass flow rate measurements in microchannel, from hydrodynamic to near free molecular regimes. J Fluid Mech 584:337–356

    Article  MATH  Google Scholar 

  • Graur IA, Perrier P, Ghozlani W, Méolans JG (2009) Measurements of tangential momentum accommodation coefficient for various gases in plane microchannel. Phys Fluids 21:102004

    Article  Google Scholar 

  • Graur I, Ho MT (2014) Rarefied gas flow through a long rectangular channel of variable cross section. Vacuum 101:328–332

    Article  Google Scholar 

  • Lee HW, Azid HA (2009) Neuro-genetic optimization of the diffuser elements for applications in a valveless diaphragm micropumps system. Sensors 9:7481–7497

    Article  Google Scholar 

  • Ohwada T, Sone Y, Aoki K (1989) Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules. Phys Fluids A 1:1588–1599

    Article  MATH  Google Scholar 

  • Perrier P, Graur IA, Ewart T, Méolans JG (2011) Mass flow rate measurements in microtubes: from hydrodynamic to near free molecular regime. Phys Fluids 23:042004

    Article  Google Scholar 

  • Porodnov BT, Suetin PE, Borisov SF, Akinshin VD (1974) Experimental investigation of rarefied gas flow in different channels. J Fluid Mech 64:417–437

    Article  Google Scholar 

  • Sharipov F, Seleznev V (1998) Data on internal rarefied gas flows. J Phys Chem Ref Data 27:657–706

    Article  Google Scholar 

  • Sharipov F (1999) Non-isothermal gas flow through rectangular microchannels. J Micromech Microeng 9:394–401

    Article  Google Scholar 

  • Sharipov F, Bertoldo G (2005) Rarefied gas flow through a long tube of variable radius. J Vac Sci Technol A 23:531–533

    Article  Google Scholar 

  • Siewert CE, Sharipov F (2002) Model equations in rarefied gas dynamics: viscous-slip and thermal-slip coefficients. Phys Fluids 14:4123–4129

    Article  MathSciNet  Google Scholar 

  • Stemme E, Stemme G (1993) Valve-less diffuser/nozzle based fluid pump. Sens Actuators A Phys 39:159–167

    Article  Google Scholar 

  • Stevanovic ND (2007) A new analytical solution of microchannel gas flow. J Micromech Microeng 17:1695–1702

    Article  Google Scholar 

  • Stevanovic ND, Djordjevic VD (2012) The exact analytical solution for the gas lubricated bearing in the slip and continuum flow regime. Publications de l’Institut Mathématique 91:83–93

    Article  MathSciNet  Google Scholar 

  • Titarev VA, Utyuzhnikov SV, Shakhov EM (2013) Rarefied gas flow into vacuum through square pipe with variable cross section. Comput Math Math Phys 53:1221–1230

    Article  MathSciNet  Google Scholar 

  • Veltzke T (2013) On gaseous microflows under isothermal conditions. PhD thesis, University of Bremen

  • Veltzke T, Baune M, Thöming J (2012) The contribution of diffusion to gas microflow: an experimental study. Phys Fluids 24:082004

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. CNRS, IUSTI UMR 7343, Aix-Marseille Université, 13453, Marseille, France

    I. Graur, J. G. Méolans & M. T. Ho

  2. Center for Environmental Research and Sustainable Technology (UFT), University of Bremen, Leobener Strasse 1, 28359, Bremen, Germany

    T. Veltzke & J. Thöming

Authors
  1. I. Graur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Veltzke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. G. Méolans
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. T. Ho
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. Thöming
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

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
Full size table
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
Full size table
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
Full size table
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
Full size table
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
Full size table
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
Full size table
Table 8 Knudsen number and experimental and numerically calculated diodicity of carbon dioxide
Full size table
Table 9 Knudsen number and experimental and numerically calculated diodicity of nitrogen
Full size table
Table 10 Knudsen number and experimental and numerically calculated diodicity of argon
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10404-014-1445-4

Keywords

Search

Navigation