Advertisement

Experiments in Fluids

, Volume 41, Issue 3, pp 487–498 | Cite as

Mass flow rate measurements in gas micro flows

  • Timothée EwartEmail author
  • Pierre Perrier
  • Irina Graur
  • J. Gilbert Méolans
Research Article

Abstract

The main objective of this experimental investigation on the gas flow slip regime is to measure the mass flow rate in isothermal steady flows through cylindrical micro tubes. Two technical procedures devoted to mass flow rate measurements are compared, and the measured values are also compared with the results yielded by different approximated analytical solutions of the gas dynamics continuum equations. Satisfactory results are obtained and the way is clearly opened to measuring mass flow rates for higher Knudsen numbers, over all the micro flow transitional regime.

Keywords

Mass Flow Rate Velocity Slip Knudsen Number Accommodation Coefficient Slip Regime 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The authors are grateful to the CNRS (Science Research Council)—project number MI2F03-45, the Conseil Régional Provence Alpes Côtes d’Azur and the SERES company for their financial support. They also thank R. Notonier and A. Tonetto from the “Service Commun de Microscopie Electronique”.

References

  1. Albertoni S, Cercignani C, Gotusso L (1963) Numerical evaluation of the slip coefficient. Phys Fluids 6:993–996CrossRefADSGoogle Scholar
  2. Arkilic EB, Breuer KS, Schmidt MA (2001) Mass flow and tangential momentum accommodation in silicon micromachined channels. J Fluid Mech 437:29–43zbMATHCrossRefADSGoogle Scholar
  3. Arkilik EB, Schmidt MA, Breuer KS (1997) Gaseous slip flow in long microchannels. J Microelectromech Syst 6(2):167–178CrossRefGoogle Scholar
  4. Barber RW, Emerson DE (2005) Challenges in modeling gas-phase flow in microchannels: from slip to transition. In: Proceeding of ICMM2005, 3rd international conference on microchannels and minichannels, Toronto, pp 13–15Google Scholar
  5. Bird G (1994) Molecular gas dynamics and the direct simulation of gas flows. Oxford University Press, New YorkGoogle Scholar
  6. Cercignani C (1964) Higher order slip according to the linearized Boltzmann equation. Institute of Engineering Research Report AS-64-19, University of California, BerkeleyGoogle Scholar
  7. Chapman S, Cowling TG (1970) The mathematical theory of non-uniform gases, 3rd edn. University Press, CambridgeGoogle Scholar
  8. Colin S, Lalonde P, Caen R (2004) Validation of a second-order slip flow model in rectangular microchannels. Heat Transf Eng 25(3):23–30CrossRefADSGoogle Scholar
  9. Deissler RG (1964) An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases. Int J Heat Mass Transf 7:681–694zbMATHCrossRefGoogle Scholar
  10. Dong W (1956) University of California report no.UCRL-3353Google Scholar
  11. Elizarova T, Sheretov Y (2001) Theoretical and Numerical Analysis of Quasi-Gasdynamic and Quasi-Hydrodynamic. Equ Comput Math Math Phys 41:219–255zbMATHMathSciNetGoogle Scholar
  12. Graur I, Méolans J, Zeitoun D (2006) Analytical and numerical description for isothermal gas flows in microchannels. Microfluid Nanofluid 2:64–77CrossRefGoogle Scholar
  13. Hadjiconstantinou NG (2003) Comment on Cercignani’s second-order slip coefficient. Phys Fluids 15(8):2352–2354MathSciNetCrossRefADSGoogle Scholar
  14. Harley J, Huang Y, Bau H, Zemel J (1995) Gas flows in microchannels. J Fluid Mech 284:257–274CrossRefADSGoogle Scholar
  15. Jang J, Wereley ST (2004) Pressure distributions of gaseous slip flow in straight and uniform rectangular microchannels. Microfluid Nanofluid 1:41–51zbMATHCrossRefGoogle Scholar
  16. Jitschin W, Röhl P (1987) Quantitative study of the thermal transpiration effect in vacuum gauges. J Vac Sci Technol A 5(3):372–375CrossRefADSGoogle Scholar
  17. Karniadakis GE, Beskok A (2002) Microflows: fundamentals and simulation. Springer, Berlin Heidelberg New YorkGoogle Scholar
  18. Kogan MN (1969) Rarefied gas dynamics. Plenum Press, New YorkGoogle Scholar
  19. Lalonde P (2001) Etude expérimentale d’écoulements gazeux dans les microsystèmes à fluides. PhD Thesis, Institut National des Sciences Appliquées, Toulouse, FranceGoogle Scholar
  20. Lang H, Loyalka SK (1984) Some analytical results for thermal transpiration and the mechanocaloric effect in a cylindrical tube. Phys Fluid 27:1616zbMATHCrossRefADSGoogle Scholar
  21. Maurer J, Tabeling P, Joseph P, Willaime H (2003) Second-order slip laws in microchannels for helium and nitrogen. Phys Fluid 15:2613–2621CrossRefADSGoogle Scholar
  22. Pong K, Ho C, Liu J, Tai Y (1994) Non-linear pressure distribution in uniform microchannels. In: Application of microfabrication to fluid mechanics, vol 197. ASME FED, pp 51–56Google Scholar
  23. Porodnov BT, Suetin PE, Borisov SF, Akinshin VD (1974) Experimental investigation of rarefied gas flow in different channels. J Fluid Mech 64:417–437CrossRefADSGoogle Scholar
  24. Poulter KF, Rodgers MJ, Nash PJ, Thompson TJ, Perkin MP (1983) Thermal transpiration correction in capacitance manometers. Vacuum 33:311–316CrossRefGoogle Scholar
  25. Sharipov F, Seleznev V (1998) Data on internal rarefied gas flow. J Phys Chem Ref Data 27(3):657–706ADSCrossRefGoogle Scholar
  26. Tison SA (1993) Experimental data and theoretical modeling of gas flows through metal capollary leaks. Vacuum 44:1171–1175CrossRefGoogle Scholar
  27. Yao Z, He F, Ding Y, Shen M, Wang X (2004) Low-speed gas flow subchoking phenomenon in long-constant-area microchannel. AIAA J 42(8):1517–1521CrossRefADSGoogle Scholar
  28. Zohar Y, Lee SYK, Lee WY, Jiang L, Tong P (2002) Subsonic gas flow in a straight and uniform microchannel. J Fluid Mech 472:125–151zbMATHCrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Timothée Ewart
    • 1
    Email author
  • Pierre Perrier
    • 1
  • Irina Graur
    • 1
  • J. Gilbert Méolans
    • 1
  1. 1.Département de Mécanique Energétique - UMR CNRS 6595Université de Provence - Ecole Polytechnique Universitaire de MarseilleMarseille cedex 13France

Personalised recommendations