Microfluidics and Nanofluidics

, Volume 9, Issue 6, pp 1103–1114 | Cite as

Comparative study between computational and experimental results for binary rarefied gas flows through long microchannels

  • Lajos Szalmas
  • Jeerasak Pitakarnnop
  • Sandrine Geoffroy
  • Stephane Colin
  • Dimitris ValougeorgisEmail author
Research Paper


A comparative study between computational and experimental results for pressure-driven binary gas flows through long microchannels is performed. The theoretical formulation is based on the McCormack kinetic model and the computational results are valid in the whole range of the Knudsen number. Diffusion effects are taken into consideration. The experimental work is based on the Constant Volume Method, and the results are in the slip and transition regime. Using both approaches, the molar flow rates of the He–Ar gas mixture flowing through a rectangular microchannel are estimated for a wide range of pressure drops between the upstream and downstream reservoirs and several mixture concentrations varying from pure He to pure Ar. In all cases, a very good agreement is found, within the margins of the introduced modeling and measurement uncertainties. In addition, computational results for the pressure and concentration distributions along the channel are provided. As far as the authors are aware of, this is the first detailed and complete comparative study between theory and experiment for gaseous flows through long microchannels in the case of binary mixtures.


Binary rarefied gas flows McCormack model Discrete velocity method Flow rate measurement 



The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no 215504.


  1. Aoki K (2001) Dynamics of rarefied gas flows: asymptotic and numerical analyses of the Boltzmann equation. In: 39th AIAA aerospace science meeting and exhibit, Reno, 2001-0874Google Scholar
  2. Bird GA (1994) Molecular gas dynamics and the direct simulation of gas flows. Oxford University Press, OxfordGoogle Scholar
  3. Breyiannis G, Varoutis S, Valougeorgis D (2008) Rarefied gas flow in concentric annular tube: estimation of the Poiseuille number and the exact hydraulic diameter. Eur J Mech B Fluids 27:609–622zbMATHCrossRefGoogle Scholar
  4. Cercignani C (1988) The Boltzmann equation and its application. Springer-Verlag, New YorkGoogle Scholar
  5. Colin S (2005) Rarefaction and compressibility effects on steady and transient gas flows in microchannels. Microfluid Nanofluidics 1:268–279CrossRefGoogle Scholar
  6. Colin S, Lalonde P, Caen R (2004) Validation of a second-order slip flow model in rectangular microchannels. Heat Transf Eng 25:23–30CrossRefGoogle Scholar
  7. De Groot SR, Mazut P (1984) Non-equilibrium thermodynamics. Dover, New YorkGoogle Scholar
  8. Ewart T, Perrier P, Graur I, Méolans JG (2006) Mass flow rate measurements in gas micro flow. Exp Fluids 41:487–498CrossRefGoogle Scholar
  9. Ewart T, Perrier P, Graur IA, Méolans JG (2007) Mass flow rate measurements in a microchannel, from hydrodynamic to near free molecular regimes. J Fluid Mech 584:337–356zbMATHCrossRefGoogle Scholar
  10. Ferziger JH, Kaper HG (1972) Mathematical theory of transport processes in gases. North Holland, AmsterdamGoogle Scholar
  11. Harley JC, Huang Y, Bau HH, Zemel JN (1995) Gas flow in micro-channels. J Fluid Mech 284:257–274CrossRefGoogle Scholar
  12. Ho CM, Tai YC (1998) Micro-electro-mechanical-systems (MEMS) and fluid flows. Annu Rev Fluid Mech 30:579–612CrossRefGoogle Scholar
  13. Ivchenko IN, Loyalka SK, Tompson RV (1997) Slip coefficients for binary gas mixture. J Vac Sci Technol A 15:2375–2381CrossRefGoogle Scholar
  14. Kandlikar SG, Garimella S, Li D, Colin S, King MR (2006) Heat transfer and fluid flow in minichannels and microchannels. Elsevier, OxfordGoogle Scholar
  15. Kestin J, Knierim K, Mason EA, NajaB B, Ro ST, Waldman M (1984) Equilibrium and transport properties of the noble gases and their mixture at low densities. J Phys Chem Ref Data 13:229–303CrossRefGoogle Scholar
  16. Kosuge S, Takata S (2008) Database for flows of binary mixtures through a plane microchannel. Eur J Mech B Fluids 27:444–465zbMATHCrossRefGoogle Scholar
  17. Lockerby DA, Reese JM (2008) On the modelling of isothermal gas flows at the microscale. J Fluid Mech 604:235–261zbMATHCrossRefMathSciNetGoogle Scholar
  18. Marino L (2009) Experiments on rarefied gas flows through tubes. Microfluid Nanofluidics 6:109–119CrossRefGoogle Scholar
  19. Maurer J, Tabeling P, Joseph P, Willaime H (2003) Second-order slip laws in microchannels for helium and nitrogen. Phys Fluids 15:2613–2621CrossRefGoogle Scholar
  20. McCormack FJ (1973) Construction of linearized kinetic models for gaseous mixtures and molecular gases. Phys Fluids 16:2095–2105CrossRefGoogle Scholar
  21. Morini GL, Lorenzini M, Spiga M (2005) A criterion for experimental validation of slip-flow models for incompressible rarefied gases through microchannels. Microfluid Nanofluidics 1:190–196CrossRefGoogle Scholar
  22. Naris S, Valougeorgis D, Kalempa D, Sharipov F (2004a) Discrete velocity modelling of gaseous mixture flows in MEMS. Superlattices Microstruct 35:629-643CrossRefGoogle Scholar
  23. Naris S, Valougeorgis D, Kalempa D, Sharipov F (2004b) Gaseous mixture flow between two parallel plates in the whole range of the gas rarefaction. Physica A 336:294–318CrossRefGoogle Scholar
  24. Naris S, Valougeorgis D, Kalempa D, Sharipov F (2005) Flow of gaseous mixtures through rectangular microchannels driven by pressure, temperature and concentration gradients. Phys Fluids 17:100607.1–100607.12Google Scholar
  25. Pitakarnnop J (2009) Analyse expérimentale et simulation numérique d’écoulements raréfiés de gaz simples et de mélanges gazeux dans les microcanaux. Ph.D. thesis, University of ToulouseGoogle Scholar
  26. Pitakarnnop J, Geoffroy S, Colin S, Baldas L (2008) Slip flow in triangular and trapezoidal microchannels. Int J Heat Technol 26:167–174Google Scholar
  27. Pitakarnnop J, Varoutis S, Valougeorgis D, Geoffroy S, Baldas L, Colin S (2010) A novel experimental setup for gas microflows. Microfluid Nanofluidics 8:57–72CrossRefGoogle Scholar
  28. Sharipov F (1994) Onsager-Casimir reciprocity relations for open gaseous systems at arbitrary rarefaction III. Theory and its application for gaseous mixtures. Physica A 209:457–476CrossRefMathSciNetGoogle Scholar
  29. Sharipov F (1999) Rarefied gas flow through a long rectangular channel. J Vac Sci Technol A 17:3062–3066CrossRefGoogle Scholar
  30. Sharipov F, Seleznev V (1998) Data on internal rarefied gas flows. J Phys Chem Ref Data 27:657–706CrossRefGoogle Scholar
  31. Sharipov F, Kalempa D (2002) Gaseous mixture flow through a long tube at arbitrary Knudsen number. J Vac Sci Technol A 20:814–822CrossRefGoogle Scholar
  32. Sharipov F, Kalempa D (2003) Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip problem. Phys Fluids 15:1800–1806CrossRefGoogle Scholar
  33. Sharipov F, Kalempa D (2005) Separation phenomena for gaseous mixture flowing through a long tube into vacuum. Phys Fluids 17:127102.1–127102.8Google Scholar
  34. Siewert CE, Valougeorgis D (2004) The McCormack model: channel flow of a binary gas mixture driven by temperature, pressure and density gradients. Eur J Mech B Fluids 23:645–664zbMATHCrossRefMathSciNetGoogle Scholar
  35. Szalmas L (2007) Multiple-relaxation time lattice Boltzmann method for the finite Knudsen number region. Physica A 379:401–408CrossRefGoogle Scholar
  36. Szalmas L, Valougeorgis D (2010) Rarefied gas flow of binary mixtures through long channels with triangular and trapezoidal cross sections. Microfluid Nanofluidics. doi: 10.1007/s10404-010-0564-9
  37. Takata S, Yasuda S, Kosuge S, Aoki K (2003) Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases. Phys Fluids 15:3745-3766CrossRefGoogle Scholar
  38. Takata S, Sugimoto H, Kosuge S (2007) Gas separation by means of the Knudsen compressor. Eur J Mech B Fluids 26:155–181zbMATHCrossRefMathSciNetGoogle Scholar
  39. Valougeorgis D, Naris S (2003) Acceleration schemes of the discrete velocity method: gaseous flows in rectangular microchannels. SIAM J Sci Comput 25:534–552zbMATHCrossRefMathSciNetGoogle Scholar
  40. Varoutis S, Naris S, Hauer V, Day C, Valougeorgis D (2009) Computational and experimental study of gas flows through long channels of various cross sections in the whole range of the Knudsen number. J Vac Sci Technol A 27:89–100CrossRefGoogle Scholar
  41. Wagner W (1992) A convergence proof for Bird direct simulation Monte Carlo method for the Boltzmann equation. J Stat Phys 66:1011–1044zbMATHCrossRefGoogle Scholar
  42. Zohar Y, Lee SYK, Lee WY, Jiang L, Tong P (2002) Subsonic gas flow in a straight and uniform microchannel. J Fluid Mech 472:125–151zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Lajos Szalmas
    • 1
  • Jeerasak Pitakarnnop
    • 2
  • Sandrine Geoffroy
    • 2
  • Stephane Colin
    • 2
  • Dimitris Valougeorgis
    • 1
    Email author
  1. 1.Department of Mechanical EngineeringUniversity of ThessalyPedion Areos, VolosGreece
  2. 2.INSA, UPS, Mines Albi, ISAE, ICA (Institut Clément Ader)Université de ToulouseToulouseFrance

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