This paper reports the experimental and numerical analysis of time-dependent rarefied gas flows through a long metallic micro-tube. The experimental methodology was conceived on the basis of the constant volume technique and adapted to measure the evolution with time of a transient mass flow rate through a micro-tube. Furthermore, the characteristic time of each experiment, extracted from the pressure measurements in each reservoir, offered a clear indication on the dynamics of the transient flow as a function of the gas molecular mass and its rarefaction level. The measured pressure evolution with time at the inlet and outlet of the micro-tube was compared to numerical results obtained with the BGK linearized kinetic equation model. Finally, we present an original methodology to extract stationary mass flow rates by using the tube conductance, which can be associated with the characteristic time of the experiment, measured for different mean pressures between two tanks. The results were obtained in a wide range of rarefaction conditions for nitrogen (\(N_2\)). A brief comparison is offered with respect to R134a (CH2FCF3), too, a heavy polyatomic gas which is typically used in the refrigeration industry.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Arkilic E, Schmidt M, Breuer K (1997) Gaseous slip flow in long microchannels. J Microelectromechanical Syst 6(2):167–178
Arkilic EB, Breuer KS, Schmidt MA (2001) Mass flow and tangential momentum accommodation in silicon micromachined channels. J Fluid Mech 437:29–43
Colin S (2005) Rarefaction and compressibility effects on steady and transient gas flows in microchannels. Microfluid Nanofluid 1(3):268–279
Ewart T, Perrier P, Graur I, Gilbert Méolans J (2006) Mass flow rate measurements in gas micro flows. Exp Fluids 41(3):487–498
Ewart T, Perrier P, Graur I, Méolans J (2007) Tangential momentum accommodation in microtube. Microfluid Nanofluid 3(6):689–695
Graur I, Sharipov F (2008) Gas flow through an elliptical tube over the whole range of the gas rarefaction. Eur J Mech B Fluids 27(3):335–345
Harley JC, Huang Y, Bau HH, Zemel JN (1995) Gas flow in micro-channels. J Fluid Mech 284:257–274
Jousten K (ed) (2008) Handbook of vacuum technology. Wiley, Weinheim
Lihnaropoulos J, Valougeorgis D (2011) Unsteady vacuum gas flow in cylindrical tubes. Fusion Eng Des 86(9):2139–2142
Perrier P, Graur I, Ewart T, Méolans J (2011) Mass flow rate measurements in microtubes: from hydrodynamic to near free molecular regime. Phys Fluids 23(042):004
Pitakarnnop J, Varoutis S, Valougeorgis D, Geoffroy S, Baldas L, Colin S (2010) A novel experimental setup for gas microflows. Microfluid Nanofluid 8(1):57–72
Porodnov B, Suetin P, Borisov S, Akinshin V (1974) Experimental investigation of rarefied gas flow in different channels. J Fluid Mech 64(3):417–437
Rojas-Cardenas M, Graur I, Meolans JG (2011) Thermal transpiration flow: a circular cross-section microtube submitted to a temperature gradient. Phys Fluids 23:031,702
Sharipov F (1997) Rarefied gas flow through a long tube at arbitrary pressure and temperature drop. J Vac Sci Technol A 15(4):2434–2436
Sharipov F (2011) Data on the velocity slip and temperature jump on a gas-solid interface. J Phys Chem Ref Data 40(2):023,101
Sharipov F (2012a) Benchmark problems in rarefied gas dynamics. Vacuum 86(11):1697–1700
Sharipov F (2012b) Transient flow of rarefied gas through an orifice. J Vac Sci Technol A 30(2):021,602
Sharipov F (2013) Transient flow of rarefied gas through a short tube. Vacuum 90:25–30
Sharipov F, Graur I (2014) General approach to transient flows of rarefied gases through long capillaries. Vacuum 100:22–25
Sharipov F, Graur I, Day C (2010) Leak rate of water into vacuum through microtubes. J Vac Sci Technol A 28(3):443–448
Silva E, Rojas-Cardenas M, Deschamps C (2016) Experimental analysis of velocity slip at the wall for gas flows of nitrogen, r134a, and r600a through a metallic microtube. Int J Refrig 66:121–132
Vargas M, Naris S, Valougeorgis D, Pantazis S, Jousten K (2014a) Hybrid modeling of time-dependent rarefied gas expansion. J Vac Sci Technol A 32(2):021,602
Vargas M, Naris S, Valougeorgis D, Pantazis S, Jousten K (2014b) Time-dependent rarefied gas flow of single gases and binary gas mixtures into vacuum. Vacuum 109:385–396
Yamaguchi H, Hanawa T, Yamamoto O, Matsuda Y, Egami Y, Niimi T (2011) Experimental measurement on tangential momentum accommodation coefficient in a single microtube. Microfluid Nanofluid 11(1):57–64
This work has been partially (authors M.-T. Ho and I. Graur) carried out in the framework of the Labex MEC (ANR-10-LABX-0092) and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French Government program managed by the French National Research Agency (ANR). Additionally, the authors E. Silva and C. J. Deschamps thank the support of EMBRACO, CNPq and EMBRAPII Unit Polo/UFSC. Finally, the author M. Rojas-Cárdenas would like to acknowledge the financial support provided by the EU network program H2020 under Grant MIGRATE No. 643095.
About this article
Cite this article
Rojas-Cárdenas, M., Silva, E., Ho, M. et al. Time-dependent methodology for non-stationary mass flow rate measurements in a long micro-tube. Microfluid Nanofluid 21, 86 (2017). https://doi.org/10.1007/s10404-017-1920-9
- Transient flows
- Gas rarefaction
- Kinetic theory