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Measurements of the Poiseuille coefficient in the slip and transitional flow regimes
Published online by Cambridge University Press: 12 December 2025
Abstract
New experimental results on gas flow through a long tube in the viscous, slip and transitional regimes are presented, obtained using an improved constant-volume measurement technique. This method is based on measuring the pressure variation in the inlet tank while the outlet tank is evacuated to a low pressure. Experimental pressure data for helium, neon, argon, nitrogen, krypton and xenon are used to extract the Poiseuille coefficient through a newly developed methodology. The obtained values show good agreement with theoretical predictions. Additionally, the velocity slip coefficient is also extracted from the same pressure data for all tested gases.
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Ameri, A.R., Imanparast, A., Passandideh-Fard, M. & Shaegh, S.A.M. 2022 Elsevier analytica chimica acta volume 1221, 15 august 2022, 340093 analytica chimica acta a whole-thermoplastic microfluidic chip with integrated on-chip micropump, bioreactor and oxygenator for cell culture applications. Anal. Chim. Acta 1221, 340093.10.1016/j.aca.2022.340093CrossRefGoogle Scholar
An, S., Gupta, N.K. & Gianchandani, Y.B. 2014 A si-micromachined 162-stage two-part a si-micromachined 162-stage two-part knudsen pump for on-chip vacuum. J. Microelectromech. Syst. 23 (2), 406–416.10.1109/JMEMS.2013.2281316CrossRefGoogle Scholar
Arkilic, E.B., Schmidt, M.A. & Breuer, K.S. 1997 Gaseous slip flow in long microchannels. J. Microelectromech. Syst. 6 (2), 167–178.10.1109/84.585795CrossRefGoogle Scholar
Basdanis, T., Valougeorgis, D. & Sharipov, F. 2023 Viscous and thermal velocity slip coefficient via the linearized boltzmann equation with ab initio potential. Microfluid. Nanofluid. 25, 75.10.1007/s10404-023-02681-0CrossRefGoogle Scholar
Bell, Ian H., Wronski, Jorrit, Quoilin, Sylvain & Lemort, Vincent 2014 Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library coolprop. Ind. Eng. Chem. Res. 53 (6), 2498–2508.10.1021/ie4033999CrossRefGoogle ScholarPubMed
Berg, R.F. & Burton, W.C. 2013 Noble gas viscosities at 25
$^\circ$
C. Mol. Phys. 111 (2), 195–199.10.1080/00268976.2012.713132CrossRefGoogle Scholar
$^\circ$
C. Mol. Phys. 111 (2), 195–199.10.1080/00268976.2012.713132CrossRefGoogle ScholarBerg, R.F., Gooding, T. & Vest, R.E. 2014 Constant pressure primary flow standard for gas flows from 0.01 cm
$^3$
min−1 (0.007–74
$\unicode{x03BC}$
mol s−1). Flow Meas. Instrument. 35, 84–91.10.1016/j.flowmeasinst.2013.12.002CrossRefGoogle Scholar
$^3$
min−1 (0.007–74
$\unicode{x03BC}$
mol s−1). Flow Meas. Instrument. 35, 84–91.10.1016/j.flowmeasinst.2013.12.002CrossRefGoogle ScholarBerman, A. 1985 Total pressure measurements in vacuum technology. In Methods for Vacuum Gauge Callibration. 242–320. Academic Press.Google Scholar
Bhandarkar, S., Parham, T. & Fair, J. 2011 Modeling and experiments of compressible gas flow through microcapillary fill tubes on NIF target. Fusion Sci. Technol. 59 (1), 51–57.10.13182/FST10-3718CrossRefGoogle Scholar
Bhatnagar, P.L., Gross, E.P. & Krook, M. 1954 A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev. 94 (3), 511–525.10.1103/PhysRev.94.511CrossRefGoogle Scholar
Caldwell, A. et al. 2016 Path to awake: evolution of the concept. Nuclear instruments and methods in physics. Res. Sect. A: Asselerat. Spectrom. Detectors Assoc. Equipm. 829, 3–16.Google Scholar
Cercignani, C. & Sernagiotto, F. 1966 Cylindrical couette flow of a rarefied gas. Phys. Fluids 10 (6), 1200–1204.10.1063/1.1762263CrossRefGoogle Scholar
Cole, W.A. & Wakeham, W.A. 1985 The viscosity of nitrogen, oxygen, and their binary-mixtures in the limit of zero density. J. Phys. Chem. Ref. Data 14 (1), 209–226.10.1063/1.555748CrossRefGoogle Scholar
Colin, S., Lalonde, P. & Caen, R. 2004 Validation of a second-order slip flow model in a rectangular microchannel. Heat Transf. Eng. 25 (3), 23–30.10.1080/01457630490280047CrossRefGoogle Scholar
Ewart, T., Perrier, P., Graur, I.A. & Méolans, J.G. 2006 Mass flow rate measurements in gas micro flows. Exp. Fluids 41 (3), 487–498.10.1007/s00348-006-0176-zCrossRefGoogle Scholar
Ewart, T., Perrier, P., Graur, I.A. & Méolans, J.G. 2007 Mass flow rate measurements in microchannel, from hydrodynamic to near free molecular regimes. Fluid Mech. 584, 337–356.10.1017/S0022112007006374CrossRefGoogle Scholar
Ferziger, J.H. & Kaper, H.G. 1972 Mathematical Theory of Transport Processes in Gases. North-Holland Publishing Company.Google Scholar
GUM 2008 Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML.Google Scholar
Hadj Nacer, M., Graur, I., Perrier, P., Méolans, J.G. & Wüest, M. 2014 Gas flow through microtubes with different surface coating. J. Vac. Sci. Technol. A
32 (2), 021601–021609.10.1116/1.4828955CrossRefGoogle Scholar
Holway, L.H. 1966 New statistical models in kinetic theory: methods of construction. Phys. Fluids 9 (9), 1658–1673.10.1063/1.1761920CrossRefGoogle Scholar
Johansson, M.V., Testa, F., Zaier, I., Perrier, P., Bonnet, J.P., Moulin, P. & Graur, I. 2018 Mass flow rate and permeability measurements in microporous media. Vacuum 158, 75–85.10.1016/j.vacuum.2018.09.030CrossRefGoogle Scholar
Jousten, K. (ed.) 2008 Handbook of Vacuum Technology. WILEY-VCH Verlag GmBH & Co. KGaA.Google Scholar
Jousten, K., Menzer, H. & Niepraschk, R. 2002 A new fully automated gas flowmeter at the ptb for flow rates between
$10^{-13}$
mol s−1 and
$10^{-6}$
mol s−1
. Metrologia 39 (6), 519.10.1088/0026-1394/39/6/2CrossRefGoogle Scholar
$10^{-13}$
mol s−1 and
$10^{-6}$
mol s−1
. Metrologia 39 (6), 519.10.1088/0026-1394/39/6/2CrossRefGoogle ScholarJousten, K., Messer, G. & Wandrey, D. 1993 A precision gas flowmeter for vacuum metrology. Vacuum 44 (2), 135–141.10.1016/0042-207X(93)90362-ECrossRefGoogle Scholar
Kadoya, K., Matsunaga, N. & Nagashima, A. 1985 Viscosity and thermal conductivity of dry air in the gaseous phase. J. Phys. Chem. Ref. Data 14 (4), 947–970.10.1063/1.555744CrossRefGoogle Scholar
Marino, L. 2009 Experiments on rarefied gas flows through tubes. Microfluid Nanofluid 6 (1), 109–119.10.1007/s10404-008-0311-7CrossRefGoogle Scholar
Maurer, J., Tabeling, P., Joseph, P. & Willaime, H. 2003 Second-order slip laws in microchannels for helium and nitrogen. Phys. Fluids 15, 2613–2621.10.1063/1.1599355CrossRefGoogle Scholar
McCulloh, K.E., Tilford, C.R., Ehrich, C.D. & Long, F.G. 1987 Low-range flowmeters for use with vacuum and leak standards. J. Vac. Sci. Technol. A Surfaces Films 5 (6), 376–381.10.1116/1.574163CrossRefGoogle Scholar
Meija, J. et al. 2016 Atomic weights of the elements 2013 (IUPAC technical report). Pure Appl. Chem. 88 (3), 265–291.10.1515/pac-2015-0305CrossRefGoogle Scholar
Peksa, L., Gronych, T., Vicar, M., Jerab, M., Repa, P., Tesar, J., Prazak, D. & Krajicek, Z. 2011 Method of measuring the change in volume of a diaphragm bellows used in a volume displacer of a constant-pressure gas flowmeter (with a practical guide). Measurement 44, 1143–1152.10.1016/j.measurement.2011.03.008CrossRefGoogle Scholar
Perrier, P., Graur, I.A., Ewart, T. & Méolans, J.G. 2011 Mass flow rate measurements in microtubes: from hygrodynamic to near free molecular regime. Phys. Fluids 23, 042004.10.1063/1.3562948CrossRefGoogle Scholar
Pitakarnnop, J., Varoutis, S., Valougeorgis, D., Geoffroy, S., Baldas, L. & Colin, S. 2010 A novel experimental setup for gas microflows. Microfluid Nanofluid 8, 57–72.10.1007/s10404-009-0447-0CrossRefGoogle Scholar
Porodnov, B.T., Suetin, P.E., Borisov, S.F. & Akinshin, V.D. 1974 Experimental investigation of rarefied gas flow in different channels. J. Fluid Mech. 64 (3), 417–437.10.1017/S0022112074002485CrossRefGoogle Scholar
Reid, R.C., Prausnitz, J.M. & Poling, B.E. 1987 The Properties of Gases and Liquids. McGraw-Hill.Google Scholar
Rojas-Cárdenas, M., Silva, E., Ho, M.T., Deschamps, C.J. & Graur, I. 2017 Time-dependent methodology for non-stationary mass flow rate measurements in a long micro-tube. Microfluid Nanofluid 21 (5), 86.10.1007/s10404-017-1920-9CrossRefGoogle Scholar
Rykov, V.A. 1975 Model kinetic equation for gases with rotational degree of freedom. J. Fluid Gases 10 (6), 959–966.Google Scholar
Seber, G.A.F. & Wild, C.J. 1989 Nonlinear Regression. Wiley-Interscience.10.1002/0471725315CrossRefGoogle Scholar
Shakhov, E.M. 1968 Generalization of the Krook kinetic relaxation equation. Fluid Dyn. 3 (5), 95–96.10.1007/BF01029546CrossRefGoogle Scholar
Shan, B., Li, S., Tang, G., Torrilhon, M., Zhang, Y. & Guo, Z. 2025 Molecular kinetic modelling of confined fluid transport – a mesoscopic approach. Acta Mech. Sin. 41, 724893.Google Scholar
Sharipov, F. 1996 Rarefied gas flow through a long tube at any temperature ratio. J. Therm. Sci. Technol. A
14 (4), 2627–2635.Google Scholar
Sharipov, F. 1997 Rarefied gas flow through a long tube at arbitrary pressure and temperature drop. J. Vac. Sci. Technol. A
15 (4), 2434–2436.10.1116/1.580904CrossRefGoogle Scholar
Sharipov, F. 2011 Data on the velocity slip and temperature jump on a gas-solid interface. J. Phys. Chem. Ref. Data 40 (2), 023101–1–28.10.1063/1.3580290CrossRefGoogle Scholar
Sharipov, F. 2016 Rarefied Gas Dynamics. Fundamentals for Research and Practice. Wiley-VCH.10.1002/9783527685523CrossRefGoogle Scholar
Sharipov, F. 2024 Ab initio modelling of transport phenomena in multi-component mixtures of rarefied gases. Int. J. Heat Mass Trans. 220, 124906.10.1016/j.ijheatmasstransfer.2023.124906CrossRefGoogle Scholar
Sharipov, F. & Benites, V.J. 2019 Transport coefficients of argon and its mixtures with helium and neon at low density based ab initio potentials. Fluid Phase Equilibr. 498, 23–32.10.1016/j.fluid.2019.06.010CrossRefGoogle Scholar
Sharipov, F. & Benites, V.J. 2021 Transport coefficients of isotopic mixtures of noble gases based on ab initio potentials. Phys. Chem. Chem. Phys. 23, 16664–16674.10.1039/D1CP01971FCrossRefGoogle ScholarPubMed
Sharipov, F. & Graur, I. 2014 General approach to transient flows of rarefied gases through long capillaries. Vacuum 100, 22–25.10.1016/j.vacuum.2013.07.017CrossRefGoogle Scholar
Sharipov, F. & Graur, I. 2025 New concept to measure the poiseuille coefficient of rarefied gas flow driven by a large pressure drop. Vacuum 240, 114585.10.1016/j.vacuum.2025.114585CrossRefGoogle Scholar
Sharipov, F., Graur, I. & Day, C. 2010 Leak rate of water into vacuum through microtubes. J. Vac. Sci. Technol. A
28 (3), 443–448.10.1116/1.3372839CrossRefGoogle Scholar
Sharipov, F., Graur, I. & Salançon, E. 2025 Field ionization intensity used to measure local pressure in gas flow. Vacuum 231, 113728.10.1016/j.vacuum.2024.113728CrossRefGoogle Scholar
Sharipov, F. & Seleznev, V. 1998 Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27 (3), 657–706.10.1063/1.556019CrossRefGoogle Scholar
Sharipov, F. & Seleznev, V.D. 1994 Rarefied gas flow through a long tube at any pressure ratio. J. Vac. Sci. Technol. A
12 (5), 2933–2935.10.1116/1.578969CrossRefGoogle Scholar
Sharipov, F. & Strapasson, J.L. 2014
Ab initio simulation of rarefied gas flow through a thin orifice. Vacuum 109, 246–252.10.1016/j.vacuum.2014.03.027CrossRefGoogle Scholar
Silva, E., Deschamps, C.J., Rojas Cárdenas, M., Barrot-Lattes, C., Baldas, L. & Colin, S. 2018 A time-dependent method for the measurement of mass flow rate of gases in microchannels. Int. J. Heat Mass Trans. 120, 422–434.10.1016/j.ijheatmasstransfer.2017.11.147CrossRefGoogle Scholar
Suetin, P.E., Porodnov, B.T., Chernyak, V.G. & Borisov, S.F. 1973 Poiseuille flow at arbitrary Knudsen number and tangential momentum accommodation. J. Fluid Mech. 60 (3), 581–592.10.1017/S0022112073000352CrossRefGoogle Scholar
Sznitman, J. 2022 Revisiting airflow and aerosol transport phenomena in the deep lungs with microfluidics. Chem. Rev. 122, 7182–7204.10.1021/acs.chemrev.1c00621CrossRefGoogle ScholarPubMed
Tantos, C., Kritikos, E., Varoutis, S. & Day, Ch 2023 Kinetic modeling of polyatomic heat and mass transfer. Heat Mass Transfer 59, 167–184.10.1007/s00231-022-03224-zCrossRefGoogle Scholar
Tantos, C., Varoutis, S. & Day, Ch 2020 Effect on the internal degree of freedom of the gas molecules on the heat and mass transfer in long circular capillaries. Microfluid Nanofluid 24, 95.10.1007/s10404-020-02400-zCrossRefGoogle Scholar
Tison, S. & A 1993 Experimental data and theoretical modeling of gas flows through metal capillary leaks. Vacuum 44 (11), 1171–1175.10.1016/0042-207X(93)90342-8CrossRefGoogle Scholar
Titarev, V.A. & Shakhov, E.M. 2012 Poiseuillle flow and thermal creep in a capillary tube on the basis of kinetic r-model. Fluid Dyn. 47 (5), 661–672.10.1134/S0015462812050146CrossRefGoogle Scholar
Wangkui, L., Dixin, Z., Qiang, L., Shiliang, L., Detian, L. & Yang, M. 1996 A gas flow standard apparatus. Vacuum 47 (6-8), 519–522.10.1016/0042-207X(96)00148-0CrossRefGoogle Scholar
Wu, L., Zhang, J., Liu, H., Zhang, Y. & Reese, J.M. 2017 A fast iterative scheme for the linearized boltzmann equation. J. Comput. Phys. 338, 431–451.10.1016/j.jcp.2017.03.002CrossRefGoogle Scholar
Grigorov et al. supplementary material
Grigorov et al. supplementary material
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