Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-27T01:32:17.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Extraction of the translational Eucken factor from light scattering by molecular gas

Published online by Cambridge University Press:  27 August 2020

Lei Wu Open the ORCID record for Lei Wu [Opens in a new window] ,
Qi Li ,
Haihu Liu Open the ORCID record for Haihu Liu [Opens in a new window]  and
Wim Ubachs
Lei Wu*
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Qi Li
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China
Haihu Liu
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, PR China
Wim Ubachs
Affiliation:
Department of Physics and Astronomy, LaserLaB, Vrije Universiteit, De Boelelaan 1081, Amsterdam1081 HV, The Netherlands
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Although the thermal conductivity of molecular gases can be measured straightforwardly and accurately, it is difficult to experimentally determine its separate contributions from the translational and internal motions of gas molecules. Yet, this information is critical in rarefied gas dynamics as the rarefaction effects corresponding to these motions are different. In this paper, we propose a novel methodology to extract the translational thermal conductivity (or equivalently, the translational Eucken factor) of molecular gases from the Rayleigh–Brillouin scattering (RBS) experimental data. From the numerical simulation of the Wu et al. (J. Fluid Mech., vol. 763, 2015, pp. 24–50) model we find that, in the kinetic regime, in addition to bulk viscosity, the RBS spectrum is sensitive to the translational Eucken factor, even when the total thermal conductivity is fixed. Thus it is not only possible to extract the bulk viscosity, but also the translational Eucken factor of molecular gases from RBS light scattering spectra measurements. Such experiments bear the additional advantage that gas–surface interactions do not affect the measurements. By using the Wu et al. model, bulk viscosities (due to the rotational relaxation of gas molecules only) and translational Eucken factors of $\textrm {N}_2$, $\textrm {CO}_2$ and $\textrm {SF}_6$ are simultaneously extracted from RBS experiments.

JFM classification

Rarefied Gas Flow: Rarefied Gas Flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 901 , 25 October 2020 , A23
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bird, G. A. 1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford University Press.Google Scholar
Boltzmann, L. 1872 Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. Sitz.ber. Akad. Wiss. Wien 66, 275–370.Google Scholar
Borgnakke, C. & Larsen, P. S. 1975 Statistical collision model for Monte Carlo simulation of polyatomic gas mixture. J. Comput. Phys. 18 (4), 405–420.CrossRefGoogle Scholar
Boyd, I. D. 1990 Rotational-translational energy transfer in rarefied nonequilibrium flows. Phys. Fluids A 2, 447–452.CrossRefGoogle Scholar
Bruno, D., Capitelli, M., Longo, S. & Minelli, P. 2006 Monte Carlo simulation of light scattering spectra in atomic gases. Chem. Phys. Lett. 422, 571–574.CrossRefGoogle Scholar
Bruno, D. & Frezzotti, A. 2019 Dense gas effects in the Rayleigh–Brillouin scattering spectra of SF6. Chem. Phys. Lett. 731, 136595.CrossRefGoogle Scholar
Bruno, D., Frezzotti, A. & Ghiroldi, G. P. 2015 Oxygen transport properties estimation by classical trajectory–direct simulation Monte Carlo. Phys. Fluids 27, 057101.10.1063/1.4921157CrossRefGoogle Scholar
Bruno, D., Frezzotti, A. & Ghiroldi, G. P. 2017 Rayleigh–Brillouin scattering in molecular oxygen by CT–DSMC simulations. Eur. J. Mech. B/Fluids 64, 8–16.CrossRefGoogle Scholar
Chapman, S. & Cowling, T. G. 1970 The Mathematical Theory of Non-uniform Gases. Cambridge University Press.Google Scholar
Eucken, A. 1913 Über das Wärmeleitvermögen, die spezifische Wärme und die innere Reibung der Gase. Phys. Z 14, 324.Google Scholar
Gallis, M. A., Rader, D. J. & Torczynski, J. R. 2004 A generalized approximation for the thermophoretic force on a free-molecular particle. Aerosol Sci. Technol. 38, 692–706.CrossRefGoogle Scholar
Gerakis, A., Shneider, M. N. & Barker, P. F. 2013 Single-shot coherent Rayleigh–Brillouin scattering using a chirped optical lattice. Opt. Lett. 38 (21), 4449.CrossRefGoogle ScholarPubMed
Gimelshein, N. E., Gimelshein, S. F. & Lavin, D. A. 2002 Vibrational relaxation rates in the direct simulation Monte Carlo method. Phys. Fluids 14, 4452.CrossRefGoogle Scholar
Gu, Z. & Ubachs, W. 2013 Temperature-dependent bulk viscosity of nitrogen gas determined from spontaneous Rayleigh–Brillouin scattering. Opt. Lett. 38 (7), 1110.CrossRefGoogle ScholarPubMed
Gu, Z., Ubachs, W., Marques, W. & van de Water, W. 2015 Rayleigh–Brillouin scattering in binary-gas mixtures. Phys. Rev. Lett. 114, 243902.CrossRefGoogle ScholarPubMed
Gu, Z., Ubachs, W. & van de Water, W. 2014 Rayleigh–Brillouin scattering of carbon dioxide. Opt. Lett. 39, 3301.CrossRefGoogle ScholarPubMed
Gu, Z., Vieitez, M. O., van Duijn, E. J. & Ubachs, W. 2012 A Rayleigh–Brillouin scattering spectrometer for ultraviolet wavelengths. Rev. Sci. Instrum. 83, 053112.Google ScholarPubMed
Guder, C. & Wagner, W. 2009 A reference equation of state for the thermodynamic properties of sulfur hexafluoride (SF6) for temperatures from the melting line to 625 K and pressures up to 150 MPa. J. Phys. Chem. Ref. Data 38, 33–94.CrossRefGoogle Scholar
Gupta, A. D. & Storvick, T. S. 1970 Analysis of the heat conductivity data for polar and nonpolar gases using thermal transpiration measurements. J. Chem. Phys. 52 (2), 742–749.CrossRefGoogle Scholar
Haas, B. L., Hash, D. B., Bird, G. A., Lumpkin III, F. E. & Hassan, H. A. 1994 Rates of thermal relaxation in direct simulation Monte Carlo methods. Phys. Fluids 6, 2191.CrossRefGoogle Scholar
Haebel, E. U. 1968 Measurement of the temperature dependence of the oscillation relaxation in sulphur hexafluoride between 10C and 215C. Acustica 20, 65.Google Scholar
Hanson, F. B. & Morse, T. F. 1967 Kinetic models for a gas with internal structure. Phys. Fluids 10, 345.CrossRefGoogle Scholar
Jaeger, F., Matar, O. K. & Muller, E. A. 2018 Bulk viscosity of molecular fluids. J. Chem. Phys. 148, 174504.CrossRefGoogle ScholarPubMed
Lambert, L. 1977 Vibrational and Rotational Relaxation in Gases. Clarendon.Google Scholar
Loyalka, S. K. & Storvick, T. S. 1979 Kinetic theory of thermal transpiration and mechanocaloric effect. III. Flow of a polyatomic gas between parallel plates. J. Chem. Phys. 71, 339–350.CrossRefGoogle Scholar
Loyalka, S. K., Storvick, T. S. & Lo, S. S. 1982 Thermal transpiration and mechanocaloric effect. IV. Flow of a polyatomic gas in a cylindrical tube. J. Chem. Phys. 76 (8), 4157–4170.CrossRefGoogle Scholar
Mason, E. A. 1963 Molecular relaxation times from thermal transpiration measurements. J. Chem. Phys. 39, 522–526.CrossRefGoogle Scholar
Mason, E. A. & Monchick, L. 1962 Heat conductivity of polyatomic and polar gases. J. Chem. Phys. 36, 1622.CrossRefGoogle Scholar
Maxwell, J. C. 1867 On the dynamical theory of gases. Phil. Trans. R. Soc. 157, 49–88.Google Scholar
Maxwell, J. C. 1879 On stresses in rarefied gases arising from inequalities of temperature. Part 1. Phil. Trans. R. Soc. Lond. 170, 231–256.Google Scholar
Meador, W. E., Miner, G. A. & Townsend, L. W. 1996 Bulk viscosity as a relaxation parameter: fact or fiction? Phys. Fluids 8, 258.CrossRefGoogle Scholar
Meijer, A. S., de Wijn, A. S., Peters, M. F. E., Dam, N. J. & van de Water, W. 2010 Coherent Rayleigh–Brillouin scattering measurements of bulk viscosity of polar and nonpolar gases, and kinetic theory. J. Chem. Phys. 133, 164315.CrossRefGoogle ScholarPubMed
Pan, X., Shneider, M. N. & Miles, R. B. 2002 Coherent Rayleigh–Brillouin scattering. Phys. Rev. Lett. 89 (18), 183001.CrossRefGoogle ScholarPubMed
Pan, X., Shneider, M. N. & Miles, R. B. 2004 Coherent Rayleigh–Brillouin scattering in molecular gases. Phys. Rev. A 69, 033814.CrossRefGoogle Scholar
Pan, X., Shneider, M. N. & Miles, R. B. 2005 Power spectrum of coherent Rayleigh–Brillouin scattering in carbon dioxide. Phys. Rev. A 71, 045801.CrossRefGoogle Scholar
Parker, G. L. 1959 Rotational and vibrational relaxation in diatomic gases. Phys. Fluids 2, 449–462.CrossRefGoogle Scholar
Porodnov, B. T., Kulev, A. N. & Tuchvetov, F. T. 1978 Thermal transpiration in a circular capillary with a small temperature difference. J. Fluid Mech. 88 (4), 609–622.CrossRefGoogle Scholar
Quinones-Cisneros, S. E., Huber, M. L. & Deiters, U. K. 2012 Correlation for the viscosity of sulfur hexafluoride (SF6) from the triple point to 1000 K and pressures to 50 MPa. J. Phys. Chem. Ref. Data 41, 023102.CrossRefGoogle Scholar
Reynolds, O. 1879 On certain dimensional properties of matter in the gaseous state. Part 1. Phil. Trans. R. Soc. Lond. 170, 727–845.Google Scholar
Shang, J. C., Wu, T., Wang, H., Yang, C. Y., Ye, C. W., Hu, R. J., Tao, J. Z. & He, X. D. 2019 Measurement of temperature-dependent bulk viscosities of nitrogen, oxygen and air from spontaneous Rayleigh–Brillouin scattering. IEEE Access 7, 136439–136451.CrossRefGoogle 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.CrossRefGoogle Scholar
Su, W., Zhu, L. H., Wang, P., Zhang, Y. H. & Wu, L. 2020 Can we find steady-state solutions to multiscale rarefied gas flows within dozens of iterations? J. Comput. Phys. 407, 109245.CrossRefGoogle Scholar
Sugawara, A., Yip, S. & Sirovich, L. 1968 Spectrum of density fluctuations in gases. Phys. Fluids 11, 925–932.CrossRefGoogle Scholar
Tenti, G., Boley, C. & Desai, R. 1974 On the kinetic model description of Rayleigh–Brillouin scattering from molecular gases. Can. J. Phys. 52, 285.CrossRefGoogle Scholar
Vieitez, M. O., van Duijn, E. J., Ubachs, W., Witschas, B., Meijer, A., de Wijn, A. S., Dam, N. J. & van de Water, W. 2010 Coherent and spontaneous Rayleigh–Brillouin scattering in atomic and molecular gases and gas mixtures. Phys. Rev. A 82, 043836.CrossRefGoogle Scholar
Wagner, W. 1992 A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation. J. Stat. Phys. 66, 1011–1044.CrossRefGoogle Scholar
Wang, Y., Liang, K., van de Water, W., Marques, W.Jr. & Ubachs, W. 2018 Rayleigh–Brillouin light scattering spectroscopy of nitrous oxide (N2O). J. Quant. Spectrosc. Radiat. Transfer 206, 63–69.CrossRefGoogle Scholar
Wang, Y., Ubachs, W. & van de Water, W. 2019 Bulk viscosity of CO2 from Rayleigh–Brillouin light scattering spectroscopy at 532 nm. J. Chem. Phys. 150, 154502.CrossRefGoogle ScholarPubMed
Wang, Y., Yu, Y., Liang, K., Marques, W.Jr., van de Water, W. & Ubachs, W. 2017 Rayleigh–Brillouin scattering in SF6 in the kinetic regime. Chem. Phys. Lett. 669, 137–142.CrossRefGoogle Scholar
Wang-Chang, C. S. & Uhlenbeck, G. E. 1951 Transport phenomena in polyatomic gases. Report No. CM-681. University of Michigan Engineering Research.Google Scholar
White, F. M. 1998 Viscous Fluid Flow. McGraw-Hill Higher Education.Google Scholar
Wu, L. & Gu, X.-J. 2020 On the accuracy of macroscopic equations for linearized rarefied gas flows. Adv. Aerodyn. 2, 2.CrossRefGoogle Scholar
Wu, L., Liu, H. H., Zhang, Y. H. & Reese, J. M. 2015 a Influence of intermolecular potentials on rarefied gas flows: fast spectral solutions of the Boltzmann equation. Phys. Fluids 27, 082002.CrossRefGoogle Scholar
Wu, L. & Struchtrup, H. 2017 Assessment and development of the gas kinetic boundary condition for the Boltzmann equation. J. Fluid Mech. 823, 511–537.CrossRefGoogle Scholar
Wu, L., White, C., Scanlon, T. J., Reese, J. M. & Zhang, Y. H. 2015 b A kinetic model of the Boltzmann equation for non-vibrating polyatomic gases. J. Fluid Mech. 763, 24–50.CrossRefGoogle Scholar