Journal of Low Temperature Physics

, Volume 196, Issue 1–2, pp 60–72 | Cite as

Molecular Tagging Velocimetry in Superfluid Helium-4: Progress, Issues, and Future Development



Helium-4 in the superfluid phase (He II) is a two-fluid system that exhibits fascinating quantum hydrodynamics with important scientific and engineering applications. However, the lack of high-precision flow measurement tools in He II has impeded the progress in understanding and utilizing its hydrodynamics. In recent years, there have been extensive efforts in developing quantitative flow visualization techniques applicable to He II. In particular, a powerful molecular tagging velocimetry (MTV) technique, based on tracking thin lines of \(\hbox {He}^*_2\) excimer molecules created via femtosecond laser-field ionization in helium, has been developed in our laboratory. This technique allows unambiguous measurement of the normal fluid velocity field in the two-fluid system. Nevertheless, there are two limitations to this technique: (1) only the velocity component perpendicular to the tracer line can be measured; and (2) there is an inherent error in determining the perpendicular velocity. In this paper, we discuss how these issues can be resolved by advancing the MTV technique. We also discuss two novel schemes for tagging and producing \(\hbox {He}^*_2\) tracers. The first method allows the creation of a tagged \(\hbox {He}^*_2\) tracer line without the use of an expensive femtosecond laser. The second method enables full-space velocity field measurement through tracking small clouds of \(\hbox {He}^*_2\) molecules created via neutron-\(^3\hbox {He}\) absorption reactions in He II.


Quantum turbulence Superfluid helium-4 Flow visualization Molecular tagging \(\hbox {He}^*_2\) excimer 



The author would like to acknowledge the contributions made by previous and current students in the laboratory, including J. Gao, A. Marakov, E. Varga, B. Mastracci, S. Bao, Y. Zhang, and H. Sanavandi. The author would also like to thank many colleagues in quantum turbulence and classical fluid dynamics research fields for valuable discussions. The work has been supported by US Department of Energy under Grant No. DE-FG02-96ER40952 and by the National Science Foundation under Grants Nos. DMR-1807291 and CBET-1801780. All the experiments have been performed at the National High Magnetic Field Laboratory, which is supported by NSF Grant No. DMR-1644779 and the state of Florida.


  1. 1.
    D.R. Tilley, J. Tilley, Superfluidity and Superconductivity, 2nd edn. (Published in association with the University of Sussex Press, Boston, 1986)zbMATHGoogle Scholar
  2. 2.
    R.J. Donnelly, Quantized Vortices in Helium II (Cambridge University Press, Cambridge, 1991)Google Scholar
  3. 3.
    W.F. Vinen, J.J. Niemela, Quantum turbulence. J. Low Temp. Phys. 129, 213–213 (2002)CrossRefGoogle Scholar
  4. 4.
    W.F. Vinen, Mutual friction in a heat current in liquid helium II. I. Experiments on steady heat currents. Proc. R. Soc. Lond. A 240, 114–127 (1957)Google Scholar
  5. 5.
    W. Van Sciver, Helium Cryogenics, 2nd edn. (Springer, New York, 2012)CrossRefGoogle Scholar
  6. 6.
    E. Blanco, A. Calzas, J. Casas-Cubillos, P. Gomes, S. Knoops, L. Serio, R. Van Weelderen, Experimental validation and operation of the LHC Test String 2 cryogenic system. AIP Conf. Proc. 710, 233–240 (2004)CrossRefGoogle Scholar
  7. 7.
    M.A. Taber, D.O. Murry, J.R. Maddocks, K.M. Burns, Operational cryogenic experience with the gravity probe B payload. AIP Conf. Proc. 613, 1241–1248 (2002)CrossRefGoogle Scholar
  8. 8.
    A. Bonitooliva, M.B. Gorbunov, K. Iyengar, J. Miller, S.W. Van Sciver, S. Welton, Thermal-analysis of the superconducting outsert of the NHMFL 45-T hybrid magnet system. Cryogenics 34, 713–716 (1994)CrossRefGoogle Scholar
  9. 9.
    R.J. Donnelly, High Reynolds Number Flows Using Liquid and Gaseous Helium (Springer, New York, 1991)CrossRefGoogle Scholar
  10. 10.
    L. Skrbek, J.J. Niemela, R.J. Donnelly, Turbulent flows at cryogenic temperatures: a new frontier. J. Phys. Condens. Matter 11, 7761–7781 (1999)CrossRefGoogle Scholar
  11. 11.
    K.R. Sreenivasan, R.J. Donnelly, Role of cryogenic helium in classical fluid dynamics: basic research and model testing. Adv. Appl. Mech. 37, 239–276 (2001)CrossRefGoogle Scholar
  12. 12.
    W. Guo, D.P. Lathrop, M.L. Mantia, S.W. Van Sciver, Visualization of two-fluid flows of superfluid helium-4 at finite temperatures. Proc. Natl. Acad. Sci. 111, 4653 (2014)CrossRefGoogle Scholar
  13. 13.
    S.W. Van Sciver, S. Fuzier, T. Xu, Particle image velocimetry studies of counterflow heat transport in superfluid helium II. J. Low Temp. Phys. 148, 225 (2007)CrossRefGoogle Scholar
  14. 14.
    T. Zhang, S.W. Van Sciver, Large-scale turbulent flow around a cylinder in counterflow superfluid He-4 (He(II)). Nat. Phys. 1, 36 (2005)CrossRefGoogle Scholar
  15. 15.
    M. La Mantia, D. Duda, M. Rotter, L. Skrbek, Lagrangian accelerations of particles in superfluid turbulence. J. Fluid Mech. 717, R9 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    M.S. Paoletti, R.B. Fiorito, K.R. Sreenivasan, D.P. Lathrop, Visualization of superfluid helium flow. J. Phys. Soc. Jpn. 77, 111007 (2008)CrossRefGoogle Scholar
  17. 17.
    G.P. Bewley, D.P. Lathrop, K.R. Sreenivasan, Superfluid helium—visualization of quantized vortices. Nature 441, 588 (2006)CrossRefGoogle Scholar
  18. 18.
    M.S. Paoletti, M.E. Fisher, K.R. Sreenivasan, D.P. Lathrop, Velocity statistics distinguish quantum turbulence from classical turbulence. Phys. Rev. Lett. 101, 154501 (2008)CrossRefGoogle Scholar
  19. 19.
    G.P. Bewley, M.S. Paoletti, K.R. Sreenivasan, D.P. Lathrop, Characterization of reconnecting vortices in superfluid helium. Proc. Natl. Acad. Sci. 105, 13707 (2008)CrossRefGoogle Scholar
  20. 20.
    E. Fonda, D.P. Meichle, N.T. Ouellette, S. Hormoz, D.P. Lathrop, Direct observation of Kelvin waves excited by quantized vortex reconnection. Proc. Natl. Acad. Sci. 111, 4707 (2014)CrossRefGoogle Scholar
  21. 21.
    D. Kivotides, Motion of a spherical solid particle in thermal counterflow turbulence. Phys. Rev. B 77, 174508 (2008)CrossRefGoogle Scholar
  22. 22.
    B. Mastracci, W. Guo, An exploration of thermal counterflow in He II using particle tracking velocimetry. Phys. Rev. Fluid 3, 063304 (2018)CrossRefGoogle Scholar
  23. 23.
    W. Guo, J.D. Wright, S.B. Cahn, J.A. Nikkel, D.N. McKinsey, Metastable helium molecules as tracers in superfluid He-4. Phys. Rev. Lett. 102, 235301 (2009)CrossRefGoogle Scholar
  24. 24.
    W. Guo, J.D. Wright, S.B. Cahn, J.A. Nikkel, D.N. McKinsey, Studying the normal-fluid flow in helium-II using metastable helium molecules. J. Low Temp. Phys. 158, 346–352 (2010)CrossRefGoogle Scholar
  25. 25.
    W. Guo, S.B. Cahn, J.A. Nikkel, W.F. Vinen, D.N. McKinsey, Visualization study of counterflow in superfluid \(^4\text{ He }\) using metastable helium molecules. Phys. Rev. Lett. 105, 045301 (2010)CrossRefGoogle Scholar
  26. 26.
    D.N. McKinsey, C.R. Brome, J.S. Butterworth, S.N. Dzhosyuk, P.R. Huffman, C.E.H. Mattoni, J.M. Doyle, R. Golub, K. Habicht, Radiative decay of the metastable \(\text{ He }_2\)(\(a^3\varSigma ^{+}_u\)) molecule in liquid helium. Phys. Rev. A 59, 200–204 (1999)CrossRefGoogle Scholar
  27. 27.
    A.V. Benderskii, J. Eloranta, R. Zadoyan, V.A. Apkarian, A direct interrogation of superfluidity on molecular scales. J. Chem. Phys. 117, 1201–1213 (2002)CrossRefGoogle Scholar
  28. 28.
    D. Mateo, J. Eloranta, G.A. Williams, Interaction of ions, atoms, and small molecules with quantized vortex lines in superfluid He-4. J. Chem. Phys. 142, 064510 (2015)CrossRefGoogle Scholar
  29. 29.
    D.E. Zmeev, F. Pakpour, P.M. Walmsley, A.I. Golov, W. Guo, D.N. McKinsey, G.G. Ihas, P.V. McClintock, S.N. Fisher, W.F. Vinen, Excimers \(\text{ He }^*_2\) as tracers of quantum turbulence in \(^4\text{ He }\) in the \(T=0\) limit. Phys. Rev. Lett. 110, 175303 (2013)CrossRefGoogle Scholar
  30. 30.
    D.N. McKinsey, W.H. Lippincott, J.A. Nikkel, W.G. Rellergert, Trace detection of metastable helium molecules in superfluid helium by laser-induced fluorescence. Phys. Rev. Lett. 95, 111101 (2005)CrossRefGoogle Scholar
  31. 31.
    W.G. Rellergert, S.B. Cahn, A. Garvan, J.C. Hanson, W.H. Lippincott, J.A. Nikkel, D.N. McKinsey, Detection and imaging of \(\text{ He }^*_2\) molecules in superfluid helium. Phys. Rev. Lett. 100, 025301 (2008)CrossRefGoogle Scholar
  32. 32.
    J. Gao, A. Marakov, W. Guo, B.T. Pawlowski, S.W. Van Sciver, G.G. Ihas, D.N. McKinsey, W.F. Vinen, Producing and imaging a thin line of \(\text{ He }^*_2\) molecular tracers in helium-4. Rev. Sci. Instrum. 86, 093904 (2015)CrossRefGoogle Scholar
  33. 33.
    A. Marakov, J. Gao, W. Guo, S.W. Van Sciver, G.G. Ihas, D.N. McKinsey, W.F. Vinen, Visualization of the normal-fluid turbulence in counterflowing superfluid He-4. Phys. Rev. B 91, 094503 (2015)CrossRefGoogle Scholar
  34. 34.
    J. Gao, W. Guo, V.S. L’vov, A. Pomyalov, L. Skrbek, E. Varga, W.F. Vinen, Challenging problem in quantum turbulence: decay of counterflow in superfluid \(^4\text{ He }\). JETP Lett. 103, 732 (2016)CrossRefGoogle Scholar
  35. 35.
    J. Gao, W. Guo, W.F. Vinen, Determination of the effective kinematic viscosity for the decay of quasiclassical turbulence in superfluid \(^4\text{ He }\). Phys. Rev. B 94, 094502 (2016)CrossRefGoogle Scholar
  36. 36.
    J. Gao, E. Varga, W. Guo, W.F. Vinen, Statistical measurement of counterflow turbulence in superfluid helium-4 using \(\text{ He }^*_2\) tracer-line tracking technique. J. Low Temp. Phys. 187, 490 (2017)CrossRefGoogle Scholar
  37. 37.
    J. Gao, E. Varga, W. Guo, W.F. Vinen, Energy spectrum of thermal counterflow turbulence in superfluid helium-4. Phys. Rev. B 96, 094511 (2017)CrossRefGoogle Scholar
  38. 38.
    J. Gao, W. Guo, W.F. Vinen, S. Yui, M. Tsubota, Dissipation in quantum turbulence in superfluid \(^4\text{ He }\). Phys. Rev. B 97, 184518 (2018)CrossRefGoogle Scholar
  39. 39.
    R.B. Miles, W. Lempert, B. Zhang, Turbulent structure measurements by relief flow tagging. Fluid Dyn. Res. 8, 9–17 (1991)CrossRefGoogle Scholar
  40. 40.
    R.B. Miles, W.R. Lempert, Quantitative flow visualization in unseeded flows. Annu. Rev. Fluid Mech. 29, 285 (1997)CrossRefGoogle Scholar
  41. 41.
    P. Hammer, S. Pouya, A. Naguib, M. Koochesfahani, A multi-time-delay approach for correction of the inherent error in single-component molecular tagging velocimetry. Meas. Sci. Technol. 24, 105302 (2013)CrossRefGoogle Scholar
  42. 42.
    F. Chen, H.X. Li, H. Hu, Molecular tagging techniques and their applications to the study of complex thermal flow phenomena. Acta Mech. Sin. 31, 425 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    D.G. Bohl, M.M. Koochesfahani, B.J. Olson, Development of stereoscopic molecular tagging velocimetry. Exp. Fluids 30, 302 (2001)CrossRefGoogle Scholar
  44. 44.
    M. Raffel, C.E. Villert, S.T. Werely, J. Kompenhans, Particle Image Velocimetry—A Practical Guide, 2nd edn. (Springer, Berlin, 2007)CrossRefGoogle Scholar
  45. 45.
    W. Guo, New techniques for visualization study of normal-fluid turbulence in superfluid He-4 using metastable \(\text{ He }^*_2\) molecules. Invited talk presented at the Workshop on Turbulence in Quantum Two-Fluid Systems, Abu Dhabi, UAE (05/2012)Google Scholar
  46. 46.
    W. Guo, Application of neutron in the study of quantum fluid hydrodynamics. Invited talk presented at the Workshop on Very Cold Neutron Source for the Second Target Station Workshop, Oak Ridge National Lab, Knoxville, TN, United States (05/2016)Google Scholar
  47. 47.
    M.E. Hayden, G. Archibald, P.D. Barnes, W.T. Buttler, D.J. Clark, M.D. Cooper, M. Espy, R. Golub, G.L. Greene, S.K. Lamoreaux, C. Lei, L.J. Marek, J.C. Peng, S.I. Penttila, Neutron-detected tomography of impurity-seeded superfluid helium. Phys. Rev. Lett. 93, 105302 (2004)CrossRefGoogle Scholar
  48. 48.
    L.D.P. King, L. Goldstein, The total cross section of the He-3 nucleus for slow neutrons. Phys. Rev. 75, 1366–1369 (1949)CrossRefGoogle Scholar
  49. 49.
    J.S. Meyer, T. Sloan, Neutron interactions in liquid He-3. J. Low Temp. Phys. 108, 345–354 (1997)CrossRefGoogle Scholar
  50. 50.
    W. Guo, D.N. McKinsey, Concept for a dark matter detector using liquid helium-4. Phys. Rev. D 87, 115011 (2013)CrossRefGoogle Scholar
  51. 51.
    T.M. Ito, G.M. Seidel, Scintillation of liquid helium for low-energy nuclear recoils. Phys. Rev. C 88, 025805 (2013)CrossRefGoogle Scholar
  52. 52.
    Collaboration of Neutron-\(^3\text{ He }\) project at the Japan Proton Accelerator Research Complex (J-PARC): T. Matsushita, V. Sonnenschein, W. Guo, H. Hayashida, K. Hiroi, K. Hirota, T. Iguchi, D. Ito, M. Kitaguchi, Y. Kiyanagi, S. Kokuryu, W. Kubo, Y. Saito, H. M. Shimizu, T. Shinohara, S. Suzuki, H. Tomita, Y. Tsuji, and N. WadaGoogle Scholar
  53. 53.
    T. Matsushita, V. Sonnenschein, W. Guo, H. Hayashida, K. Hiroi, K. Hirota, T. Iguchi, D. Ito, M. Kitaguchi, Y. Kiyanagi, S. Kokuryu, W. Kubo, Y. Saito, H. M. Shimizu, T. Shinohara, S. Suzuki, H. Tomita, Y. Tsuji, N. Wada, Generation of \(^4\text{ He }_2\) clusters via neutron-\(^3\text{ He }\) absorption reaction towards visualization of full velocity field in quantum turbulence. J. Low Temp. Phys., this Special Issue QFS2018 (2019)Google Scholar
  54. 54.
    Collaboration of Neutron-\(^3\text{ He }\) project at the Oak Ridge National Lab: S. Bao, L. Crow, M. Fitzsimmons, G. Greene, W. Guo, L. McDonald, T. Mezzacappa, J. Pierce, X. Tong, X. Wen, and Y. ZhaoGoogle Scholar
  55. 55.
    S. Kakac, Y. Yener, A. Pramuanjaroenkij, Convective Heat Transfer, 3rd edn. (Taylor and Francis, Boca Raton, 2013)zbMATHGoogle Scholar
  56. 56.
    J.J. Niemela, K.R. Sreenivasan, The use of cryogenic helium for classical turbulence: promises and hurdles. J. Low Temp. Phys. 143, 163 (2006)CrossRefGoogle Scholar
  57. 57.
    J.J. Niemela, L. Skrbek, K.R. Sreenivasan, R.J. Donnelly, Turbulent convection at very high Rayleigh numbers. Nature 404, 837 (2000)CrossRefGoogle Scholar
  58. 58.
    P.E. Roche, F. Gauthier, R. Kaiser, J. Salort, On the triggering of the ultimate regime of convection. New J. Phys. 12, 085014 (2010)CrossRefGoogle Scholar
  59. 59.
    P. Urban, P. Hanzelka, T. Kralik, V. Musilova, A. Srnka, L. Skrbek, Effect of boundary layers asymmetry on heat transfer efficiency in turbulent Rayleigh–Benard convection at very high Rayleigh numbers. Phys. Rev. Lett. 109, 154301 (2012)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.National High Magnetic Field Laboratory, Mechanical Engineering DepartmentFlorida State UniversityTallahhasseeUSA

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