Mutual Friction in Superfluid 4He Near the λ-Line


We present experimental results for the thermal resistivity ρ of superfluid 4He along several isobars between saturated vapor pressure and the melting pressure. The measurements are for the temperature range 1−T c(q)/T λ<t<2×10−5 and the heat-flux range 3<q<70 μW/cm2. Here t≡1−T/T λ, T λ is the transition temperature in the limit of zero q, and T c is the transition temperature at finite q. The data suggest that the resistivity has an incipient singularity at T λ which can be described by the power law ρ=(t/t 0)−(mν+α) where t 0=(q/q 0)x. However, the singularity is supplanted by the transition to a more highly dissipative phase at T c(q)<T λ. The results suggest a mild dependence of mν+α on the pressure P, but can be described quite well by mν+α=2.76, x=0.89, and q 0=q 0, 0q 0, 1 P with q 0, 0=401Wċcm−2 and q 0, 1=−5.0Wċcm−2bars−1. The results imply that the Gorter–Mellink mutual friction exponent m has a value close to 3.46 and is distinctly larger than the classical value m=3.

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  1. 1.

    H. Baddar, G. Ahlers, K. Kuehn, and H. Fu, J. Low Temp. Phys. 119, 1 (2000).

    Google Scholar 

  2. 2.

    C. J. Gorter and J. H. Mellink, Physica 15, 285 (1949).

    Google Scholar 

  3. 3.

    W. F. Vinen, Proc. Roy. Soc. (London) A 242, 493 (1957).

    Google Scholar 

  4. 4.

    L. E. de Long, O. G. Symko, and J. C. Wheatley, Rev. Sci. Instrum. 42, 147 (1971).

    Google Scholar 

  5. 6.

    H. Fu, H. Baddar, K. Kuehn, M. Larson, N. Mulders, A. Schegolev, and G. Ahlers, J. Low Temp. Phys. 111, 49 (1998).

    Google Scholar 

  6. 8.

    K. H. Müller, G. Ahlers, and F. Pobell, Phys. Rev. B 14, 2096 (1976).

    Google Scholar 

  7. 9.

    V. Steinberg and G. Ahlers, J. Low Temp. Phys. 53, 255 (1983).

    Google Scholar 

  8. 10.

    G. C. Straty and E. D. Adams, Rev. Sci. Instrum. 40, 1393 (1969). The particular version used in our work was very similar to the melting-pressure thermometer described by L. S. Goldner, N. Mulders, and G. Ahlers, in Temperature: Its Measurement and Control in Science and Industry, Vol. 6, J. F. Schooly (ed.), American Institute of Physics, N.Y. (1992), pp. 113–116.

    Google Scholar 

  9. 11.

    A more detailed discussion of the proposed fitting function is given in G. Ahlers, K. Kuehn, and H. Fu, J. Low Temp. Phys. 119, 1 (2000) Ref. 1}.

    Google Scholar 

  10. 12.

    G. Ahlers, Phys. Rev. Lett. 22, 54 (1969).

    Google Scholar 

  11. 13.

    W. Y. Tam and G. Ahlers, Phys. Rev. B 32, 5932 (1985); 33, 183 (1986).

    Google Scholar 

  12. 14.

    P. Leiderer and F. Pobell, J. Low Temp. Phys. 3, 577 (1970).

    Google Scholar 

  13. 15.

    J. T. Tough, Superfluid turbulence, in Prog. Low Temp. Phys. VIII, D. F. Brewer (ed.), North Holland, Amsterdam (1982), Chap. 3.

    Google Scholar 

  14. 16.

    R. J. Donnelly, Quantized Vortices in Hell, Cambridge University Press (1991); J. Phys. Cond. Matter 11, 7783 (1999); and J. Phys.: Condens. Matter 11, 7783 (1999).

  15. 17.

    R. Haussmann, Phys. Rev. B 60, 12349 (1999).

    Google Scholar 

  16. 18.

    C. E. Swanson and R. J. Donnelly, J. Low Temp. Phys. 61, 363 (1985) (see also Ref. 16).

    Google Scholar 

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Kuehn, K., Ahlers, G. Mutual Friction in Superfluid 4He Near the λ-Line. Journal of Low Temperature Physics 126, 1515–1528 (2002).

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  • Transition Temperature
  • Vapor Pressure
  • Magnetic Material
  • Thermal Resistivity
  • Saturated Vapor