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, 0−q 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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
H. Baddar, G. Ahlers, K. Kuehn, and H. Fu, J. Low Temp. Phys. 119, 1 (2000).
C. J. Gorter and J. H. Mellink, Physica 15, 285 (1949).
W. F. Vinen, Proc. Roy. Soc. (London) A 242, 493 (1957).
L. E. de Long, O. G. Symko, and J. C. Wheatley, Rev. Sci. Instrum. 42, 147 (1971).
H. Fu, H. Baddar, K. Kuehn, M. Larson, N. Mulders, A. Schegolev, and G. Ahlers, J. Low Temp. Phys. 111, 49 (1998).
K. H. Müller, G. Ahlers, and F. Pobell, Phys. Rev. B 14, 2096 (1976).
V. Steinberg and G. Ahlers, J. Low Temp. Phys. 53, 255 (1983).
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.
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}.
G. Ahlers, Phys. Rev. Lett. 22, 54 (1969).
W. Y. Tam and G. Ahlers, Phys. Rev. B 32, 5932 (1985); 33, 183 (1986).
P. Leiderer and F. Pobell, J. Low Temp. Phys. 3, 577 (1970).
J. T. Tough, Superfluid turbulence, in Prog. Low Temp. Phys. VIII, D. F. Brewer (ed.), North Holland, Amsterdam (1982), Chap. 3.
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).
R. Haussmann, Phys. Rev. B 60, 12349 (1999).
C. E. Swanson and R. J. Donnelly, J. Low Temp. Phys. 61, 363 (1985) (see also Ref. 16).
Rights and permissions
About this article
Cite this article
Kuehn, K., Ahlers, G. Mutual Friction in Superfluid 4He Near the λ-Line. Journal of Low Temperature Physics 126, 1515–1528 (2002). https://doi.org/10.1023/A:1014247500834
- Transition Temperature
- Vapor Pressure
- Magnetic Material
- Thermal Resistivity
- Saturated Vapor