Anomalous Thermal Conductivity in Very Dilute 3He-4He Solutions

  • Richard A. Ferrell
Part of the NATO ASI Series book series (NSSB, volume 257)


The measurements of Meyer’s group1 at Duke University have revealed an unexpected deviation from Khalatnikov’s theory of very dilute 3He-4He solutions. The theoretical prediction is that K eff , the effective thermal conductivity in the superfluid phase, should diverge as the reciprocal of the X, 3He mole fraction. In contrast, Meyer and coworkers have found K eff leveling off at a finite value and apparently becoming nearly independent of X. This finding was corroborated by one measurement by Lipa and Chui at the very low value of X = 10−7. We have been able to account phenomenologically for this extremely puzzling behavior by means of a “3-fluid model,” which postulates that there is an additional normal component that interacts both with the 3He and with the gas of excitations in the liquid 4He (i.e., with the usual normal component). By fitting the parameters to the observed plateau, the 3-fluid model predicts that K eff should rise again for even lower concentrations, in the range X < 10−7. Although difficult, this test ought to be feasible with the advanced thermometric techniques that are now available. The search for the predicted rise at X < 10−7 and the development of “quasi-Khalatnikov” behavior at the ultra-low concentrations will be a crucial test for the 3-fluid hypothesis.


Mole Fraction Drag Coefficient Effective Thermal Conductivity Heat Current Normal Fluid 
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  1. 1.
    M. Dingus, F. Zhong, J. Tuttle, and H. Meyer, J. Low Temp. Phys. 65, 213 (1986). See also M. Dingus, F. Zhong, and H. M. yer, Phys. Rev. Letters 54, 2347 (1985).Google Scholar
  2. 2.
    For a general review and complete bibliography of this subject, see H. Meyer, these proceedings.Google Scholar
  3. 3.
    J.A. Lipa and T.C.P. Chuff, Phys. Rev. Letters 58, 1340 (1987); Proceedings of the 18th International Conference on Low Temperature Physics, Kyoto, 1987 [Jpn. J. Appl. Phys. Suppl. 26–3 13 (1987)].Google Scholar
  4. 4.
    F. Zhong, J. Tuttle, and H. Meyer, J. Low Temp. Phys. 49, 9 (1990).ADSCrossRefGoogle Scholar
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    T.C.P. Chuff and J.A. Lipa, Phys. Rev. B40, 4306 (1989).ADSGoogle Scholar
  6. 6.
    I am indebted to Prof. Meyer for providing this fit to the data of reference 1.Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Richard A. Ferrell
    • 1
  1. 1.Center for Theoretical Physics and Center for Superconductivity Research, Department of Physics and AstronomyUniversity of MarylandCollege ParkUSA

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