Journal of Low Temperature Physics

, Volume 65, Issue 3–4, pp 213–245 | Cite as

Thermal transport properties of helium near the superfluid transition. II. Dilute3He-4He mixtures in the superfluid phase

  • M. Dingus
  • F. Zhong
  • J. Tuttle
  • H. Meyer


Measurements of the average thermal conductivity κexphQ/ΔT and of the thermal relaxation time τ to reach steady-state equilibrium conditions are reported in the superfluid phase for dilute mixtures of3He in4He. Hereh is the cell height,Q is the heat flux, andΔT is the temperature difference across the fluid layer. The measurements were made over the impurity range 2×10−9<X(3He)<3×10−2 and with heat fluxes 0.3<Q<160 µW/cm2. Assuming the boundary resistanceR b , measured forX<10−5, to be independent ofX over the whole range ofX, a calculation is given for κexp. ForQ smaller than a well-defined critical heat fluxQ c (X) ∝X0.9, κexp is independent of Q and can be identified with the local conductivity κeff, which is found to be independent of the reduced temperature ɛ = (T−Tλ)/Tλ for −ɛ≤10−2. Its extrapolated value at Tλ is found to depart forX≲10−3 from the prediction κλX −1 , tending instead to a weaker divergence κλX −a witha≈0.08. A finite conductivity asX tends to zero is not excluded by the data, however. ForQ >Q c (X), a nonlinear regime is entered. ForX≲10−6, the measurements with the available temperature resolution are limited to the nonlinear conditions, but can be extrapolated into the linear regime forX≳2×10−7. The results for κexp(Q),Q c (X), and κeff(XX) are found to be internally consistent, as shown by comparison with a theory by Behringer based on Khalatnikov's transport equations. Furthermore, the observed relaxation times τ(X) in the linear regime are found to be consistent forX>10−5 with the hydrodynamic calculations using the measured κeff(X). ForX<10−5, a faster relaxation mechanism than predicted seems to dominate. The transport properties in the nonlinear regimes are presented and unexplained observations are discussed.


Heat Flux Linear Regime Thermal Relaxation Nonlinear Regime Boundary resistanceR 


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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • M. Dingus
    • 1
  • F. Zhong
    • 1
  • J. Tuttle
    • 1
  • H. Meyer
    • 1
  1. 1.Department of PhysicsDuke UniversityDurham

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