Common Approximations that Can Invalidate Calculations of the Flow of Superfluid Helium

  • H. A. Snyder
  • A. J. Mord
Part of the Advances in Cryogenic Engineering book series (ACRE, volume 43)


Calculations of the flow of He II are difficult because of its two-fluid nature and unusual boundary conditions. Investigators made many assumptions and approximations, over the years, to simplify the calculations and make them tractable. We find in scanning the literature that in a large number of situations approximations have been used beyond their range of validity. In some cases, this has resulted in substantially incorrect predictions. We have made a list of commonly used approximations and analyzed the range of validity of each. Examples of approximations are: assuming a critical velocity for the onset of turbulence in the superfluid when no critical velocity exists; attempting to specify the problem with less than four boundary conditions; neglect of the pressure gradient in evaluating the gradient of the chemical potential; neglect of property variations in one-dimensional flow; assuming the normal component flows like a Navier-Stokes fluid; attributing a dependence of the Gorter-Mellink coefficient to the structure of the material; using formulas for heat flow that apply only to counterflow situations when there is not mass flow; and assuming the normal fluid is clamped in porous flows. We made a comparison of calculations with and without the assumptions where possible.


Critical Velocity Landau Equation Superfluid Helium Mutual Friction Porous Plug 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L. Landau, The theory of superfluidity of helium II, J. Physics (Moscow), 5:71–90 (1941).Google Scholar
  2. 2.
    C. J. Gorter and J. H. Mellink, On the irreversible processes in liquid helium II, Physica, 15: 285–304 (1949).CrossRefGoogle Scholar
  3. 3.
    H. E. Hall and W. F. Vinen, I. Experiments on propogation of second sound in uniformly rotating helium II, Proc. Roy. Soc. (London), A238:204–214 (1956).CrossRefGoogle Scholar
  4. 4.
    I. M. Khalatnikov, “Introduction to the Theory of Superfluidity,” Benjamin, New York, (1965).Google Scholar
  5. 5.
    H. A. Snyder and A. J. Mord, Calculation of He II flow in tubes, J. Low Temp. Physics, 86:177–209 (1992).CrossRefGoogle Scholar
  6. 6.
    G. L. Mills, A. J. Mord and H. A. Snyder, Pressure maxima in the flow of superfluid He II in tubes, Phys. Rev. B, 49:666–669 (1994).CrossRefGoogle Scholar
  7. 7.
    H. A. Snyder, A. J. Mord and G. L. Mills, Comparison of modeling predictions and experimental data for He II flow in porous materials, Adv. Cryo. Eng. 39:1821–1828 (1994).CrossRefGoogle Scholar
  8. 8.
    W. E. Keller, “Helium-3 and Helium-4,” Plenum Press, New York, (1969).Google Scholar
  9. 9.
    A. J. Mord, D. A. Newell and H. A. Snyder, End to end modeling of He II flow systems, Cryogenics, 32:291–299(1991).CrossRefGoogle Scholar
  10. 10.
    H. A. Snyder and A. J. Mord, Modeling phase separator systems, Presented at the Cryogenics Engi neering Conference, Portland, OR (1997).Google Scholar
  11. 11.
    P. H. Roberts and R. J. Donnelly, in “Annual Review of Fluid Mechanics”, Vol. 6, M. VanDyke, W. G. Vincenti and J. V. Wehausen, eds., Annual Reviews, Palo Alto (1974), p 179–200.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • H. A. Snyder
    • 1
  • A. J. Mord
    • 1
  1. 1.University of Colorado at Boulder and Ball Aerospace & Technologies Corp.BoulderUSA

Personalised recommendations