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Superfluid Thermodynamic Transport Limits for Liquid Helium II

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Advances in Cryogenic Engineering

Part of the book series: Advances in Cryogenic Engineering ((ACRE,volume 19))

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Abstract

Recent advances in liquid He II technology pose questions concerning the utilization of “superphenomena.” In particular, it is useful to know the transport conditions that separate classical flow (with large flow resistances) from nonclassical phenomena (with small or entirely negligible resistances). The purpose of the present investigation, therefore, is a thermodynamic evaluation of the critical flow rates at the initiation of observable flow resistance (upper stability limit at which superfluidity becomes thermodynamically unstable). The critical flow rate is evaluated on the basis of the modified (Gorter-Casimir) two-fluid model [1] and the extended theory of second-order phase transitions [2,3] The comparison with experiment shows that in general the thermodynamic critical rate is an upper bound to experimental data which approach the limit closely when T → T λ. Good agreement also is obtained for specific geometries in a limited temperature range below the λ-point

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Abbreviations

C :

= specific heat (volumetric)

ƒ :

= free energy density (Δƒ difference between disordered and ordered 4He)

h :

= Planck’s constant divided by 2π

j eff :

= effective mass flux

m :

= mass of 4He atom

n :

= exponent

ΔP T :

= thermomechanical pressure difference

q :

= heat flux

S :

= entropy (volumetric)

T :

= temperature

T λ :

= temperature at λ-point

t :

= T/T λ

U c :

= condensation energy (U o = Δƒ o)

v :

= velocity

y :

= superfluid density ratio, ρ s /ρ

α:

= parameter in equation (8)

β:

= parameter in equation (8)

γ:

= volumetric entropy coefficient

ε:

= exponent in equation (1)

ξ:

= coherence length

ρ:

= density

ψ:

= wave function, ψ∞ at T = 0

|ψ0|2 :

= equilibrium order parameter

c :

= critical

con:

= condensate

n :

= normal component

R :

= reference quantity

s :

= superfluid component

0:

= T → 0

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Authors and Affiliations

  1. University of California at Los Angeles, Los Angeles, California, USA

    C. Linnet, R. C. Amar, Y. G. Wang & T. H. K. Frederking

Authors
  1. C. Linnet
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  2. R. C. Amar
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  3. Y. G. Wang
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  4. T. H. K. Frederking
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Editor information

Editors and Affiliations

  1. Engineering Research Center, University of Colorado, Boulder, Colorado, USA

    K. D. Timmerhaus

  2. Engineering Division, National Science Foundation, Washington, D.C., USA

    K. D. Timmerhaus

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Linnet, C., Amar, R.C., Wang, Y.G., Frederking, T.H.K. (1995). Superfluid Thermodynamic Transport Limits for Liquid Helium II. In: Timmerhaus, K.D. (eds) Advances in Cryogenic Engineering. Advances in Cryogenic Engineering, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-9847-9_44

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  • DOI: https://doi.org/10.1007/978-1-4613-9847-9_44

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-9849-3

  • Online ISBN: 978-1-4613-9847-9

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