Two-Fluid Theory of Liquid Helium II below 1°K

1950 ◽  
Vol 80 (5) ◽  
pp. 923-923 ◽  
Author(s):  
S. Nakajima ◽  
M. Shimizu
Keyword(s):  
Liquid Helium ◽  
Helium Ii ◽  
Fluid Theory ◽  
Two Fluid

scholarly journals Two Fluid Theory of Liquid Helium II. below 1 K

1951 ◽  
Vol 6 (1) ◽  
pp. 122-125 ◽  
Author(s):  
S. Nakajima ◽  
M. Shimizu
Keyword(s):  
Liquid Helium ◽  
Helium Ii ◽  
Fluid Theory ◽  
Two Fluid

The two-fluid theory and second sound in liquid helium

Physics Today ◽  
2009 ◽  
Vol 62 (10) ◽  
pp. 34-39 ◽  
Author(s):  
Russell J. Donnelly
Keyword(s):  
Liquid Helium ◽  
Second Sound ◽  
Fluid Theory ◽  
Two Fluid

A note on the effects of healing and relaxation in helium II due to heat transfer at a wall

1978 ◽  
Vol 362 (1710) ◽  
pp. 375-382 ◽  
Keyword(s):  
Heat Transfer ◽  
Equilibrium State ◽  
Liquid Helium ◽  
Half Space ◽  
Superfluid Density ◽  
Governing Equations ◽  
Helium Ii ◽  
Relaxation Coefficient ◽  
Two Fluid ◽  
Superfluid Velocity

The problem of heat transfer at a wall bounding a half-space ( z > 0) containing liquid helium II is considered. The helium is modelled as a two-fluid continuum (after Landau & Lifshitz) with both relaxation and healing terms incorporated into the governing equations. The heat transfer is taken to be small so that the problem can be treated as the perturbation of the equilibrium state (i. e. at zero heat transfer). It is shown that if the relaxation coefficient varies as (superfluid density) - m (1 > m ≽ 1/2) then the superfluid velocity behaves like cz 2 m -1 as z → 0. The constant c can be obtained by invoking a scaling property of the full equations. It is found that the healing parameter can be scaled out of the full equations although c can be found explicitly for small healing: c , and the related temperature at the wall, are therefore known for all values of the healing coefficient. These results reduce to those obtained by Clark (1963) when healing and relaxation are ignored.

Thermodynamics of the Two-Fluid Model of Liquid Helium II

Nature ◽  
1954 ◽  
Vol 174 (4424) ◽  
pp. 322-323 ◽  
Author(s):  
J. W. HERIVEL
Keyword(s):  
Liquid Helium ◽  
Fluid Model ◽  
Helium Ii ◽  
Two Fluid Model ◽  
Two Fluid

The rotation of liquid helium II I. Experiments on the propagation of second sound in uniformly rotating helium II

1956 ◽  
Vol 238 (1213) ◽  
pp. 204-214 ◽  
Keyword(s):  
Liquid Helium ◽  
Fluid Model ◽  
Mutual Friction ◽  
Second Sound ◽  
Order Unity ◽  
Helium Ii ◽  
Axis Of Rotation ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Excess Attenuation

An experimental investigation of the propagation of second sound in uniformly rotating resonators filled with liquid helium II has been made. It is found that in the uniformly rotating liquid the velocity of the second sound is not changed by more than 0·1%, but there is an excess attenuation which is, except near the λ point, proportional to the angular velocity ω , independent of second-sound amplitude, and independent of frequency in the range 1·5 to 4·5 kc/s. These results are described phenomenologically by a mutual friction force B ( ρ s ρ n / ρ ) ω (v s — v n ) per unit volume in the two-fluid model. The constant B is of order unity for second sound propagated at right angles to the axis of rotation; it is smaller by a factor of at least 5 when the second sound is propagated parallel to the axis of rotation. It is suggested that the mutual friction in rotating helium may contain a component perpendicular to (v s — v n ), and that there should be no mutual friction in an irrotational circulation. Experiments to verify these predictions are proposed.

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