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

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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The stability of the Couette flow of helium II

Journal of Fluid Mechanics ◽

10.1017/s0022112088003362 ◽

1988 ◽

Vol 197 ◽

pp. 551-569 ◽

Cited By ~ 39

Author(s):

C. F. Barenghi ◽

C. A. Jones

Keyword(s):

Couette Flow ◽

Fluid Model ◽

Taylor Instability ◽

Mutual Friction ◽

Helium Ii ◽

Two Fluid Model ◽

The Stability ◽

Superfluid Vortices ◽

Two Fluid

The stability of Couette flow in HeII is considered by an analysis of the HVBK equations. These equations are based on the Landau two-fluid model of HeII and include mutual friction between the normal and superfluid components, and the vortex tension due to the presence of superfluid vortices. We find that the vortex tension strongly affects the nature of the Taylor instability at temperatures below ≈ 2.05 K. The effect of the vortex tension is to make non-axisymmetric modes the most unstable, and to make the critical axial wavelength very long.We compare our results with experiments.

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Liquid Helium II: Bose-Einstein Condensation and Two-Fluid Model

Physical Review ◽

10.1103/physrev.92.1106 ◽

1953 ◽

Vol 92 (5) ◽

pp. 1106-1112 ◽

Cited By ~ 12

Author(s):

P. R. Zilsel

Keyword(s):

Liquid Helium ◽

Fluid Model ◽

Einstein Condensation ◽

Bose Einstein Condensation ◽

Helium Ii ◽

Two Fluid Model ◽

Bose Einstein ◽

Two Fluid

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Mutual friction in a heat current in liquid helium II I. Experiments on steady heat currents

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1957.0071 ◽

1957 ◽

Vol 240 (1220) ◽

pp. 114-127 ◽

Cited By ~ 253

Keyword(s):

Relative Velocity ◽

Fluid Model ◽

Rectangular Cross Section ◽

Heat Current ◽

Mutual Friction ◽

Second Sound ◽

Helium Ii ◽

Two Fluids ◽

Two Fluid Model ◽

Steady Heat

Experiments have been carried out on the conduction of heat through helium II in channels of large rectangular cross-section (~ 2 × 6 mm) for small heat current densities. The observed relationship between temperature gradient and heat-current density can be interpreted phenomenologically in terms of the Gorter-Mellink (1949) mutual friction force, F sn ≈ Aρ s ρ n ( v s - v n ) 3 per unit volume, in the two-fluid model, and observed values of A have been found to agree fairly well with those deduced from earlier measurements. Evidence is presented to show that the magnitude of the mutual friction is determined entirely by the value of ( v s - v n ), independently of the boundary conditions imposed on the flow. A study of the propagation of second sound across the heat currents has shown that, while the presence of the heat current leads to no observable change in the velocity of the second sound, it does lead to an attenuation; the attenuation is linear and approximately proportional to the square of the heatcurrent density. This behaviour can be described phenomenologically in terms of the twofluid model, if it is assumed that, in the presence of both a steady heat current and a second sound wave, the Gorter-Mellink mutual friction must be generalized to the form F sn = Aρ s ρ n U 2 u, where u is the instantaneous relative velocity between the two fluids and U is the time-average of this relative velocity. This result shows that in the presence of a steady heat current one or both of the fluids must become modified in some way, and that an essentially linear mutual friction is associated with this modification. Observation of changes in the attenuation of second sound provides a more sensitive method of measuring mutual friction than does the observation of temperature gradients, and it has been shown by the former technique that in the channels used in the present work there is a critical heat current below which the mutual friction is either absent or very small.

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