Motion of vortex lines and mutual friction in superfluid4He nearT ?

1992 ◽  
Vol 87 (2) ◽  
pp. 247-255 ◽  
Author(s):  
R. Haussmann
Keyword(s):  
Mutual Friction ◽  
Vortex Lines

scholarly journals Superfluid vortex-mediated mutual friction in non-homogeneous neutron star interiors

2020 ◽  
Vol 499 (3) ◽  
pp. 3690-3705
Author(s):  
M Antonelli ◽  
B Haskell
Keyword(s):  
Neutron Star ◽  
Normal Component ◽  
Homogeneous Medium ◽  
Outer Core ◽  
Two Dimensions ◽  
Pinning Force ◽  
Mutual Friction ◽  
Momentum Exchange ◽  
Drag Forces ◽  
Vortex Lines

ABSTRACT Understanding the average motion of a multitude of superfluid vortices in the interior of a neutron star is a key ingredient for most theories of pulsar glitches. In this paper, we propose a kinetic approach to compute the mutual friction force that is responsible for the momentum exchange between the normal and superfluid components in a neutron star, where the mutual friction is extracted from a suitable average over the motion of many vortex lines. As a first step towards a better modelling of the repinning and depinning processes of many vortex lines in a neutron star, we consider here only straight and non-interacting vortices: we adopt a minimal model for the dynamics of an ensemble of point vortices in two dimensions immersed in a non-homogeneous medium that acts as a pinning landscape. Since the degree of disorder in the inner crust or outer core of a neutron star is unknown, we compare the two possible scenarios of periodic and disordered pinscapes. This approach allows us to extract the mutual friction between the superfluid and the normal component in the star when, in addition to the usual Magnus and drag forces acting on vortex lines, also a pinning force is at work. The effect of disorder on the depinning transition is also discussed.

Kinetic theory of mutual friction force in superfluid 4He with vortex lines

1990 ◽  
Vol 165-166 ◽  
pp. 773-774
Author(s):  
Kazuo Yamada ◽  
Kazumasa Miyake ◽  
Shohei Kashiwamura
Keyword(s):  
Kinetic Theory ◽  
Friction Force ◽  
Superfluid 4He ◽  
Mutual Friction ◽  
Vortex Lines

Mutual friction in a heat current in liquid helium II III. Theory of the mutual friction

1957 ◽  
Vol 242 (1231) ◽  
pp. 493-515 ◽  
Keyword(s):  
Friction Force ◽  
Unit Volume ◽  
Unit Length ◽  
Heat Current ◽  
Mutual Friction ◽  
Superfluid Turbulence ◽  
Vortex Lines ◽  
Magnus Effect ◽  
The Individual ◽  
Dimensional Argument

As was shown in part II, the Gorter-Mellink mutual friction force in a heat current is probably associated with turbulence in the superfluid. Following Feynman, it is suggested that this turbulence takes the form of a tangled mass of quantized vortex lines, so that the mutual friction probably arises from collisions between thermal excitations and these vortex lines. From the observed properties of the mutual friction it is deduced that the walls of the channel carrying the heat current play no essential role in the generation, maintenance or decay of the turbulence, but merely introduce a number of incidental complications; the present paper ignores these complications and deals therefore with the idealized case of a homogeneous heat current in an unbounded volume of helium. The turbulence in this idealized case must be homogeneous, and it is shown from experimental evidence that it is probably also isotropic. Values of the force exerted on unit length of a vortex line, which have been derived from the study of the attenuation of second sound in uniformly rotating helium, are used to calculate the Gorter-Mellink force per unit volume in terms of the length of line per unit volume; then by a simple dimensional argument it is shown that the force must depend on (v s — v n ) in a manner agreeing with experiment. An attempt is made to produce a detailed theory of the generation and decay of superfluid turbulence: it is shown first that owing to the Magnus effect the turbulence can probably be built up by the action of the mutual friction force exerted on the individual lines, although the way in which turbulence can be initiated in undisturbed helium is not known, and secondly that the turbulence can probably decay in a manner closely analogous to the decay of homogeneous turbulence in an ordinary fluid. Equations for the rate of generation and decay of turbulence are obtained by dimensional arguments, and by analogy with formulae known to apply to turbulence in an ordinary fluid. Comparison of the equations with the experimental results described in parts I and II reveals good agreement, and makes it possible to deduce the form and magnitude of a term describing the effect of the unknown initiation process.

Mutual friction in a heat current in liquid heliumn. II. IV. Critical heat currents in wide channels

1958 ◽  
Vol 243 (1234) ◽  
pp. 400-413 ◽  
Keyword(s):  
Vortex Line ◽  
Unit Volume ◽  
Critical Value ◽  
Channel Width ◽  
Heat Current ◽  
Mutual Friction ◽  
Superfluid Turbulence ◽  
Wide Channel ◽  
Vortex Lines ◽  
Single Term

Experiments are described in which a heat current in a wide channel is suddenly increased from a small value W 1 to a large value W 2 ; the time characterizing the build-up of the Gorter-Mellink mutual friction to its equilibrium value in the heat current W 2 is studied as a function of W 1 . Interpretation of the results on the basis of the idea that the mutual friction is associated with turbulence (in the form of vortex lines) in the superfluid shows that some mutual friction exists in the heat current W 1 even when the latter is less than the critical value described in parts I and II, and that, as the channel width is increased or the temperature raised, the magnitude of the subcritical mutual friction increases until the critical heat current ceases to exist. It is shown that these observations on mutual friction in small heat currents can be described semi-quantitatively if a single term is added to the expression obtained in part III for the length of vortex line per unit volume in a heat current in a channel of infinite width, and that this term can probably arise either from an annihilation of vortex lines at the walls of the channel or from interference by the walls with the mechanisms of growth and decay of superfluid turbulence discussed in part III. Finally, an explanation is suggested of some of the results described in part II on the decay of mutual friction in the presence of a subcritical heat current.

The rotation of liquid helium II II. The theory of mutual friction in uniformly rotating helium II

1956 ◽  
Vol 238 (1213) ◽  
pp. 215-234 ◽  
Keyword(s):  
Vortex Line ◽  
Transverse Motion ◽  
Mutual Friction ◽  
Detailed Calculation ◽  
Normal Fluid ◽  
Line Model ◽  
Vortex Sheets ◽  
Helium Ii ◽  
Vortex Lines ◽  
Magnus Effect

A discussion is given of models for the rotation of helium II involving regions of concentrated vorticity, and it is shown thermodynamically that an arrangement of vortex lines is energetically preferable to an arrangement of vortex sheets. It is suggested that such models exhibit the property of mutual friction, owing to the possibility of collisions between normal fluid excitations and the regions of concentrated superfluid vorticity; the observed anisotropy of this mutual friction (part I of this paper) is consistent only with a vortex-line model, so that the theoretical decision in favour of this model is confirmed by experiment. A detailed calculation of the magnitude and temperature-dependence of this mutual friction is given for the quantized vortex-line model of Onsager (1949) and Feynman (1955). The vortex lines are treated as classical vortex lines belonging entirely to the superfluid. The force of mutual friction arising from the collision of rotons with these lines is calculated in terms of the roton-line collision diameter σ̅, taking into account a tendency for the lines to drag the gas of excitations (i. e. the normal fluid) in their vicinity, and a transverse motion of the lines due to the Magnus effect. The calculated mutual friction contains two components: one parallel to, and one perpendicular to, (v s — v n ). The magnitude of the former component agrees well with the experimental results if σ̅ is taken to be about 10 Å. The agreement between theory and experiment confirms that the normal fluid is dragged by the lines, and shows that the spacing of the lines must be close to the theoretical value given by Feynman; but it provides no evidence for or against a motion of the lines due to the Magnus effect. A rough value for σ̅ is calculated in an appendix, and shown to agree as well as can be expected with the value derived from experiment.

A continuum theory of the isothermal flow of liquid helium II

1961 ◽  
Vol 10 (1) ◽  
pp. 113-132 ◽  
Author(s):  
A. A. Townsend
Keyword(s):  
Pressure Gradient ◽  
Liquid Helium ◽  
Flow Rate ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Isothermal Flow ◽  
Mutual Friction ◽  
Normal Fluid ◽  
Helium Ii ◽  
Vortex Lines

Recent work by Hall and Vinen has established that mutual friction between the normal and superfluid components of liquid helium II is caused by interactions between quantized vortex-lines and the normal fluid. If the mean separation of the vortex-lines is small compared with the channel width, the general character of the flow may not depend on the discrete nature of the lines except in so far as this is the cause of the mutual friction. Equations of motion are developed which refer to components of the velocity field with a scale large compared with the line separation, and these are used to discuss the nature of possible turbulent motions. Reasons are given for believing that isothermal flow is very similar to that of a Newtonian fluid, and the theory is developed for turbulent pressure flow along a channel and a circular pipe. The predicted variation of flow rate with pressure gradient is in good agreement with experimental measurements for Reynolds numbers (based on tube diameter and normal fluid viscosity) above 1400, and it is likely that turbulent flow can exist only above this critical Reynolds number. For Reynolds numbers which are not too small, the equations of motion apply to steady ’laminar’ flow and these lead to a relation between flow rate and pressure gradient in reasonable agreement with experiment.

Vortex Mutual Friction in Superfluid 3He

1997 ◽  
Vol 109 (3-4) ◽  
pp. 423-459 ◽  
Author(s):  
T. D. C. Bevan ◽  
A. J. Manninen ◽  
J. B. Cook ◽  
H. Alles ◽  
J. R. Hook ◽  
...  
Keyword(s):  
Superfluid 3He ◽  
Mutual Friction

AC Measurements of a Coupling Between Dissipative Heat Flux and Mutual Friction Force in He II

1974 ◽  
pp. 324-327
Author(s):  
Félix Vidal ◽  
Michel Le Ray ◽  
Maurice François ◽  
Daniel Lhuillier
Keyword(s):  
Heat Flux ◽  
Friction Force ◽  
Mutual Friction ◽  
Dissipative Heat
Sign in / Sign up

Export Citation Format

Share Document