VISCOSITY MEASUREMENTS IN LIQUID HELIUM II

1960 ◽  
Vol 38 (10) ◽  
pp. 1376-1389 ◽  
Author(s):  
C. B. Benson ◽  
A. C. Hollis Hallett
Keyword(s):  
Liquid Helium ◽  
Significant Contribution ◽  
Normal Component ◽  
Circular Disk ◽  
Viscous Drag ◽  
Normal Fluid ◽  
Helium Ii ◽  
Torsion Suspension ◽  
Thermal Data ◽  
Cylinder Method

Measurements of the viscosity of liquid helium II have been made using an oscillating sphere. This method avoids the necessity of a "corner" correction unavoidable when a circular disk is used, and therefore eliminates the uncertainty associated with such a correction. Calibration experiments showed the presence of a significant contribution to the observed damping of the oscillations which arose from the viscous drag of the gas surrounding the rod which connected the sphere with the torsion suspension fiber. This damping has been calculated and when applied to the results obtained in liquid helium II, the values of the viscosity of the normal component which were obtained agree with those obtained by the rotating cylinder method within the combined experimental uncertainties. The assumed density of the normal fluid was that obtained from the velocity of second sound, and the most accurate thermal data available.

scholarly journals The Transport of Heat Through Narrow Channels by Liquid Helium II

1955 ◽  
Vol 8 (2) ◽  
pp. 206 ◽  
Author(s):  
PG Klemens
Keyword(s):  
Temperature Gradient ◽  
Liquid Helium ◽  
Heat Transport ◽  
Reasonable Agreement ◽  
Normal Fluid ◽  
Narrow Channels ◽  
Helium Ii ◽  
Internal Convection

In narrow channels (~10?4 cm) the observed heat transport is considerably larger than calculated by the internal convection theory. It is suggested that, because of the anisotropy of the distribution cf phonons in the channel walls resulting from the temperature gradient, the normal fluid in the immediate vicinity of the walls is not at rest but flows towards the colder region. The magnitude of the resulting heat transport is in reasonable agreement with the observed discrepancy.

Normal Fluid Concentration in Liquid Helium II below 1°K

1953 ◽  
Vol 89 (3) ◽  
pp. 662-663 ◽  
Author(s):  
D. de Klerk ◽  
R. P. Hudson ◽  
J. R. Pellam
Keyword(s):  
Liquid Helium ◽  
Normal Fluid ◽  
Helium Ii ◽  
Fluid Concentration

Experiments with a rotating cylinder viscometer in liquid helium II

1953 ◽  
Vol 49 (4) ◽  
pp. 717-727 ◽  
Author(s):  
A. C. Hollis-Hallett
Keyword(s):  
Liquid Helium ◽  
Normal Component ◽  
Rotating Cylinder ◽  
Mutual Friction ◽  
Rotating Fluid ◽  
Helium Ii ◽  
Lambda Point ◽  
New Type ◽  
Coefficient Of Viscosity ◽  
Cylinder Viscometer

ABSTRACTLiquid helium II was contained in the annular space between two co-axial cylinders, the inner of which was suspended by a torsion fibre while the outer was rotated at constant speeds. The torque upon the inner cylinder produced by the rotating fluid was measured for various steady velocities between 0·1 and 3 cm.sec.1, and was not found to be directly proportional to the velocity of rotation at any temperature between the lambda-point and 1·15° K. This result suggests that there must be some new type of non-linear frictional force acting in the liquid, possibly in addition to the Gorter-Mellink force of mutual friction.Extrapolation of the experimental results to zero velocity gives values of the coefficient of viscosity of the normal component which agree with the oscillating disk values between the lambda-point and about 1·6° K. At lower temperatures, the present results are significantly lower, suggesting, perhaps, that the values of the normal component density used in the analysis of the oscillating disk results were too low.

Experiments with oscillating disk systems in liquid helium II

1952 ◽  
Vol 210 (1102) ◽  
pp. 404-426 ◽  
Keyword(s):  
Liquid Helium ◽  
Normal Component ◽  
Logarithmic Decrement ◽  
Navier Stokes ◽  
Disk System ◽  
Navier Stokes Equation ◽  
Helium Ii ◽  
Superfluid Component ◽  
Single Disk ◽  
Frictional Forces

An experimental study has been made of the period and logarithmic decrement of a single disk and of a pile of equally spaced disks performing torsional oscillations in liquid helium II. For small amplitudes (less than about 0.1 radian), the decay of amplitude is exponential, and from the solution of the Navier-Stokes equation deduced in the appendix, values of the viscosity were deduced from the results obtained with the single disk, and of the density of the normal component of helium n from the results from the pile of disks; the values found are in good agreement with earlier work. For larger amplitudes, the logarithmic decrement of both systems increases considerably with amplitude, and for the pile of disks the period also increases with amplitude. From the increase of period, it is concluded that the superfluid component is dragged more and more with the disk system at higher velocities, while the increase of decrement is interpreted as being due to additional frictional forces associated with the dragging of the superfluid component. The mutual frictional force proposed by Gorter & Mellink proves inadequate to explain the observed effects.

THE VISCOSITY OF LIQUID HELIUM II

1955 ◽  
Vol 33 (8) ◽  
pp. 420-435 ◽  
Author(s):  
W. J. Heikkila ◽  
A. C. Hollis Hallett
Keyword(s):  
Liquid Helium ◽  
Normal Component ◽  
Rotating Cylinder ◽  
Helium Ii ◽  
Fluid Velocities ◽  
Cylinder Viscometer

It has been found possible to use the rotating cylinder viscometer to measure the viscosity of liquid helium II between 1.13°K. and 2.18°K. provided that the fluid velocities do not exceed about 0.08 cm. sec.−1. The results, which are calculated directly from experimental observations and do not require any knowledge of the density of the normal component, can be made to fit the Landau and Khalatnikov theory for the temperatures below 1.8°K. for which the theory is applicable. The results are somewhat higher than the oscillating disk results above 1.4°K.

Normal-Fluid Densities in Liquid Helium II under Pressure

1969 ◽  
Vol 186 (1) ◽  
pp. 255-262 ◽  
Author(s):  
R. H. Romer ◽  
R. J. Duffy
Keyword(s):  
Liquid Helium ◽  
Normal Fluid ◽  
Helium Ii

THE VISCOSITY OF LIQUID HELIUM II BETWEEN 0.79° K AND THE LAMBDA POINT

1963 ◽  
Vol 41 (4) ◽  
pp. 596-609 ◽  
Author(s):  
A. D. B. Woods ◽  
A. C. Hollis Hallett
Keyword(s):  
Liquid Helium ◽  
Normal Component ◽  
Rotating Cylinder ◽  
Helium Ii ◽  
Temperature Range ◽  
Lambda Point

Values of the viscosity of the normal component of liquid helium II have been determined using the rotating cylinder (Couette type) viscometer. Primary attention has been given to the temperature range between 0.79° K and 1.1° K; values at higher temperatures have been determined to provide a check on previous determinations. The results over the whole temperature range are closely fitted by an equation of the form given by Khalatnikov (Uspekhi Fiz. Nauk, 59, 673 (1956)).

THE OSCILLATING SPHERE AT LARGE AMPLITUDES IN LIQUID HELIUM

1956 ◽  
Vol 34 (7) ◽  
pp. 668-678 ◽  
Author(s):  
C. B. Benson ◽  
A. C. Hollis Hallett
Keyword(s):  
Liquid Helium ◽  
Reynolds Numbers ◽  
Total Density ◽  
Normal Fluid ◽  
Helium Ii ◽  
Onset Of Turbulence ◽  
Helium Gas ◽  
Critical Amplitudes ◽  
Period Of Oscillation ◽  
Oscillating Sphere

Measurements of the damping of the oscillations of a sphere which decay from an initial deflection ~ 10 radians show that two critical amplitudes, denoted by [Formula: see text] and [Formula: see text], may be defined in liquid helium II. The decrement is constant at amplitudes below [Formula: see text] (a few tenths of a radian), and is caused by the damping due to the viscosity of the normal fluid. [Formula: see text] is found to be proportional to the square root of the period of oscillation. Above [Formula: see text] the decrement increases, the superfluid becoming involved in the motion, until it attains another constant value, which is attributed to the viscosity of a single fluid whose density is equal to the total density (ρn+ρδ) of liquid helium II. At a larger amplitude [Formula: see text] (~ 2 radians) the decrement begins to increase linearly with amplitude, and this behavior, which is also found in liquid helium I and in helium gas at 4 °K., is attributed to the onset of turbulence. Reynolds numbers calculated at [Formula: see text] are ~ 200 for helium II, helium I, and helium gas at 4 °K.

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.

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