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The Observed Properties of Liquid Helium
at the Saturated Vapor Pressure

Chapter 12. Viscosity and Kinematic Viscosity

Adopted Database

Author(s)	Key #	Method	Range(K)
Woods & Hollis Hallett	1	Couette viscometer	0.78 T 2.079
Tough et al.	2	vibrating wire	1.52 T 2.16
Goodwin	3	vibrating wire	1.2 T 4.2
Webeler & Allen	4	quartz crystal	1.75 T 2.195
Wang et al.	5	torsional oscillator	1.8 T 4.4

Comments and Key to Authors

1) Ref. 13.
2) Ref. 14.
3) Ref. 18, 22, 23.
4) Ref. 21.
5) Ref. 28.
6) The absolute accuracy of viscosity measurements is very hard to evaluate. The best guide is probably the deviation plot in Figure 12.2.
7) To convert Pa-s or kg/m-s to P, multiply by 107, to convert from m²/s to cm²/s, multiply by 10⁴

Table 12.1. Adopted database for the viscosity of liquid ⁴He.

T90 (K)	(Pa s)	Key	T90 (K)	(Pa s)	Key
0.7913	1.73E-05	1	1.8241	1.34E-06	2
0.8014	1.58E-05	1	1.8441	1.34E-06	2
0.8054	1.62E-05	1	1.8441	1.30E-06	5
0.8164	1.31E-05	1	1.8541	1.29E-06	3
0.8565	8.50E-06	1	1.8641	1.35E-06	2
0.9266	5.50E-06	1	1.8641	1.31E-06	5
1.0108	3.70E-06	1	1.8841	1.36E-06	2
1.122	2.18E-06	1	1.8841	1.32E-06	5
1.132	2.04E-06	1	1.9042	1.34E-06	5
1.142	2.06E-06	1	1.9042	1.32E-06	3
1.162	1.96E-06	1	1.9042	1.35E-06	2
1.2033	1.72E-06	2	1.9242	1.41E-06	2
1.2033	1.60E-06	3	1.9442	1.40E-06	2
1.2161	1.77E-06	1	1.9442	1.39E-06	5
1.2231	1.69E-06	2	1.9542	1.35E-06	3
1.2432	1.64E-06	2	1.9642	1.43E-06	2
1.2532	1.52E-06	3	1.9832	1.46E-06	1
1.2632	1.61E-06	2	1.9842	1.45E-06	2
1.2833	1.56E-06	2	1.9842	1.46E-06	5
1.3033	1.52E-06	2	2.0042	1.47E-06	2
1.3234	1.51E-06	2	2.0042	1.41E-06	3
1.3434	1.49E-06	2	2.0243	1.53E-06	2
1.3534	1.43E-06	3	2.0243	1.56E-06	5
1.3635	1.47E-06	2	2.0443	1.57E-06	2
1.3835	1.44E-06	2	2.0543	1.50E-06	3
1.4035	1.40E-06	2	2.0643	1.65E-06	2
1.4035	1.39E-06	3	2.0833	1.65E-06	1
1.4536	1.40E-06	2	2.0843	1.72E-06	2
1.4536	1.36E-06	3	2.0843	1.80E-06	4
1.5036	1.36E-06	2	2.0843	1.68E-06	5
1.5036	1.32E-06	3	2.0944	1.84E-06	4
1.5536	1.37E-06	2	2.1044	1.81E-06	2
1.5536	1.29E-06	3	2.1044	1.73E-06	3
1.6037	1.36E-06	2	2.1044	1.87E-06	4
1.6037	1.26E-06	3	2.1144	1.92E-06	4
1.6428	1.29E-06	1	2.1245	1.89E-06	2
1.6538	1.33E-06	2	2.1245	2.00E-06	5
1.6538	1.24E-06	3	2.1245	1.98E-06	4
1.7039	1.34E-06	2	2.1345	2.06E-06	4
1.7039	1.24E-06	3	2.1445	2.10E-06	2
1.754	1.32E-06	2	2.1445	2.14E-06	4
1.754	1.31E-06	4	2.1495	2.19E-06	4
1.754	1.25E-06	3	2.1546	2.11E-06	3
1.8041	1.33E-06	2	2.1546	2.24E-06	4
1.8041	1.30E-06	5	2.1596	2.28E-06	4
1.8041	1.26E-06	3	2.1646	2.28E-06	2
1.8231	1.28E-06	1	2.1646	2.33E-06	4
2.1696	2.38E-06	4	2.6054	3.36E-06	5
2.1768	2.54E-06	5	2.7057	3.40E-06	3
2.1778	2.49E-06	4	2.806	3.47E-06	5
2.1798	2.50E-06	4	3.0063	3.51E-06	5
2.1846	2.53E-06	4	3.2066	3.57E-06	3
2.1896	2.56E-06	4	3.2066	3.52E-06	5
2.1946	2.59E-06	4	3.4069	3.51E-06	5
2.1996	2.62E-06	4	3.607	3.47E-06	5
2.2046	2.69E-06	5	3.7071	3.51E-06	3
2.3047	2.94E-06	3	3.8071	3.41E-06	5
2.3047	2.98E-06	5	4.007	3.34E-06	5
2.4049	3.16E-06	5	4.2071	.26E-06	3
2.5052	3.24E-06	3	4.2071	3.26E-06	5
2.5052	3.28E-06	5	4.407	3.16E-06	5

Figure 12.1. The recommended values of the viscosity of liquid 4He as a function of temperature at saturated vapor pressure.

Table 12.2. Knots and coefficients for the spline fit of the viscosity of liquid 4He. The spline returns the viscosity in Pa?s.

Knots	Coefficients
K(1) = 7.913364E-1	C(1) = 1.730865E-5
K(2) = 7.913364E-01	C(2) = 6.577810E-6
K(3) = 7.913364E-1	C(3) = 4.956473E-6
K(4) = 7.913364E-1	C(4) = 1.862435E-6
K(5) = 9.705100E-1	C(5) = 1.452672E-6
K(6) = 1.064730E+0	C(6) = 1.308345E-6
K(7) = 1.285930E+0	C(7) = 1.273173E-6
K(8) = 1.582100E+0	C(8) = 1.338821E-6
K(9) = 1.747010E+0	C(9) = 1.613257E-6
K(10) = 2.025680E+0	C(10) = 1.956558E-6
K(11) = 2.051740E+0	C(11) = 2.296259E-6
K(12) = 2.146961E+0	C(12) = 2.514817E-6
K(13) = 2.176800E+0	C(13) = 2.487748E-6
K(14) = 2.176800E+0	C(14) = 2.715638E-6
K(15) = 2.176800E+0	C(15) = 3.125798E-6
K(16) = 2.212906E+0	C(16) = 3.487019E-6
K(17) = 2.221800E+0	C(17) = 3.564378E-6
K(18) = 2.618000E+0	C(18) = 3.486451E-6
K(19) = 3.253700E+0	C(19) = 3.270547E-6
K(20) = 3.784200E+0	C(20) = 3.226615E-6
K(21) = 4.025400E+0	C(21) = 3.160000E-6
K(22) = 4.406982E+0
K(23) = 4.406982E+0
K(24) = 4.406982E+0
K(25) = 4.406982E+0

Figure 12.2. The fractional deviation of values of the adopted database from the recommended values for the viscosity of liquid 4He expressed in percent.

Table 12.3. Recommended values of the viscosity of liquid ⁴He at the saturated vapor pressure.

T90 (K)	(Pa-s)	T90 (K)	(Pa-s)
0.8	1.582E-5	2.18	2.512 E-6
0.85	9.537E-6	2.19	2.553 E-6
0.9	6.288E-6	2.2	2.635 E-6
0.95	4.806E-6	2.25	2.840 E-6
1.0	3.873E-6	2.3	2.956 E-6
1.05	3.028E-6	2.35	3.053 E-6
1.1	2.391E-6	2.4	3.135 E-6
1.15	1.980E-6	2.45	3.203 E-6
1.2	1.736E-6	2.5	3.259 E-6
1.25	1.604E-6	2.55	3.306 E-6
1.3	1.527E-6	2.6	3.346 E-6
1.35	1.466E-6	2.65	3.380 E-6
1.4	1.416E-6	2.7	3.410 E-6
1.45	1.377E-6	2.75	3.436 E-6
1.5	1.346E-6	2.8	3.459 E-6
1.55	1.323E-6	2.85	3.478 E-6
1.6	1.306E-6	2.9	3.494 E-6
1.65	1.295E-6	2.95	3.507 E-6
1.7	1.290E-6	3.0	3.517 E-6
1.75	1.290E-6	3.05	3.524 E-6
1.8	1.298E-6	3.1	3.529 E-6
1.85	1.316E-6	3.15	3.532 E-6
1.9	1.347E-6	3.2	3.534 E-6
1.95	1.397E-6	3.25	3.533 E-6
2.0	1.468E-6	3.3	3.532 E-6
2.05	1.569E-6	3.35	3.528 E-6
2.1	1.803E-6	3.4	3.524 E-6
2.11	1.868E-6	3.45	3.517 E-6
2.12	1.936E-6	3.5	3.509 E-6
2.13	2.008E-6	3.55	3.499 E-6
2.14	2.083E-6	3.6	3.487 E-6
2.15	2.161E-6	3.65	3.472E-6
2.16	2.252E-6	3.7	3.456E-6
2.17	2.385E-6	3.75	3.437E-6
2.171	2.402E-6	3.8	3.415E-6
2.172	2.419E-6	3.85	3.392E-6
2.173	2.438E-6	3.9	3.367E-6
2.174	2.457E-6	3.95	3.342E-6
2.175	2.477E-6	4.0	3.319E-6
2.176	2.498E-6	4.05	3.298E-6
2.1768	2.515E-6	4.1	3.279E-6
2.177	2.514E-6	4.15	3.261E-6
2.178	2.513E-6	4.2	3.244E-6
2.179	2.512E-6

Figure 12.3. The recommended values of the kinematic viscosity of liquid 4He, ?=?/?, as a function of temperature at the saturated vapor pressure.

Table 12.4. Recommended values of the kinematic viscosity of liquid ⁴He.

T90 (K)	V(m2 s-1)	T90 (K)	V(m2 s-1)
0.80	1.090E-7	2.65	2.349E-8
0.85	6.572E-8	2.70	2.375E-8
0.90	4.333E-8	2.75	2.399E-8
0.95	3.311E-8	2.80	2.421E-8
1.00	2.669E-8	2.85	2.441E-8
1.05	2.086E-8	2.90	2.459E-8
1.10	1.648E-8	2.95	2.475E-8
1.15	1.364E-8	3.00	2.490E-8
1.20	1.197E-8	3.05	2.503E-8
1.25	1.106E-8	3.10	2.515E-8
1.30	1.052E-8	3.15	2.526E-8
1.35	1.010E-8	3.20	2.536E-8
1.40	9.756E-9	3.25	2.545E-8
1.45	9.484E-9	3.30	2.553E-8
1.50	9.273E-9	3.35	2.561E-8
1.55	9.114E-9	.40	2.567E-8
1.60	8.997E-9	3.45	2.574E-8
1.65	8.918E-9	3.50	2.579E-8
1.70	8.878E-9	3.55	2.583E-8
1.75	8.880E-9	3.60	2.586E-8
1.80	8.929E-9	3.65	2.588E-8
1.85	9.048E-9	3.70	2.589E-8
1.90	9.263E-9	3.75	2.588E-8
1.95	9.598E-9	3.80	2.586E-8
2.00	1.008E-8	3.85	2.582E-8
2.05	1.077E-8	3.90	2.579E-8
2.10	1.237E-8	3.95	2.575E-8
2.15	1.481E-8	4.00	2.573E-8
2.20	1.804E-8	4.05	2.574E-8
2.25	1.945E-8	4.10	2.576E-8
2.30	2.027E-8	4.15	2.581E-8
2.35	2.097E-8	4.20	2.587E-8
2.40	2.157E-8	4.25	2.593E-8
2.45	2.207E-8	4.30	2.600E-8
2.50	2.250E-8	4.35	2.605E-8
2.55	2.287E-8	4.40	2.609E-8
2.60	2.320E-8

Chronological Bibliography for Mutual Friction

1	D. Coster, "The Rotational Oscillation of a Cylinder in a Viscous Liquid," Phil. Mag. 37, 587-595 (1919).
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21	R. W. H. Webeler and G. Allen, “Lambda-Point Measurement of ??n for Pure 4He and for Three 3He-4He Mixtures,” Phys. Rev. A 5, 1820-1827 (1972).
22	J. M. Goodwin, “A Vibrating Wire Viscometer for Measurements at Elevated Pressures,” J. Phys. E 6, 452-456 (1973).
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