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The Observed Properties of Liquid Helium
at the Saturated Vapor Pressure


Chapter 9. Surface Tension

Adopted Database


Author(s)

Key #

Method

Range (K)
Iino et al. 1 Surface waves 0.35 T 5.199
Magerlein & Sanders 2 Capillary rise -0.5 ,t,0.05
t = 1 - T / T

Comments and Key to Authors

1) Ref. 17. Data is absolute and revises the value of surface tension at T=0 K to 354.4?0.5 mdyne/cm. Note that the temperature dependence of the surface tension agrees with earlier data of Ekhart et al.16 almost exactly. Uncertainty is ?0.3 mdyne/cm.
2) Refs. 13 & 15. We have incorporated this data set by adjusting the absolute surface tension to fit the only two points overlapping Iino et al. Uncertainty is ?0.03%.
3) On the original database, Tc was taken to be 5.199 K on the T58 scale. It has been corrected to 5.189 K. Upon conversion to ITS-90, Tc = 5.1958 K.
4) According to M.R. Moldover 18 around (on the T58 scale), the surface tension can be expressed as

Table 9.1. Adopted database for the surface tension of liquid 4He.

1

T90 (K)

(N/m)

Key

T90

(N/m)

Key
0.000000 3.54400E-4 1 2.154326 2.88358E-4 2
0.100365 3.54370E-4 1 2.156094 2.88180E-4 2
0.200706 3.54240E-4 1 2.157890 2.88001E-4 2
0.301026 3.53990E-4 1 2.159730 2.87817E-4 2
0.401326 3.53600E-4 1 2.161561 2.87633E-4 2
0.501608 3.53040E-4 1 2.163420 2.87444E-4 2
0.601874 3.52300E-4 1 2.165243 2.87263E-4 2
0.702125 3.51360E-4 1 2.166176 2.87163E-4 2
0.802362 3.50200E-4 1 2.167094 2.87073E-4 2
0.902586 3.48770E-4 1 2.167131 2.87069E-4 2
1.002777 3.47040E-4 1 2.168069 2.86977E-4 2
1.102955 3.44970E-4 1 2.168971 2.86887E-4 2
1.203267 3.42510E-4 1 2.169895 2.86792E-4 2
1.303324 3.39590E-4 1 2.170832 2.86696E-4 2
1.403515 3.36170E-4 1 2.171979 2.86596E-4 2
1.503598 3.32160E-4 1 2.172908 2.86504E-4 2
1.603690 3.27510E-4   2.173388 2.86456E-4 2
1.703882 3.22160E-4 1 2.173840 2.86415E-4 2
1.804065 3.16060E-4 1 2.174321 2.86367E-4 2
1.904151 3.09160E-4 1 2.174679 2.86334E-4 2
2.004234 3.01470E-4 1 2.175047 2.86300E-4 2
2.079869 2.95624E-4 2 2.175435 2.86276E-4 2
2.082083 2.95431E-4 2 2.175795 2.86240E-4 2
2.087213 2.94947E-4 2 2.176193 2.86210E-4 2
2.092275 2.94469E-4 2 2.176591 2.86179E-4 2
2.097406 2.93974E-4 2 2.177009 2.86141E-4 2
2.102724 2.93466E-4 2 2.177009 2.86137E-4 2
2.104399 2.92980E-4 1 2.177399 2.86107E-4 2
2.107993 2.92960E-4 2 2.177827 2.86072E-4 2
2.113455 2.92430E-4 2 2.178246 2.86040E-4 2
2.118900 2.91894E-4 2 2.178666 2.86005E-4 2
2.124429 2.91342E-4 2 2.179057 2.85973E-4 2
2.128622 2.90927E-4 2 2.179459 2.85945E-4 2
2.132810 2.90504E-4 2 2.180023 2.85896E-4 2
2.136982 2.90092E-4 2 2.180618 2.85849E-4 2
2.141155 2.89676E-4 2 2.180915 2.85832E-4 2
2.143769 2.89418E-4 2 2.181194 2.85804E-4 2
2.146368 2.89154E-4 2 2.181721 2.85747E-4 2
2.149038 2.88883E-4 2 2.182695 2.85674E-4 2
2.151739 2.88615E-4 2 2.183738 2.85594E-4 2

Table 9.1. (continued)


T90 (K)

(N/m)

Key

T90

(N/m)

Key
2.185086 2.85487E-4 2 2.605385 2.53500E-4 1
2.186419 2.85383E-4 2 2.705694 2.44660E-4 1
2.187845 2.85275E-4 2 2.805957 2.35360E-4 1
2.189845 2.85119E-4 2 2.906140 2.25630E-4 1
2.191956 2.84954E-4 2 3.006300 2.15530E-4 1
2.194914 2.84729E-4 2 3.106442 2.05110E-4 1
2.197996 2.84485E-4 2 3.206578 1.94460E-4 1
2.201022 2.84251E-4 2 3.306723 1.83640E-4 1
2.204070 2.84013E-4 2 3.406851 1.72730E-4 1
2.204624 2.84500E-4 1 3.506953 1.61810E-4 1
2.207112 2.83784E-4 2 3.607030 1.50920E-4 1
2.212391 2.83375E-4 2 3.707067 1.40130E-4 1
2.217529 2.82980E-4 2 3.807062 1.29490E-4 1
2.222839 2.82571E-4 2 3.907038 1.19020E-4 1
2.228186 2.82154E-4 2 4.007034 1.08740E-4 1
2.233636 2.81737E-4 2 4.107060 9.86700E-5 1
2.239167 2.81309E-4 2 4.207083 8.88000E-5 1
2.246959 2.80707E-4 2 4.306979 7.91200E-5 1
2.247050 2.80704E-4 2 4.406982 6.96100E-5 1
2.254904 2.80095E-4 2 4.507062 6.02400E-5 1
2.263157 2.79440E-4 2 4.607173 5.09800E-5 1
2.271323 2.78802E-4 2 4.707276 4.18300E-5 1
2.279781 2.78143E-4 2 4.807336 3.27600E-5 1
2.287614 2.77514E-4 2 4.907327 2.38000E-5 1
2.287627 2.77516E-4 2 5.007230 1.50500E-5 1
2.304706 2.77290E-4 1 5.107032 6.75000E-6 1
2.404936 2.69780E-4 1 5.195767 0  
2.505156 2.61870E-4 1      

Figure 9.1. The recommended values of the surface tension of liquid 4He as a function of temperature at saturated vapor pressure.

Table 9.2. Knots and coefficients for the spline fit of the surface tension of liquid


Knots

Coefficients
K(1) = 0.000000 C(1) = 3.543998E-4
K(2) = 0.000000 C(2) = 3.545090E-4
K(3) = 0.000000 C(3) = 3.524383E-4
K(4) = 0.000000 C(4) = 3.366694E-4
K(5) = 6.482413E-4 C(5) = 2.921292E-4
K(6) = 2.004234 C(6) = 2.860852E-4
K(7) = 2.176800 C(7) = 2.796835E-4
K(8) = 2.176800 C(8) = 2.747804E-4
K(9) = 2.178377 C(9) = 2.346234E-4
K(10) = 2.412388 C(10) = 1.357632E-4
K(11) = 2.412896 C(11) = 5.361123E-5
K(12) = 3.807062 C(12) = 1.263761E-5
K(13) = 4.868895 C(13) = 3.795854E-6
K(14) = 5.035567 C(14) = 5.599775E-12
K(15) = 5.195767  
K(16) = 5.195767  
K(17) = 5.195767  
K(18) = 5.195767  

Figure 9.2. Detail of the surface tension about the lambda transition.

Table 9.3. Recommended values of the surface tension of liquid 4He.

1

T90 (K)

(N/m)

T90

(N/m)
0.1000 3.544E-4 2.3000 2.770E-4
0.1500 3.543E-4 2.3500 2.735E-4
0.2000 3.543E-4 2.4000 2.699E-4
0.2500 3.541E-4 2.4500 2.662E-4
0.3000 3.540E-4 2.5000 2.623E-4
0.3500 3.538E-4 2.5500 2.582E-4
0.4000 3.536E-4 2.6000 2.540E-4
0.4500 3.533E-4 2.6500 2.497E-4
0.5000 3.530E-4 2.7000 2.452E-4
0.5500 3.527E-4 2.7500 2.406E-4
0.6000 3.523E-4 2.8000 2.359E-4
0.6500 3.519E-4 2.8500 2.311E-4
0.7000 3.514E-4 2.9000 2.262E-4
0.7500 3.508E-4 2.9500 2.212E-4
0.8000 3.502E-4 3.0000 2.161E-4
0.8500 3.496E-4 3.0500 2.110E-4
0.9000 3.488E-4 3.1000 2.058E-4
0.9500 3.480E-4 3.2000 1.952E-4
1.0000 3.471E-4 3.3000 1.844E-4
1.1000 3.451E-4 3.4000 1.735E-4
1.2000 3.426E-4 3.5000 1.626E-4
1.3000 3.397E-4 3.6000 1.517E-4
1.4000 3.362E-4 3.6500 1.463E-4
1.5000 3.322E-4 3.7000 1.409E-4
1.5500 3.300E-4 3.7500 1.355E-4
1.6000 3.276E-4 3.8000 1.302E-4
1.6500 3.251E-4 3.8500 1.249E-4
1.7000 3.224E-4 3.9000 1.197E-4
1.7500 3.195E-4 3.9500 1.146E-4
1.8000 3.164E-4 4.0000 1.095E-4
1.8500 3.131E-4 4.0500 1.044E-4
1.9000 3.096E-4 4.1000 9.942E-5
1.9500 3.060E-4 4.1500 9.445E-5
2.0000 3.021E-4 4.2000 8.954E-5
2.0500 2.980E-4 4.2500 8.466E-5
2.1000 2.936E-4 4.3000 7.983E-5
2.1500 2.889E-4 4.3500 7.503E-5
2.1760 2.862E-4 4.4000 7.028E-5
2.1761 2.862E-4 4.4500 6.556E-5
2.1762 2.862E-4 4.5000 6.087E-5
2.1763 2.862E-4 4.5500 5.622E-5
2.1764 2.862E-4 4.6000 5.160E-5
2.1765 2.862E-4 4.6500 4.701E-5
2.1766 2.862E-4 4.7000 4.245E-5
2.1767 2.862E-4 4.7500 3.792E-5
2.1768 2.861E-4 4.8000 3.341E-5
2.1769 2.861E-4 4.8500 2.893E-5
2.1770 2.861E-4 4.9000 2.447E-5
2.2000 2.843E-4 4.9500 2.005E-5
2.2500 2.805E-4 5.0000 1.570E-5

 

Figure 9.3. The fractional deviation of the values of the adopted database from the recommended values of the surface tension of liquid 4He expressed in percent.

Chronological Bibliography for Entropy


1

A. T. Van Urk, W. H. Keesom, and K. H. Onnes, "Measurements of the Surface Tension of Liquid Helium," Proc. Roy. Acad. Amsterdam 28, 958-962 (1925).
2 J. F. Allen and A. D. Misner, “The Surface Tension of Liquid Helium,” in The Cambridge Philosophical Society (1938), Vol. 34, pp. 299-300.
3 B. N. Esel'son and Berezniak, “Surface Tension of 3He-4He Mixtures,” Dokl. Akad. Nauk. USSR 98, 569-571 (1954).
4 K. R. Atkins, “Third and Fourth Sound in Liquid Helium II,” Phys. Rev. 113, 962-965 (1959).
5 Y. Narahara, “The Surface Tension of Liquid 4He at Low Temperatures Near Lambda-Point,” Ph.D. Thesis, University of Pennsylvania, 1963 (unpublished).
6 N. Devaraj and A. C. Hollis Hallett, “The Surface Tension of Liquid Helium I and the Law of Corresponding States,” Can. Jour. Phys. 45, 2113-2120 (1967).
7 K. N. Zinov'eva and S. T. Boldarev, “Surface Tension of Dilute 3He-4He,” Sov. Phys. JETP 29, 585-590 (1969).
8 D. P. E. Dickson, D. Caroline, and E. Mendoza, “Surface Tension of Liquid 4He,” Phys. Lett 33A, 139-140 (1970).
9 H. M. Guo, D. O. Edwards, R. E. Sarwinski, and J. T. Tough, “Fermi-Liquid Behavior of 3He Adsorbed on Liquid Helium,” Phys. Rev. Lett. 27, 1259-1263 (1971).
10 P. J. King and A. F. G. Wyatt, “Surface Waves on Liquid 4He,” Proc. Roy. Soc. Lond. A322, 355-359 (1971).
11 S. T. Boldarev and V. P. Peshkov, “Measurements of the Surface Tension in Liquid Helium by Means of Surface Waves,” Physica 69, 141-147 (1973).
12 F. M. Gasparini, J. R. Eckardt, D. O. Edwards, and S. Y. Shen, “Surface Tension of Helium II Near the Lambda-Point,” J. Low Temp. Phys. 13, 437-443 (1974).
13 J. H. Magerlein, “The Surface Tension of Liquid 4He Near T-Lambda,” Ph.D. Thesis, University of Michigan, 1974 (unpublished).
14 D. O. Edwards, P. P. Fatouros, G. G. Ihas, and P. Mrozinski, “Surface Tension of 4He Below 0.35 K,” Phys. Rev. B 11, 4734-4735 (1975).
15 J. H. Magerlein and J. Sanders, T. M., “Surface Tension of 4He Near T-Lambda,” Phys. Rev. Lett. 36, 258-260 (1976).
16 J. R. Eckart, D. O. Edwards, S. Y. Shen, and F. M. Gasparini, “Surface Tension and Surface Entropy of Superfluid 4He,” Phys. Rev. B 16, 1944-1953 (1977).
17 M. Iino, M. Suzuki, and A. J. Ikushima, “Surface Tension of Liquid 4He Surface Energy of the Bose-Einstein Condensate,” J. Low Temp. Phys. 61, 155-169 (1985).
18 M. R. Moldover, “Interfacial Tension of Fluids near Critical Points and Two-Scale-Factor Universality,” Phys. Rev. A 31, 1022-1033 (1985).
19 S. Herminghaus and P. Leiderer, “Surface Tension of 4He Near the Critical Point,” Phys. Lett. A 115-9, 455-458 (1986).
20 M. Iino, M. Suzuki, and A. J. Ikushima, “Surface Tension of Liquid 3He and 4He Near the Liquid-Gas Critical Point,” J. Low Temp. Phys. 63, 495-506 (1986)

 

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