Viscosity anomaly of normal and superfluid3He

PflYSICA

Physica B 194-196 (1994) 781-782 North-Holland

V i s c o s i t y a n o m a l y o f n o r m a l and superfluid 3 H e M. Nakagawaa, O.Ishikawab, T. Hatab, and T. Kodamab aFaculty of Science, Himeji Institute of Technology, Ako-gun, Hyogo 678-12, Japan bFaculty of Science, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka, 558, Japan

We derived the viscosity and the slip length of normal and superfluid 3He by using a torsional oscillator with no adjustable parameter. We report the bulk shear viscosity of normal liquid 3He deviates from the T-2 dependence near the superfluid transition and the slip length of superfluid 3He must be enhanced.

1.INTRODUCTION The shear viscosity vl of normal liquid 3He at low temperatures has been considered to obey a temperature dependence T-2. For superfluid 3He, the shear viscosity has been considered to approach a nearly constant value, following a rapid drop of "q just below the superfluid transition temperature Tc. So far there have been several shear viscosity experiments which showed qualitative discrepancies between theory and experiment. For normal liquid 3He, the viscosity rl is deviated from the theoretical prediction ~qT2=const. near Tc. [1-3] and for superfluid 3He the viscosity is persistently decreasing down to T/Tc=0.3.[4] Measurements were interpreted by a hydrodynamic theory with a long mean free path effect, so-called a slip length approximation. On deriving the bulk viscosity it is usually assumed that ~=0.58~.~1 [5] or both rl and obey T -2 for normal liquid 3He.(~ is a slip length, ~..q is a viscous mean free path) For superfluid 3He, the theoretical length[5] is assumed. Here, we report a new experimental method to determine the shear viscosity and the slip length independently with no fitting parameter both normal liquid and superfluid 3He.

about 1.49 kHz. The temperature of the liquid is measured by both a melting curve thermometer attached to a nuclear stage and the Lanthanum Cerium Magnesium Nitrate thermometer in the liquid. When a torsional oscillator which has a small internal height is used, only the effective viscosity is derived from a Q-value. On the other hand, when a hollow cylinder torsional oscillator is used, you can measure the complex transverse surface impedance whose real part is related to a Q-value and imaginary part is to a resonance frequency. Though these quantities are complicated functions of the shear viscosity vl and the slip length ~, we can derive both rl and ~ numerically with no fitting parameter in the slip approximation. The numerical method will be reported elsewhere.

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2. EXPERIMENTAL The torsional oscillator which resembles that of Ritchie et al. [6] consists of a hollow cylinder of diameter D = l l mm and internal height d=6 mm machined from Stycast 1266. It is glued to a hollow Be-Cu torsion rod and it resonates at a frequency of

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TEMPERATURE(mK) F i g u r e 1. rlT2 vs. T for normal liquid 3He at 5 bar.

0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0970-R

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Figure 3. Wrlc vs. T/Tc. Solid circles are our data.. Solid line is Archie's result and dashed line is its slip correction at 5 bar.

Finally Figure 3 shows the viscosity of superfluid 3He normalized by the viscosity at T=Tc vs. T/Tc at 5 bar. A slip approximation seems to be valid above T/Tc=0.6. The dashed line is the slip corrected results of a torsional oscillator of Archie et al.[4] at 5 bar. Our results are larger than the slip corrected viscosity. Note that in this correction the considered scattering of quasiparticles off the wall is only diffusive one. But an elastic scattering process is known to exist, which is called Andreev scattering. This Andreev scattering leads to an enhancement of the slip length. When the slip correction including Andreev scattering applies to Archie's results, it is expected to have a larger value than the dashed line. As our calculation is not affected by the scattering process, our results are thought to be the real bulk viscosity. Our experimental method has the advantage for the viscosity measurement because we can calculate both the bulk shear viscosity and the slip length independently in a slip approximation. In normal liquid 3He the decrease from the theoretical prediction "qT2 =const. is observed below 5 mK and we get the smaller slip length than the theoretical value. In superfluid 3He, the bulk shear viscosity is obtained which is larger than the slip corrected value of the previous experiment including only the diffusive scattering at the wall. This indicates the slip length must be more long. The long slip length is predicted by the slip approximation including the Andreev scattering.[8]

3.RESULTS AND DISCUSSIONS

REFERENCES

In our experimental condition, the slip approximation is valid for normal liquid 3He. Figure 1 shows ~IT2 vs. T of normal liquid 3He at pressure 5 bar. It can be seen that there is a small but significant decrease of vlT2 with decreasing temperature below about 5 inK. Until now, such decreases were reported by different kind of experiments.[1-3] The reason of this decrease is not clear. In Fig.2, we show, for the first time, the ratio of ~ . r l vs. T. Solid line is the theoretical result of Jensen et al.[ 5] It seems that the ratio of ~J~.B is smaller than the theoretical value of 0.58. Parpia et at.[7] reported the same reduction of slip length, ~kxl=0.34. These results implies the additional transverse momentum transfer might occur at the wall boundary.

1. D.C.Carless, H.E.HalI, and J.R.Hook, J. Low Temp. Phys. 50 (1983) 583. 2. G.Eska, K.Neumaier, W.Schoepe, K.Uhlig, and W.Wiedemann et al. Phys.Rev.B 27 (1983) 5534. 3. J.R.Hook, E.Faraj, S.G.Gould, and H.E.Hall, J.Low Temp. Phys. 74 (1988) 45. 4. C.N.Archie, T.A.Alvesalo, J.D.Reppy, and R.C. Richardson, J. Low Temp. Phys. 42 (1981) 295. 5. H.H.Jensen, H.Smith, P.Wolfle, K.Nagai, and T.M.Bisgaard, J. Low Temp. Phys. 41 (1980) 473. 6. D.A.Richie, J.Saunders, and D.F.Brewer, Phys. Rev.Lett. 59 (1987) 465. 7. J.M.Parpia and T.L.Rhodes, Phys.Rev.Lett. 51 (1983) 805. 8. D.Einzel and J.M.Parpia, Phys.Rev.Lett. 58 (1987 ) 1937.

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Figure 2. ~.Vl vs. T. Solid circles are our data. Solid line is the theoretical result.[5] 0.2

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