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Submitted on 1 Jan 1978
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SOME OSCILLATION VISCOMETER RESULTS FOR
3He : A AND B PHASE RESONANCES AND
NORMAL PHASE VISCOSITY
M. Steinback, J. Lyden, R. Guernsey, Jr
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-22
SOME OSCILLATION VISCOMETER RESULTS FOR 3H e : A AND B PHASE RESONANCES
AND NORMAL PHASE VISCOSITY
M. S t e i n b a c k , J . K . Lyden and R.W. G u e r n s e y , J r .
Department of Vhyaics, CoVwrib-ia University, New York, N. I. 10027 USA.
Résumé.- Les données de l'amortissement d'un viscosimètre oscillant sont présentées pour les phases normales A et B de 3He. La dépendance de r|T2 en fonction de la pression dans la phase normale est
donnée et quelques résonances intéressantes dans les phases A et B sont discutées.
Abstract.- Damping data from an oscillation viscometer are presented for the A, B and normal liquid phases of 3He. The pressure dependence of r)T2 in the normal phase is given, and some interesting resonances in the A and B phases are documented.
There is continuing interest in the hydrodyna-mics of 3He both superfluid and normal. We offer he-re some observations of the liquid damping of an oscillating cylinder at nine pressures (10-31 bar) and from 2 to 5 mK. For the normal liquid phase we find a pressure dependence for T)T2 that corrobora-tes earlier results /l/ at higher pressures but that at low pressure is not as steep as reported recent-ly by Parpia et al. /2/ (PSBR). In the A and B su-perfluid phases, we find resonances that appear not to be ordinary sound.
The sample cylinder is fitted with 20 disks (thickness = 251 um) spaced 50 um apart. Each has a hole in its center, and all are rigidly attached to the cylinder wall. The liquid space, then, con-sists of 21 disk shaped regions (diameter = 2.70cm) simply connected by a central hole (diameter = 0.471 cm). The cylinder is driven in rotational os-cillation about its axis at 355 Hz and at a constant amplitude sufficiently small to avoid non-linear effects. The disk spacing is small enough and the frequency low enough to ensure that the gap axis remains perpendicular to the disks everywhere ex-cept, of course, in the central hole. The cylinder is part of the bob of a torsion pendulum that is maintained on resonance by an electromagnetic dri-ve and feedback system dedri-veloped in our laboratory for earlier work /3/ on the helium liquids. The inertial and dissipative liquid torques acting on the container are determined from the pendulum re-sonant period and damping. From these data we ex-tract the normal fluid density and the viscosity.
IBM T.J. Watson Research Center,Yorktown Heights New York 10598 USA.
At the peak wall velocity used in the work (2.3 Vlm/s) (peak azimuthal dispalcement = 10 A ) , the period is stable to ±1 part in 107 and we can resol
ve damping to ± 0.2 %.
The sample was cooled by adiabatic demagne-tization of CMN. Temperature was measured by a CMN magnetic thermometer mounted directly on the sample cylinder. This was calibrated against a germanium thermometer and the zeros of (8P/3T) for 3He. At
lower temperatures, this magnetic temperature (T ) was corrected for ordering by reference to the La Jolla IM values for T . We could resolve T to
c
± 0.05 yK. A typical warm-up rate was 7 yK/h near T , and so with our signal averaging time of about 30 seconds we could obtain data at 0.06 yK interval The viscometer was magnetically shielded to reduce fields there to less than 1 gauss. The sample pres-sure varied by less than 0.02 bar over the three to five days that were required to complete a data set.
For temperatures low enough for the liquid to be nearly fully locked to the disks by its vis-cosity bu not so low as to give significant damping in the central hole, we expect the liquid damping to be proportional to p2/n or p2T2/(nT2 where nT2
n n
is a constant characteristic of the normal Fermi liquid. We find the pendulum damping to be linear in T2 above 7 to 13 mK2 (depending on the pressure) A least square fit up to about 36 mK2 gives the slope and so nT to within a geometry dependent factor.
At this writing we have some uncertainty in our geometrical parameters and so quote only rela-tive values of r|T2. Since the earlier experiments /1,2/ are in reasonable agreement at 19 bar, we
choose this as a reference and use the average va- from viscous effects would be lowest there- lue given by Wheatley /I/ (17~' = 1.27 poise m~') in
calculating
W 2
at other pressures. FigureI
shows our results, those of PSBR /2/ and Wheatley's fit / I / of earlier data. There is reasonable agreement ex- cept at lower pressures where the PSBR data rise more steeply than the rest.1 1
I I II
0 10 20 30 PRESSURE (BAR) 2.5 2.0 TEMPERATURE (mlo,
-o
A THIS WORK o PARPIA. el 01.2-
FIT TO EARLIER WORK^0
-
Fig. 3 : Details of the resonances near Tc at 13.04 bar.
0
"1 1.5-
Cr 0
1.0
-
\-
Our sample space is too small to support simple sound resonances at our frequency, and we have been unable to find a Helmholtz mode that fits our data. Fjg- 1 : Pressure dependence of the viscosity coef- We have had some success in fitting the large broad flcient in the normal phase of liquid '~e.
peak and the largest sharp peak near Tc to second sound modes propagating vertically between the disks. Both our damping and period data show marked
In this case, the resonance width and height may be resonances in the superfluid phases. The damping
dominated by the spread in disk spacings. resonances are shown in figures 2 and
3.
We also have tried to fit fourth sound cy- lindrical modes to our data. These cannot explain
TEMPERATURE (mK)
the large broad resonance and fit rather poorly to the sharper resonances near T
.
This analysis and the second sound fitting are still in progress. We present these data now in the hope of stimulating some discussion.We are pleased to acknowledge the very va- luable assistance of Dr. R.J. McCoy and the support of the National Science Foundation, USA.
References
/2/ Parpia, J.M., Sandiford,D. J., Berthold, J
.E.
and Reppy,J.D,, Phys. Rev. Lett.-40 (1978) 565 ~ i 2 ~: .Liquid damping as a function of pressure / 3 / Guernsey,R.W. Jr., Proc 12th Int' 1.
Conf. LOWand temperature. Temp. Phys. (1970)
79
; Biskeborn,R. and Guern-sey,R.W.Jr., Phys. Rev. Lett. s(1975) 455 ;
Guernsey,R.W.Jr., McCoy,R.J., Steinback,M. and Note that the amplitude of the large broad peak as Lyden,J.K., Phys. Lett.
