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Submitted on 1 Jan 1978
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DISSIPATION IN THE SUPERFLUID FILM BELOW
IK
J. Armitage, J. Allen, M. Toft
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, suppl~ment au no 8, Tome 39, aozit 1978, page C6-302
DISSIPATION
I N
THE
S U P E R F L U I D F I L M BELOW
I K
+J.G.M. Armitage, J.F. Allen and M. Toft d
Department of Physics, University of S t Andrews North Haugh, S t Andrews, ScotZmd *Now a t CEGB, S c i e n t i f i c Services Department, Withenshaw, Manchester, England.
Rbsum6.- Nous avons mesurb la vitesse du film d'helium superfluide a w tempdratures 1 1 mK
-
1 K. Si la difference de hauteur du niveau liquide, Ah, est moins que 50 pm la dissipation augmente ra- pidement mais plus lentement que exp(-v /v ) . Au-dessous de 20 mK, nous observons que la dissipa- tion a un terme v.
A toutes les tempgra'?ures les vitesses sont discrstes et trss stables si Ah est plus grand que 30 pm.Abstract.- We have measured the transfer rate of the surperfluid helium film at temperatures from
1 1 mK to 1 K. If the level difference, Ah, is less than 50 pm the dissipation rises rapidly butmore slowly than exp(-v /v ) . Below 20 mK, we observe that the dissipation has a term a v
.
At all tem- peratures there arz vgry stable discrete rates if Ah is greater than 50 pm.Two mechanism can cause dissipation in su- perfluid film flow /1,2/. Robinson /3/ showed that thermal effects in the reservoirs at either end of the film produce a term in the dissipation a v the
s' superfluid velocity. The other mechanism, vortex motion /4,5/, gives tise to a term which is highly non-linear in v
.
Vortices can originate in thermal fluctuations /6,7/ or may be generated mechanically /8/.~arris- owe used the latter to explain the mul- tiplicity of transfer rates which are observed /8,9/ it involves a critical velocity below which no dis- sipation occurs.We have made measurements at very low tempe- ratures where Robinson dissipation can be neglected and where thermal fluctuations are much reduced. A demagnetization cryostat was used to cool pure '~e
( 3 ~ e concentration < 30 ppb) down to 1 1 mK. Film flow took place over the polished stainless steel walls of a beaker, and the liquid levels inside and outside the beaker were monitored by capacitors with resolution of 1 pm. The base of the reservoir con- tained a bellows whereby the bath level could be changed at a uniform rate either to drive the film flow at constant level difference or to initiate inertial oscillations.
The Harris-Lowe theory /8/ which predicts dissipation a (vs
-
vC)'I2
is not supported by our results below 1 K, since no dissipation free region,v < vc, was observed. Values of v down to 15 cm
5 1
s still showed measurable dissipation, while the 312 power law gave too low an increase in dissipa- tion with incrasing v
.
Robinson damping a v was observed to fade out below 1 K, but below 20 mK dissipation linear in v dramatically reappeared roughly a T - ~ and strong enough at 11 mK to cause the amplitude of inertial
-
1oscillations to decay to e in 2. 7 periods.
The data for both driven and oscillatory flow from 15 mK to 740 mK could be divided into a region A covering level differences Ah less than 50 pm, and a region B where Ah extended from 5 0 pm to our maximum 800 pm. In A the dissipation showed a vs
dependence to be discussed below, while in B the flow was dominated by persistent rates which could remain constant to f
$
% despite driving Ah's changing from 100 to 400m.
The transfer rate as a function of Ah showed a rise to a maximum at %120 pm followed by a slow decline at least as far as Ah = 800 pm. We can find no model which descri- bes the dissipation in region B.
The data of region A has been analysedinterms of a model which has dissipation a exp(-vB/vs),this was so we could compare it with Campbell
g
&
/2/ where their data is analysed in the same manner.The basic equation of motion is
+ This research was supported by the Science Re-
search Council Grant No GR/A 2338.6.
,ys
+ Cpo(p,~)-
ad-" + gh) = -KAV exp(-vg/vs)where d is the film thickness, A is the cross-sec- tional area of the film, K is the quantum of cir- culation, and V and vB are adjustable parameters. This equation was numerically integrated over the length of the film to give a relation between the steady state transfer rate as a function of Ah, and also by integrating over time to give the rate of decay of the oscillations.
Using oscillations one can examine the dissipation at lower values of v than is possible using driven flows. With oscillations the range was
-
15 < vs < 32 cm s while for driven flow it was
25 < vs < 36 cm s-
,
where vs was always taken at the thinnest part of the film. The best fits to the data in region A were obtained with the values ofv and vB given below :
-
i) decay of the oscillations :
T mK : 20 : 3 3 : 60 : 338 : 740
begins at the same temperature as that where the term linear in v appears in the damping of the oscillations. These things may be associated with the likelihood that below 200 mK the 3 ~ e impurities are being trapped in states at the free surface of the liquid / l o / .
References
/ I / Saunders, B.L., Thesis, University of StAndrews
(1 9 7 4 ) .
/ 2 / Campbell, L.J., Hammell, E.F., Hoffer, J.K. and Keller, W.E., J. Low Temp. Physics
2
( 1 9 7 6 ) 5 2 7131 Robinson, J.E., Phys. Rev.
8
(1951) 440. / 4 / Anderson, P.W., Rev. Mod. Phys.2
(1966) 298.151 Campbell, L.J., J. Low Temp. Phys.
8
(1972) 105. / 6 / Lordanski, S.V., J.E.T.P.2
(1965) 467./ 7 / Langer, J.S. and Fisher, M.E., Phys. Rev. Letters
19
(1967) 560.:.---.-.
--
1 - 3
V s cm x 10' : 1.0: 2 6 : 26 : 12 : 1 . 0
/ a /
Harris-Lowe, R.F., J.Low Temp. Phys.8
(1977).
-a
.-
489.-
1vB cm s : 8 5 : 1 2 4 : 1 2 4 : 9 0 : 79 / 9 / Allen, J.F. and Armitage, J.G.M., Phys. Lett.
22 (1966) 121.
-
ii) driven flow : (T < K) = 1 . 0 l 0 1 cm-3 / l o / Crum, D.B., Edwards, D.O.and Sarwinski, R.E.,
-
1 Phys. Rev.A9
(1974) 1312.v = 220 cm s
.
BFor comparison, our driven flow data for 1.14 Kover the full range 2 pm < Ah i 250 Um could be fitted by the values :
v = 3 . 6 x 1017s-I cm-3
-
1v = 450 cm s
.
BBelow 1 K it is apparent that vB decreases with decreasing superfluid velocity and this means that the onset of dissipation is much more gradual than that predicted by the value for vB = 1400 cm
-
1s which was found by Campbell
g
/ 2 / above 1 K, but it should be noted that their results were dominated by values of Ah greater than 200 pm. They also reported that the first few oscillations had anomalously high damping, and this is qualitatively consistent with our result that vg decreases with decreasing v.
Below 200 aK the transfer rate at large
level differences varied significantly with tempe- rature. The transfer rate decreased from
2 -1
1 0 . 4 ~ I O - ~ C ~ s at 200mK to 9 . 3 ~ l o q 5 c m 2 c 1 at 2 0 mK and then rose sharply again to 1 0 . 2 x l c 5
2 - 1
