PERSISTENT CAPILLARY FLOW OF He II

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PERSISTENT CAPILLARY FLOW OF He II

A. Hartoog, H. van Beelen, R. de Bruyn Ouboter, K. Taconis

To cite this version:

A. Hartoog, H. van Beelen, R. de Bruyn Ouboter, K. Taconis. PERSISTENT CAPILLARY FLOW OF He II. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-140-C6-141. �10.1051/jphyscol:1978662�.

�jpa-00218109�

JOURNAL DE PHYSIQUE

Colloque C6, suppl6ment au no 8, Tome 39, aozit 1978, page C6-140

P E R S I S T E N T C A P I L L A R Y FLOW OF

H e I 1

A. Hartoog, H. Van Beelen, R. De Bruyn Ouboter and K.W. Taconis

KmerZingh Onnes Laboratoriwn der Rijksuniversiteit, Niewsteeg 18, Leiden, The NetherZands.

Rlsum6.- L'Ctude du courant isotherme de l'h&lium superfluide dans un tube capillaire trSs long a conduit

l'observation de circulations permanentes.

Abstract.- The study of isothermal flow of superfluid helium in a very long capillary has led to the observation of persistent currents.

During our study of fourth sound

in a device that consisted of a very long glass capilla- ry connecting two vertical standpipes (i.d.0.34

it was observed that, apart from a standing fourth- sound wave, a damped u-tube oscillation could also be generated.

The damping of such oscillations has in principle three contributions

one due to a net heat flow from the standpipes to the bath, one by viscous flow of the normal fluid (which can be ex- pected to be very small), and one due to a possible dissipative interaction between superfluid and nor- mal fluid. The first two contributions can be cal- culated straightforwardly /2,3,4/. The viscous con- tribution appears to be unmeasurably small in the present geometry. Neglecting second order effects, the thermal-damping constant is proportional to the heat resistance between the helium in both standpipes.

It appears that, when taking for R the Kapit-

za

heatresistance of the effective surface-area of the standpipes of about 0.7 cm2, the thermal dam- ping can well account for the observed damping, suggesting that the internal friction must be very small.

To get a better estimate of this mutual friction, we improved the heat contact between the standpipes by mounting

large bellows in a drum (see inset figure I), which has a heat-exchanging surface-area of about

cm2. Furthermore, to reach a more convenient period of oscillation, we replaced the standpipes by wider ones, having an inner diameter of 3.2 mm. From figure 1, showing parts of a run at bathtemperature To

1.445 K, it follows that the damping now leads to a relaxation- time of more than

hours. It appears that the measured damping-constant has decreased with a

factor of

in agreement with the increase in heat-exchanging surface-area. An independent measu- rement of the heat contact between the reservoirs via the fountain effect confirms this, so that almost no room is left for mutual friction. (The viscous contribution is still negligibly small).

Fig.

The level difference

versus time. In the inset a schematical drawing of the apparatus (capillary length I06 m, i.d. 0.17 mm).

It should be remarked here that there appears to

a maximum amplitude of the u-tube oscillation which, independently of temperature, corresponds to a su- perf luid-velocity amplitude of about 1.8 cm. s-I .

When an initial level difference is produced lar- ger than this"maximum, a decay of the Az with al- most constant superfluid velocity is observed, after which the u-tube oscillation starts, as can also be seen in figure 1. It will be clear that in this initial region an internal friction force must be present. This force balances the pressure diffe- rence, since the acceleration of the superfluid and grad T in the capillary are practically zero.

The magnitude of this force is however still orders of magnitude smaller than could be expected from measurements on adiabatic superfluid flow

The extremely small, or perhaps non-existent mutual friction at low velocities indicates that

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978662

p e r s i s t e n t c a p i l l a r y f l o w should be p o s s i b l e . A c l o s e d c i r c u i t i s t h e r e f o r e formed by mounting a v a l v e between t h e two ends of t h e g l a s s c a p i l l a r y

( s e e i n s e t f i g u r e 2 ) .

F i g . 2 : Az v e r s u s time. The v e r t i c a l b a r s mark t h e time of opening and c l o s i n g t h e v a l v e . During t h e flow i n t h e c l o s e d c i r c u i t , t h e s u p e r f l u i d v e l o c i - t y remained c o n s t a n t (0.17 cm. s-l) w i t h i n t h e mea- s u r i n g accuracy.

The method used to c r e a t e and d e t e c t t h e flow i n t h e c i r c u i t i s analogous t o t h a t used by Van Alphen e t a1./6/ i n a s u p e r l e a k and by Verbeek e t a 1 . / 7 / i n t h e He I1 f i l m . A u-tube o s c i l l a t i o n i s s t a r t e d w i t h c l o s e d v a l v e which i s opened t h e moment Az r e a c h e s z e r o . I n t h e c a s e t h a t t h e r e i s no mutual f r i c t i o n t h e c i r c u l a t i o n b Gs.dT should be conser- ved. When a f t a r some time t h e v a l v e i s c l o s e d a u-tube o s c i l l a t i o n w i l l s t a r t a g a i n w i t h an energy equal t o t h e k i n e t i c energy of t h e flow i n t h e system.

Experimentally, t h e v e l o c i t y i n t h e c l o s e d c i r c u i t appeared t o decay s y s t e m a t i c a l l y w i t h time t o a v a l u e of about 0.2 cm. s - l , a f t s r which howe- v e r no f u r t h e r decay was found. The o b s e r v a t i o n of a decay i s r a t h e r s u r p r i s i n g i n view of t h e absen- c e of t h e i n f l u e n c e of i n t e r n a l f r i c t i o n d u r i n g t h e u-tube o s c i l l a t i o n s .

U n t i l now no s a t i s f a c t o r y e x p l a n a t i o n can b e given. Runs however, s t a r t i n g w i t h low i n i t i a l v e l o c i t i e s showed no decay, even a t t h e maximum measuring time of a b o u t 20 hours. T h i s f i r s t obser- v a t i o n of what might b e c a l l e d p e r s i s t e n t c a p i l l a r y flow i s demonstrated even more s p e c t a c u l a r l y by t h e example shown i n f i g u r e 2, where d u r i n g t h e time t h a t a c u r r e n t i n t h e c i r c u i t was p r e s e n t , t h e temperature was lowered i n 10 hourss from TO=2.089K down t o 1.410 K, r e s u l t i n g i n an i n c r e a s e i n t h e d e t e c t e d l e v e l o s c i l l a t i o n s i n agreement w i t h t h e

i n c r e a s e i n t h e f a c t o r ( p s / p ) l / 2 and a c o n s t a n t su- p e r f l u i d v e l o c i t y . Notice t h a t t h e same f a c t o r i s found i n t h e s h o r t e n i n g of t h e period.

It should be remarked h e r e t h a t , i n view of t h e d e t e c t e d decay a t h i g h e r v e l o c i t i e s , one could d e b a t e on t h e q u e s t i o n whether t h e above r e s u l t proves t h a t t h e flow i s p e r s i s t e n t i n i t s l i t e r a l s e n s e . I n g e n e r a l t h i s can never be concluded. Ana- l y z i n g t h e d a t a i n t h e whole v e l o c i t y r e g i o n shows, however, t h a t t h e h a l f l i f e t i m e of t h e c u r r e n t grows sufficientlyrapidwithdecreasingvelocity, t h a t t h e q u e s t i o n of p e r s i s t e n c e i s reduced t o a m a t t e r of semantics.

CONCLUDING REMARKS.- t h e p r e s e n t measurements prove t h a t t h e u s e of extremely l o n g c a p i l l a r i e s f o r t h e s t u d y of pure s u p e r f l u i d flow l e a d s t o a dramatic r e d u c t i o n i n t h e i n t e r n a l f r i c t i o n a s compared t o t h e c a s e of a d i a b a t i c flow i n r e l a t i v e l y s h o r t c a p i l l a r i e s . Because of t h e o b s e r v a t i o n / 5 / t h a t i n t h e a d i a b a t i c c a s e t h e main c o n t r i b u t i o n t o t h e chemical p o t e n t i a l d i f f e r e n c e i s s u p p l i e d by t h e temperature d i f f e r e n c e , we tend t o a t t r i b u t e t h i s r e d u c t i o n t o t h e v e r y small v a l u e of grad T i n such a l o n g flow p a t h . I f t h i s i n t e r p r e t a t i o n i s correct, i t would mean t h a t t h e v o r t e x p r o c e s s e s , a s s o c i a t e d w i t h t h e m u t u a l - f r i c t i o n phenomenon, a r e a f f e c t e d by t h e s u p p r e s s i o n of grad T, which would b e a c h a l l e n g i n g conclusion.

References

/ I / Hartoog,A., Van Beelen, H., De Bruyn Ouboter,R.

and Taconis, K.W. Proc. LT X I V (1975) Otaniemi, F i n l a n d , p. 241.

/ 2 / Hartoog,A;, O o s t e r l i n g , H., Van Beelen, H., De Bruyn Ouboter, R. and Taconis, K.W., submitted f o r p u b l i c a t i o n i n P h y s i c a .

/3/ Van Spronsen, E., Verbeek, H . J . , Van Beelen,H.

De Bruyn Ouboter, R. and Taconis, K.W.,Physica 77 (1974) 570.

-

141 Robinson, J.E., Phys. Rev.

82

151 De Hass, W., Hartoog, A., Van Beelen, H., De Bruyn Ouboter, R. and Taconis,K.W., Physica 75

(1974) 331.

161 Van Alphen, W .M., De Bruyn Ouboter, R . , Taconis K.W. and Van Spronsen, E., Physica 2 ( 1 9 6 8 ) 1 0 9 . 171 Verbeek, H . J . , Van Spronsen, E . , Mars, H., Van

Eeelen, H . , De Bruyn Ouboter, R. and Taconis, K.W., physica

2

I such a long p e r i o d i s n e c e s s a r y t o o b t a i n a uni- form c o o l i n g . Otherwise t h e d i f f e r e n c e i n thermal c o n t a c t t o t h e b a t h of t h e r e s e r v o i r s would l e a d t o a temperature d i f f e r e n c e d i s t u r b i n g t h e flow i n t h e system.