SUPERFLOW IN VERY LONG GLASS-CAPILLARIES

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SUPERFLOW IN VERY LONG

GLASS-CAPILLARIES

R. de Bruyn Ouboter

To cite this version:

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JOURNAL DE PHYSIQUE

Colloque C6, suppl6ment au

no

8,

Tome

39,

aoiit

1978,

page

C6-

13

14 SUPERFLOW

I N

VERY LONG GLASS-CAPILLARIES

R. de Bruyn Ouboter

Kwnerlingh Onnes Laboratory, Leiden, the Nederlands

Rdsum6.- L'dcoulement s u p e r f l u i d e d e 4 ~ e - 1 1 e s t d t u d i d dans d e t r S s longs e t d t r o i t s c a p i l l a i r e s de v e r r e 5 l a f o i s e n volume e t dans l e f i l m . Les p o i n t s s u i v a n t s s o n t p r s s e n t d s :

I/ Dans l e f i l m s a t u r d : o s c i l l a t i o n de A t k i n , e f f e t Kontorovich (analogue du thdorsme de B e r n o u l l i ) , c o u r a n t p e r s i s t a n t , ondes de t r o i s i e m e son (en p a r t i c u l i e r p r o p a g a t i o n e t r d f l e x i o n de p u l s e s e t ddplacement Doppler a s s o c i d au mouvement du f i l m .

11/ En volume : ondes s t a t i o n n a i r e s de q u a t r i s m e son, a t t d n u a t i o n des o s c i l l a t i o n s dans d e s condi- t i o n s q u a s i - i s o t h e r m e s , c o u r a n t p e r s i s t a n t .

A b s t r a c t . - Superflow of '~e-11 i s s t u d i e d i n v e r y l o n g and narrow g l a s s - c a p i l l a r i e s b o t h i n t h e f i l m a s w e l l a s i n the bulk. The f o l l o w i n g i t e m s w i l l b e reviewed :

I/ I n t h e s a t u r a t e d f i l m : t h e A t k i n s o s c i l l a t i o n , t h e Kontorovich e f f e c t ( analogue of t h e Bernoulli- theorem), p e r s i s t e n t f l o w , s t a n d i n g and t r a v e l i n g t h i r d sound waves i n p a r t i c u l a r t h e p r o p a g a t i o n and r e f l e c t i o n of p u l s e s and t h e D o p p l e r s h i f t when t h e f i l m i s i n motion.

I P / I n t h e bulk : s t a n d i n g f o u r t h sound waves, t h e damping of U-tube o s c i l l a t i o n s i n a l m o s t i s o , t h e r - ma1 c o n d i t i o n s and p e r s i s t e n t flow.

I n t r o d u c t i o n . - A t t h e Kamerlingh Onnes L a b o r a t o r y v e r y l o n g and narrow g l a s s - c a p i l l a r i e s a r e used t o s t u d y v a r i o u s p r o p e r t i e s of t h e flow of s u p e r f l u i d He-11, b o t h i n t h e f i l m a s w e l l a s i n t h e b u l k . I n t h i s review t h e f o l l o w i n g phenomena w i l l b e d i s c u s - sed : I. I n t h e ' ~ e - 1 1 film.- 1 ) The A t k i n s o s c i l l a t i o n which i s t h e p e r i o d i c m a s s - t r a n s f e r through t h e f i l m r e s u l t i n g i n a p e r i o d i c o s c i l l a t i o n of t h e li- q u i d l e v e l s i n t h e s t a n d p i p e s , formed a t t h e b o t h ends of t h e l o n g g l a s s c a p i l l a r y , s e e f i g u r e l a . 2) The Kontorovich e f f e c t / I / , which can be conside- r e d t o be t h e analogue of t h e B e r n o u l l i theorem i n the helium f i l m : a s t a t i o n a r y moving f i l m i s t h i n - n e r t h a n a s t a t i c one by an amount

A & / & ,

--bs

v: /3pg H.

3)

S t a n d i n g t h i r d sound waves, wnich a r e r e s o n a n c e s of s u r f a c e waves i n t h e f i l m between t h e l i q u i d l e v e l s i n t h e s t a n d p i p e s .

4) P e r s i s t e n t flow, which has been g e n e r a t e d i n a c l o s e d c i r c u i t by means of an A t k i n s o s c i l l a t i o n and u s i n g a v a l v e t e c h n i q u e a s w e l l a s by r o t a t i o n of t h e a p p a r a t u s as a whole. 5) The p r o p a g a t i o n and r e f l e c t i o n of t h i r d sound p u l s e s and t h e i r Doppler s h i f t i n t h e v e l o c i t y when t h e f i l m i s i n motion. 11. I n t h e '~e-11 bulk.- The a p p a r a t u s of f i g u r e l a i s now t u r n e d u p s i d e down a s shown i n f i g u r e Ib :

1) S t a n d i n g f o u r t h sound waves, which a r e resonan- c e s of waves i n t h e s u p e r f l u i d d e n s i t y between b o t h ends o f t h e c a p i l l a r y . 2 ) The damping of U-tube os- c i l l a t i o n s i n almostisothermalconditions. 3) P e r - s i s t e n t flow, which h a s been g e n e r a t e d i n a c l o s e d

c i r c u i t by a U-tube o s c i l l a t i o n and u s i n g a v a l v e technique.

F i g u r e 1

These i n v e s t i g a t i o n s have been performed by H. van Beelen, K.W. T a c o n i s , R. de Bruyn Ouboter, E. van Spronsen ( t h e s i s on i t e m s I 1 , 2, 3 ) , H . J . Verbeek ( i t e m s I 4 , 5) and A. Hartoog ( i t e m s 11 1 , 2 , 3 ) .

I. The ' ~ e - 1 1 f i l m . - Our f i l m e x p e r i m e n t s s t a r t e d i n t h e b e g i n n i n g of t h e s e v e n t i e s , when i t was re- p o r t e d i n t h e l i t e r a t u r e t h a t a t t e m p t s t o measure

t h e Kontorovich e f f e c t had f a i l e d / 2 / and t h a t i t seemed i m p o s s i b l e t o c r e a t e p e r s i s t e n t f i l m flow

/ 3 / . S i n c e t h e Kontorovich e f f e c t a s w e l l a s t h e e x i s t e n c e of p e r s i s t e n t f l o w a r e a d ? r e c t consequen- ce of t h e Landau two f l u i d t h e o r y , t h e s e experiments p o i n t e d towards a d e v i a t i n g b e h a v i o u r of t h e moving f i l m 131. S u b c r i t i c a l f i l m f l o w i s e x t r e m e l y s u i t a - b l e t o i n v e s t i g a t e t h e n o n - l i n e a r n o n - d i s s i p a t i v e hydrodynamical p r o p e r t i e s of t h e s u p e r f l u i d i n con-

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n e c t i o n w i t h t h e Landau e q u a t i o n s s i n c e l a r g e super- f l u i d v e l o c i t i e s , up t o 40 cm/s can be o b t a i n e d whi- l e the i n t e r p r e t a t i o n of t h e r e s u l t s i s s t r o n g l y s i m p l i f i e d by the f a c t t h a t t h e normal component i s

clamped t o the w a l l due t o i t s v i s c o s i t y . I n t h i s review i t w i l l be shown t h a t t h e very long and narrow g l a s s - c a p i l l a r i e s o f f e r a p o s s i b i l i t y t o s t u d y t h e v a r i o u s phenomena j u s t mentioned i n t h e i n t r o - d u c t i o n both i n t h e f i l m a s i n t h e bulk i n a r a t h e r unique way. The a p p a r a t u s (Figure 2 ) c o n s i s t s mainly of a long g l a s s - c a p i l l a r y wound i n t o a c o i l and c l o - sed i n i t s e l f through a v a l v e , which i s e s s e n t i a l l y a h e a t e r e n a b l i n g one t o h e a t a small s e c t i o n of t h e c a p i l l a r y above T

A.

Two narrow v e r t i c a l s t a n d p i p e s a r e f l e x i b l y connec- t e d t o t h e c a p i l l a r y on e i t h e r s i d e of the v a l v e . A f i x e d amount of helium gas i s s e a l e d o f f i n t h e system s o t h a t i n a temperature r e g i o n below T i bulk l i q u i d i s formed i n t h e s t a n d p i p e s w h i l e t h e i n n e r - w a l l of t h e c a p i l l a r y i s covered w i t h a s a t u r a t e d f i l m . D i f f e r e n t c a p i l l a r i e s were used, a l l having an i n n e r diameter of about 300

u

b u t t h e i r l e n g t h v a r i e d between 120 and 200 m, now even a 660 m l o n g

c a p i l l a r y i s used. The f i l m i s s e t i n t o motion i n one of two ways : by the c r e a t i o n of a l e v e l d i f f e - r e n c e , which can be performed by g i v i n g t h e s t a n d p i - pes a v e r t i c a l displacement, o r by r o t a t i o n of t h e a p p a r a t u s as a whole. A l l d a t a a r e o b t a i n e d from t h e motion of t h e l i q u i d l e v e l s i n t h e s t a n d p i p e s , which a r e r e a d by means of a cathetometer. P o s s i b l e chan- g e s i n f i l m t h i c k n e s s a r e d e r i v e d from changes i n t h e mean l e v e l h e i g h t . I n o r d e r t o measure small changes i n t h i c k n e s s a l a r g e f i l m a r e a hence a ve- r y long c a p i l l a r y and narrow s t a n d p i p e s a r e neces- s a r y . Changes i n f i l m t h i c k n e s s of

11

correspond t o changes of t h e o r d e r of 0.1 mm i n t h e mean h e i g h t of t h e l i q u i d l e v e l s i n the s t a n d p i p e s . The t h i c k n e s s , 6 , of t h e s a t u r a t e d f i l m i s approximately 100

1

and

i s determined p r i n c i p a l l y by g r a v i t y and t h e Van d e r Waals f o r c e s . For t h e purpose of t h e p r e s e n t survey i t i s s u f f i c i e n t t o approximate t h e Van d e r Waals p o t e n t i a l by

-

y/&i3. With t h i s a p p a r a t u s a l s o t h e v a r i a t i o n of t h e s t a t i c f i l m t h i c k n e s s w i t h t h e h e i g h t H of t h e f i l m above the b u l k l e v e l ir. t h e s t a n d p i p e s has been determined from t h e correspon- d i n g changes i n t h e bulk l e v e l h e i g h t i n t h e c l o s e d volume. The r e s u l t s a r e i n agreement w i t h t h e accu- r a t e d a t a of Sabisky and Anderson

141.

1 ) The Atkins o s c i l l a t i o n . - The v a l v e V i n t h e shor- t e r branch of t h e a p p a r a t u s i s closed and both stand- p i p e s a r e v e r t i c a l l y d i s p l a c e d i n o p p o s i t e d i r e c t i o n s o t h a t a l e v e l d i f f e r e n c e i s c r e a t e d , which g i v e s r i s e t o a p e r i o d i c mass-transport through t h e f i l m . F i g u r e 3 g i v e s a n i c e example of such an Atkins os- c i l l a t i o n

151,

generated i n a 200 m c a p i l l a r y having a p e r i o d of about 30 minutes. The graph shows t h a t t h e l e v e l s a r e i n a s l i g h t l y damped harmonic motion. t h e damping i s found t o b e t h e s m a l l e r t h e l o n g e r t h e c a p i l l a r y

(-I/L).

T h i s i s s t r o n g evidence t h a t t h e d i s s i p a t i o n does n o t t a k e p l a c e i n t h e f i l m i t s e l f , b u t i n t h e s t a n d p i p e s . Indeed i t was found t h a t t h e observed damping can be f u l l y accounted f o r by t h e energy-loss i n t h e h e a t flow over t h e K a p i t z a - r e s i s - t a n c e from t h e l i q u i d i n t h e s t a n d p i p e s t o t h e b a t h , a s s u p e r f l u i d t r a n s p o r t g i v e s a temperature r i s e i n one of t h e s t a n d p i p e s and lowers t h e temperature i n t h e o t h e r .

2 ) The Kontorovich e f f e c t . - The curve i n t h e middle

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C6-1316

JOURNAL DE PHYSIQUE v e l o c i t y i n t h e f i l m i s a t i t s maximum and t h e acce-

l e r a t i o n i s zero.

Figure 3

We remark t h a t t h e f i l m i s t h i c k e r t h a n t h e s t a t i c one a l s o i n d i c a t e d i n f i g u r e 3 when t h e v e l o c i t y i s e q u a l t o zero b u t t h e a c c e l e r a t i o n i s a t i t s maximum a s f o l l o w s from t h e Landau e q u a t i o n s . The t h i n n i n g

i s i n q u a n t i t a t i v e agreement / 5 / w i t h t h e p r e d i c t i o n of Kontorovich / I / which follows from the Landau e q u a t i o n s t o g e t h e r w i t h t h e vapour-liquid e q u i l i - brium c o n d i t i o n s . For a s t a t i o n a r y moving f i l m one f i n d s a type of B e r n o u l l i theorem which determines t h e f i l m t h i c k n e s s d u r i n g s t e a d y flow, the r e d u c t i o n i n t h i c k n e s s being p r o p o r t i o n a l t o t h e square of t h e s u p e r f l u i d t r a n s p o r t v e l o c i t y . We have not o n l y veri- f i e d t h e Kontorovich p r e d i c t i o n d u r i n g t h e A t k i n s o s c i l l a t i o n , which i s s t r i c t l y speaking non-statio- nary flow, b u t a l s o f o r c o n s t a n t s u b c r i t i c a l , c r i t i - c a l and p e r s i s t e n t flow

151.

These f i n d i n g s on t h e t h i n n i n g of t h e moving f i l m have been confirmed by Williams and Packard, by Banton, Hoffer and K e l l e r , by F l i n t and Hallock and by Graham and ~ i t t o r a t o s / b / . 3) Standing t h i r d sound, s u r f a c e , waves.- Besides t h e A t k i n s o s c i l l a t i o n s t a n d i n g t h i r d sound waves a r e u s u a l l y a l s o p r e s e n t i n t h e system. F i g u r e 4a shows an A t k i n s o s c i l l a t i o n on which a t h i r d sound wave i s superimposed. I t s p e r i o d T~ i s of t h e o r d e r

of a few hundred seconds. Combining t h i s w i t h t h e third-sound v e l o c i t y u = /3

?A

g

H

of about 1 m/s shows t h a t t h e wavelenlht A, r 3 u 3 i s a few hundred meters. I t i s a c t u a l l y found t h a t

X 3

= 2L (L = l e n g t h of t h e c a p i l l a r y ) , corresponding t o t h e fundamental mode. Figure 4b g i v e s a n i c e example of such a s t a n - d i n g t h i r d sound wave i n t h e absence of an Atkins o s c i l l a t i o n , both l e v e l s i n d i c a t e d by c r o s s e s and t r i a n g l e s a r e now moving i n phase. Higher modes can a l s o be generated. By manipulation of t h e f l e x i b l e s t a n d p i p e s one can g e t r i d of t h e s t a n d i n g t h i r d sound waves and observe t h e appearance of t h e Atkins o s c i l l a t i o n i n i t s pure form a s shown i n f i g u r e 3 .

4) P e r s i s t e n t flow.- We f i r s t d i s c u s s p e r s i s t e n t flow induced and d e t e c t e d by, means of an Atkins os- c i l l a t i o n

171

s e t up along t h e longer branch (123 m) while V i s closed. When t h e f i l m i s a t maximum velo- c i t y , a t time t i i n f i g u r e 5 , t h e v a l v e V i s opened ( s e e f i g u r e 2) and t h e l e v e l d i f f e r e n c e , which i s

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and t h e remaining c i r c u l a t i o n i s conserved. L

-

F i g u r e 4 The p e r s i s t e n t flow i s d e t e c t e d a f t e r an a r b i t r a r y time i n t e r v a l a t tf i n f i g u r e 5 , by c l o s i n g t h e v a l v e V s o t h a t the k i n e t i c energy i n t h e f i l m shows up a s an A t k i n s o s c i l l a t i o n .

5 min _I

I A t 1 ,

t_ 1, t t mln

F i g u r e 5

No decay h a s been observed, even a f t e r 18 hours. A

n i c e r , non-destructive b u t more s u b t l e way of d e t e c - t i n g t h e p e r s i s t e n t flow i s by t h e thinning of t h e f i l m i n motion due t o t h e Kontorovich e f f e c t , which has indeed been observed. The i n c r e a s e of t h e t o t a l amount of b u l k l i q u i d i n t h e s t a n d p i p e s confirms the Kontorovich p r e d i c t i o n . We have a l s o g e n e r a t e d s m a l l

p e r s i s t e n t c u r r e n t s using t h e Van Alphen /8/ method, i . e . by c r e a t i n g a l e v e l d i f f e r e n c e when t h e v a l v e V

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C6-1318

G a l k i e w i c z and H a l l o c k

/I11

confirmed t h e s e r e s u l t s on p e r s i s t e n t f i l m flow i n t h e s a t u r a t e d f i l m and l a t e r on Telschow, G a l k i e w i c z and H a l l o c k /11/ p e r - formed e x p e r i m e n t s on p e r s i s t e n t f l o w i n t h e u n s a t u - r a t e d h e l i u m f i l m d e t e c t e d by t h e D o p p l e r s h i f t i n t h i r d sound. Already i n 1968 Henkel, Kukich and Rep- py / I I / d e t e c t e d p e r s i s t e n t a n g u l a r momentum i n t h e u n s a t u r a t e d h e l i u m f i l m a d s o r b e d on a p o r o u s medium by u s i n g a s e n s i t i v e g y r o s c o p i c t e c h n i q u e .

5) The p r o p a g a t i o n and r e f l e c t i o n of t h i r d sound p u l s e s and t h e D o p p 1 e r s h i f t . - These v e r y l o n g g l a s s c a p i l l a r i e s o f f e r t h e o p p o r t u n i t y t o s t u d y t h e pro- p e r t i e s of t h i r d sound p u l s e s of l o n g p u l s e l e n g t h 191. T h i r d sound p u l s e s c a n b e g e n e r a t e d by r a i s i n g o r l o w e r i n g one of t h e f l e x i b l e s t a n d p i p e s d u r i n g a g i v e n time i n t e r v a l . A v e r t i c a l d i s p l a c e m e n t of one of t h e b u l k l e v e l s c a u s e s a l o c a l change i n f i l m t h i c k n e s s , which p r o p a g a t e s w i t h t h e t h i r d sound v e l o c i t y t o t h e o t h e r end of t h e c a p i l l a r y , where upon a r r i v a l i t exchanges mass t h e r e b y changing t h e l e v e l h e i g h t . The p u l s e i s r e f l e c t e d and t r a v e l s up and down t h e c a p i l l a r y . Each time i t r e a c h e s one of t h e b u l k l e v e l s a change i n h e i g h t i s o b s e r v e d . The a t t e n u a t i o n of s u c h a p u l s e a p p e a r s t o be v e r y small. The p r o p a g a t i o n v e l o c i t y u 3 c a n b e d e t e r m i n e d d i r e c - t l y from t h e time of f l i g h t of t h e p u l s e . F i g u r e 7 shows t h e o b s e r v a t i o n of a t h i r d sound d o u b l e p u l s e w i t h a p u l s e l e n g t h of 70 m e t e r , t r a v e l l i n g on a f i l m of 205 m e t e r l e n g t h . An a l m o s t r e c t a n g u l a r dou- b l e p u l s e of 40 s e c o n d s i s g e n e r a t e d by moving one of t h e s t a n d p i p e s i n t h e i n d i c a t e d way. The s i g n of t h e p u l s e i s r e v e r s e d on r e f l e c t i o n a t t h e b u l k l e - v e l s i n t h e s t a n d p i p e , a s i s shown by t h e s i g n a l s i n b o t h s t a n d p i p e s b e i n g of o p p o s i t e s i g n . r - i

1

F i g u r e 7 The i n c r e a s e of t h e l e v e l h e i g h t s c o r r e s p o n d t o t h e a r r i v a l o f t h e p o s i t i v e b l o c k d u r i n g which mass i s dumped i n t o t h e s t a n d p i p e , t h e n e g a t i v e s l o p e s t o t h e a r r i v a l of t h e n e g a t i v e b l o c k , d u r i n g which t h e same amount i s withdrawn. The b e h a v i o u r o f a p u l s e d u r i n g r e f l e c t i o n i s governed by t h e c o n s e r v a t i o n o f e n e r g y 191. The e n e r g y p e r u n i t a r e a of a p u l s e , w i t h p u l s e h e i g h t

5,

i s p r o p o r t i o n a l t o

c2.

C o n s i d e r a r e f l e c t i o n a t a b u l k l e v e l of l a r g e c r o s s - s e c t i o - n a l a r e a s o t h a t t h e p o t e n t i a l of t h e exchange li- q u i d i n t h e r e f l e c t i n g r e s e w o i r i s n e a r l y e q u a l t o z e r o . T h i s i s r e a l i z e d when t h e two b u l k l e v e l s a r e i n e q u i l i b r i u m . I n t h i s s i t u a t i o n

5:

=

52

and s i n c e t h e r e i s no f o r c e t o r e v e r s e t h e momentum i n t h e p u l s e , t h e p u l s e h e i g h t r e v e r s e s s i g n :

5,

=

-ci.

I f o n t h e o t h e r hand, t h e p u l s e r e f l e c t s a g a i n s t a n empty s t a n d p i p e i t c o n s e r v e s i t s s i g n :

5,

=

5;

and t h e momentum i s r e v e r s e d / 9 / . T h i s b e h a v i o u r i s i n agreement w i t h t h e o b s e r v a t i o n t h a t t h e fundamental f r e q u e n c y of t h e s t a n d i n g waves between two b u l k l e v e l s , which c o r r e s p o n d t o a wavelength h = 2L i s t w i c e a s h i g h a s t h e f r e q u e n c y f o r s i m i l a r waves w i t h one of t h e s t a n d p i p e s empty ( A = 4L). The si-

t u a t i o n i s a n a l o g u o u s t o t h a t of s t a n d i n g waves i n a c l o s e d , r e s p e c t i v e l y open, o r g a n p i p e . I n t h e con- t r i b u t e d c o n f e r e n c e p a p e r by Verbeek e t a l . i s con- s i d e r e d t h e c a s e of a p u l s e a r r i v i n g a t a b r a n c h i n g p o i n t o f two c a p i l l a r i e s , which o c c u r s when t h e s t a n d p i p e s a r e a l s o c o n n e c t e d by t h e s h o r t e r b r a n c h a s i s t h e c a s e when t h e D o p p l e r s h i f t on p e r s i s t e n t f l o w i s s t u d i e d .

11. 4 ~ e b u l k . - The b u l k p r o p e r t i e s a r e s t u d i e d - ~ ~ i n e s s e n t i a l l y t h e same a p p a r a t u s a s i s used f o r t h e f i l m , now b e i n g t u r n e d u p s i d e down however ( f i g u r e I b ) . Although t h e whole d e v i c e i s immersed i n t h e He-I1 b a t h a l a r g e h e a t - e x c h a n g e r

1121

(con- t a c t a r e a o f a b o u t 350 cm2) h a s been i n s t a l l e d b e t - ween t h e s t a n d p i p e s t o keep t h e t e m p e r a t u r e d i f f e - r e n c e o v e r t h e c a p i l l a r y a s s m a l l a s p o s s i b l e . F i g u r e 8 shows t h e a p p a r a t u s s c h e m a t i c a l l y w i t h s t a n d - p i p e s and a v e r y l o n g g l a s s c a p i l l a r y (117 m) wound i n t o a c o i l . Again a s h o r t e r c o n n e c t i o n p r o v i d e d w i t h a v a l v e V ( i n most c a s e s a s u p e r l e a k w i t h a h e a t e r / 8 / ) , b u t a l s o a m e c h a n i c a l v a l v e i s some- t i m e s u s e d , c a n b e i n s t a l l e d whenever a c l o s e d f l o w c i r c u i t is r e q u i r e d . The c a p i l l a r y i s chosen t o b e even n a r r o w e r (170 i . d . ) t h a n f o r t h e c a s e of t h e f i l m i n o r d e r t o clamp t h e v i s c o u s normal component t o t h e w a l l s s o t h a t t h e mass t r a n s p o r t i s a l m o s t e n t i r e l y c a r r i e d by t h e s u p e r f l u i d component.

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F i g u r e 8

I t can b e g e n e r a t e d i n s i t u a t i o n s i n which t h e n o r - mal f l u i d i s clamped t o t h e w a l l and i s t h e r e f o r e u s u a l l y s t u d i e d i n a s u p e r l e a k , a s was done by Rud- n i c k and S h a p i r o 1131 i n 1962 i n t h e f r e q u e n c y r a n g e of 200

-

5000 Hz. The l o n g and narrow ( g l a s s ) c a p i l - l a r i e s o f f e r a u n i q u e p o s s i b i l i t y t o s t u d y v e r y low f r e q u e n c y f o u r t h - s o u n d waves i n a w e l l - d e f i n e d geometry. I n o r d e r t o g e n e r a t e a fourth-sound wave i n t h e s y s t e m shown i n f i g u r e 8 ( w i t h t h e v a l v e V i n t h e s h o r t e r b r a n c h c l o s e d ) one of t h e f l e x i b l e s t a n d - p i p e s i s moved p e r i o d i c a l l y up and down, w i t h a n ad- j u s t a b l e f r e q u e n c y , i n t h e r a n g e of 0.5

-

3.5 Hz. At t h e same time t h e l e v e l i n t h e f i x e d s t a n d p i p e i s ob- s e r v e d . On v a r y i n g t h e f r e q u e n c y t h i s l e v e l a p p e a r s t o remain a t r e s t e x c e p t f o r a s p e c i a l v a l u e of t h e d r i v i n g f r e q u e n c y when t h e s u p e r f l u i d r e s o n a t e s and a s t a n d i n g wave i n t h e L = h / 2 mode i s g e n e r a t e d between t h e l i q u i d l e v e l s . The fourth-sound v e l o c i t y u,

i s d e t e r m i n e d from t h e l e n g t h of t h e c a p i l l a r y and t h e r e s o n a n c e f r e q u e n c y . The o b s e r v e d d e v i a t i o n s

/

141

from t h e well-known r e l a t i o n u t =

oS

$) ps / 9 / c a n be f a i r l y w e l l a c c o u n t e d f o r by t h e i n f e u e n c e of t h e

F i g u r e 9

2 ) The damvina of U-tube o s c i l l a t i o n s i n a l m o s t i s o - -- t h e r m a l c i r c u m s t a n c e s . - During o u r s t u d y of t h e fourth-sound p r o p e r t i e s i t was n o t i c e d t h a t a l s o damped U-tube o s c i l l a t i o n s c o u l d b e g e n e r a t e d i n t h e d e v i c e i n f i g u r e 8. Again v a l v e V i s c l o s e d , At l e a s t t h r e e c o n t r i b u t i o n s t o t h e damping c a n be d i s - t i n g u i s h e d i n p r i n c i p l e : 1) A n e t h e a t f l o w from t h e s t a n d p i p e s t o t h e b a t h o v e r t h e s m a l l b u t f i n i t e t h e r m a l K a p i t z a r e s i s t a n c e formed by t h e w a l l s of t h e r e s e r v o i r s 1121. T h i s e f f e c t Leads t o a t h e r m a l damping c o n s t a n t p r o p o r t i o n a l t o t h e t o t a l K a p i t z a r e s i s t a n c e between t h e l i q u i d i n b o t h s t a n d p i p e s , and i s t h u s s t r o n g l y reduced by t h e i n s t a l l a t i o n of t h e l a r g e b e l l o w s , which h a s a heat-exchanging s u r - f a c e a r e a d a b o u t 350 cn2

11

21, p r o v i d i n g a l m o s t i s o t h e r m a l c o n d i t i o n s ( i n n e r d i a m e t e r s t a n d p i p e s 3.2 mm). 2 ) The c o n t r i b u t i o n due t o v i s c o u s f l o w of t h e normal f l u i d , which can be e x p e c t e d t o b e u n m e a s u r a b l y s m a l l i n t h i s p a r t i c u l a r geometry. 3) Mutual f r i c t i o n , a p o s s i b l e d i s s p a t i v e i n t e r a c t i o n between t h e s u p e r - and n o r m a l - f l u i d . A t y p i c a l r e s u l t i s shown i n f i g u r e 10.

v i s c o u s motion of t h e normal component, n o t b e i n g

clamped p e r f e c t l y i n t h e c a p i l l a r y . T h i s l a t t e r e f - T,,E 1 . 4 4 5 ~

f e c t a l s o g i v e s t h e main c o n t r i b u t i o n t o t h e damping, which h a s a l s o been d e t e r m i n e d e x p e r i m e n t a l l y from

t h e r a t e of d e c r e a s e of t h e a m p l i t u d e o b s e r v e d a f t e r

-LY%+-.--'

1210 rntn

t u r n i n g o f f t h e d r i v i n g system. F i g u r e 9 shows s u c h F i g u r e 10 a d e c a y , a s i t i s r e c o r d e d f o r a 280 m l o n g c o p p e r

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t h e r a n g e 1.4

-

2.1 K. The damping o f t h e o s c i l l a - t i o n i s v e r y s m a l l ( a h a l f l i f e t i m e of a b o u t 10 h o u r s i s shown i n f i g u r e 10) and can s t i l l be accounted f o r by t h e r e s i d u a l K a p i t z a damping ( 1 ) .

The i n f l u e n c e of mutual f r i c t i o n o n l y shows up i n t h e i n i t i a l decay where, s i n c e t h e a c c e l e r a t i o n and t h e g r a d i e n t i n t h e t e m p e r a t u r e a r e c o m p l e t e l y ne- g l i g i b l e , mutual f r i c t i o n must b a l a n c e t h e l e v e l d i f f e r e n c e . A l s o i n t h i s r e g i o n , however, t h e mu- t u a l f r i c t i o n i s v e r y s m a l l , o r d e r s of magnitude s m a l l e r t h a n could be e x p e c t e d from measurements on a d i a b a t i c s u p e r f l u i d f l o w i n s h o r t c a p i l l a r i e s . I n a d i a b a t i c f l o w 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 found t o be s u p p l i e d by t h e t e m p e r a t u r e d i f f e r e n c e 1151. The d r a s t i c r e d u c t i o n i n mutual f r i c t i o n f o r i s o t h e r m a l f l o w may t h e r e f o - r e be a t t r i b u t e d t o t h e e x t r e m e l y s m a l l v a l u e of t h e t e m p e r a t u r e g r a d i e n t (and n o t t o t h e reduced i n f l u e n c e o f e n d - e f f e c t s i n t h e l o n g c a p i l l a r i e s ) . 3) P e r s i s t e n t flow.- As t h e s e o b s e r v a t i o n s i n d i c a t e t h a t below a c e r t a i n s u p e r f l u i d v e l o c i t y t h e r e might be no mutual f r i c t i o n , i t i s s u g g e s t e d t h a t p e r s i s - t e n t c a p i l l a r y f l o w i s p o s s i b l e and c a n be c r e a t e d i n t h e same way a s a l r e a d y d i s c u s s e d f o r t h e 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 t h e v a l v e V c l o s e d , s e e f i g u r e 8. When t h e f l u i d i s a t maximum v e l o c i t y (AZ

-

0 ) V i s opened and t h e c i r c u l a t i o n s h o u l d be conserved. A f t e r some t i m e V i s c l o s e d and 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 . E x p e r i - m e n t a l l y i t was found t h a t 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 decayed w i t h time t o a v a l u e o f a b o u t 0.2 cm/s, a f t e r which no f u r t h e r d e c a y was found, even a f t e r t h e maximum measuring t i m e of a b o u t 2 0 h o u r s . I n f i g u r e I 1 a r u n i s shown f o r vs z 0.16ctq/s where d u r i n g t h e time t h a t t h e c u r r e n t was p r e s e n t i n t h e c i r c u i t , t h e t e m p e r a t u r e was s l o w l y lowered from 2.09 K down t o 1.41 K , r e s u l t i n g i n a n 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 with t h e i n c r e a s e i n and a c o n s t a n t s u p e r f l u i d v e l o c i t y / 8 / . The 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 p e r i o d . The q u e s t i o n why d u r i n g t h e f l o w i n t h e c l o s e d c i r c u i t i n t h e v e l o c i t y r e g i o n 0.2 cm/s

<

vs

<

1 . 8 cm/s t h e f r i c t i o n a p p e a r s t o b e l a r g e r t h a n d u r i n g t h e U-tube o s c i l l a t i o n , s t i l l h a s t o b e i n v e s t i g a t e d . F i g u r e 11 R e f e r e n c e s

/ I / Kontorovich, V.M., Sov. Phys. J.E.T.P.

2

(1956) 7 70

/ 2 / K e l l e r , W.E., Phys. Rev. L e t t .

26

(1970) 569 / 3 / Wang, T.G. and Rudnick, I . , Proc. LT 13, Boulder

U.S.A., 1972; Wagner, F., J. Low Temp. Phys. 13 (1973) 185; s e e a l s o : P u t t e r m a n , S.J. and

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Rudnick, I . , P h y s i c s Today, August 1971; Good- s t e i n , D.L. and Saffman, P.G., Phys. Rev. L e t t . 24 (1970) 1402; Proc. R. Soc. London A325 (1971)

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447; J . Low Temp. Phys.

18

(1975) 435-

141 Van Spronsen, E., Verbeek, H.J., v a n B e e l e n , H..

d e Bruyn Ouboter, R. and T a c o n i s , K.W., P h y s i c a 81B (1976) 91; S a b i s k y , E.S. and Anderson, C.H.,

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Phys. Rev. L e t t .

2

(1970) 1049; Phys. Rev. (1973) 790

/ 5 / Van Spronsen, E., Verbeek, H.J., d e Bruyn Oubo- t e r , R . , T a c o n i s , K.W. and van Beelen, H., Phys. L e t t .

45A

(1973) 49; P h y s i c a

61

(1972) 129;

77

(1974) 570

1 6 1 W i l l i a m s , G.A. and P a c k a r d , R., Phys. Rev. L e t t 32 (1974) 587; Banton, M.E., H o f f e r , J.K. and

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K e l l e r , W.E., B u l l . Am. Phys. Soc.

19

(1974) 436; F l i n t , E.B. and H a l l o c k , R.B., Phys. Rev. B11 (1975) B u l l . Am. Phys. Soc.

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(1974) 436;

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Graham, G.M. and V i t t o r a t o s , E., Phys. Rev. L e t t . 33 (1974) 1136; Cambell, L . J . , Hammel, E.F., H o f f e r , J . K . and K e l l e r , W.E., J. Low Temp. Phys.

2

(1976) 527

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12

(1974) 131

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181 Van Alphen, W.M., d e Bruyn Ouboter, R.. Taconis, K.W. and v a n Spronsen, E., P h y s i c a

39

(19681109 / 9 / Verbeek, H.J., A r s a l a , N.K., v a n Beelen,

H.,

d e

Bruyn Ouboter, R. and T a c o n i s , K.W., P h y s i c a 84B (1976) 334

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1101

Telschow, K.L., Wang, T. and Rudnick, J.,J.Low Temp. Phys.

18

(1975) 43

/ I 1 1 G a l k i e w i c z , R.K. and H a l l o c k , R.B., Phys. Rev. L e t t .

2

(1974) 1073; Telschow, X.L., Galkie- w i c z , R.K. and H a l l o c k , R.B., Phys. Rev. L e t t . 37 (1976) 1484; Henkel, P.P., Kukich, G. and

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Reppy, J . D . , P r o c . LT 1 1 , St-Andrews (1968) A3.4 p. 178

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1131 Rudnick, I . and S h a p i r o , K.A., Phys. Rev. L e t t . 9 (1962) 191; Phys. Rev.

137

(1965) A1383; -