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Measurements of dissipation of AC pressure-driven superflow of4He in aerogel
PHYSICA
Physica B 194-196 (1994) 663-664 North-HoUand
M e a s u r e m e n t s of d i s s i p a t i o n of AC p r e s s u r e - d r i v e n s u p e r f l o w of 4He in Aerogel D.B. Hannon and A. T y l e r The S c h u s t e r L a b o r a t o r y , University of Manchester, Manchester M13 9PL, U.K.
Using a t w o - c h a n n e l Helmholtz r e s o n a t o r we have m e a s u r e d t h e complex conductance a s s o c i a t e d w i t h ac p r e s s u r e - d r i v e n s u p e r f l o w of liquid 4He t h r o u g h aergoel g l a s s close to the t r a n s i t i o n t e m p e r a t u r e . From t h i s we have c a l c u l a t e d a d i s s i p a t i o n f u n c t i o n which a p p e a r s to f o l l o w a power law in t h e a r g u m e n t of the s u p e r f l u i d d e n s i t y divided by the f l o w velocity.
The s u p e r f l u i d t r a n s i t i o n in aerogels is s h a r p y e t w i t h c r i t i c a l exponents t h a t d i f f e r s i g n i f i c a n t l y f r o m those of bulk helium (1,2). In t h i s work we have used a helmholtz resonator technique (3) to s t u d y the dissipation of pressure driven a.c. superflow through aerogel close to its transition at SVP to provide information about the dynamical processes o c c u r r i n g in t h e s e systems. The r e s o n a t o r (3) c o n s i s t s of two cavities of equal volume s e p a r a t e d by a baffle. Through t h i s t h e r e are two p a r a l l e l f l o w channels: an open tube -3 and a 0.287gcm silica aerogel superleak. At t h e end wall of each c a v i t y is a p i e z o e l e c t r i c t r a n s d u c e r . One is used as a s p e a k e r and the o t h e r as a microphone. The pressure f l u c t u a t i o n d e t e c t e d a t the microphone was m e a s u r e d using a lock-in a m p l i f i e r at the r e s o n a n t f r e q u e n c y , f, for which it was in q u a d r a t u r e to t h a t g e n e r a t e d by the speaker. From t h i s p r e s s u r e , we can c a l c u l a t e the r m s m a s s c u r r e n t t h r o u g h the aerogel in t e r m s of the pressure d i f f e r e n c e a c r o s s it, AP, and Q (the
ratio of pressure)
I - AAP { [ f z 1 2 2~fl fl Q
to
drive
rms
QB]I- i f[~12 - 1] }
w h e r e f l and QB r e p r e s e n t t h e open channel c o n t r i b u t i o n s to f and Q. A is t h e c r o s s - s e c t i o n a l a r e a and 1 t h e length of t h e open channel. We d e f i n e a dimensionless c o n d u c t i v i t y f o r the s u p e r l e a k w i t h dissipative and i n e r t i a l components CD and ¢I so t h a t
ApAP
I = 2nf l p where Ap superleak.
(O.D - io.i ) and
lp
refer
to
the
The e x p e r i m e n t was conducted in two ways. In t h e f i r s t , a power sweep, d a t a w a s t a k e n as the s p e a k e r drive was i n c r e a s e d and the t e m p e r a t u r e held constant. Secondly, the s p e a k e r drive w a s f i x e d and the t e m p e r a t u r e T swept slowly t h r o u g h t h e t r a n s i t i o n a t Tc.
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0912-Z
detected
664
0.4
-
03
--
-
I
I
r
I
I
I
I
"" ""
o 0 . 7 0 10 - a * 1.40
L
02
--
0.1
-
b
- 3.64
,. ~
5.82 7.04 8.06
• 0.0
--
• o
-0.1
9.20
I
I
I
I
I
I
I
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Go I FIGURE 1. P o w e r
s w e e p d a t a p l o t t e d i n t h e p l a n e of t h e c o m p l e x c o n d u c t i v i t y (Data have been scaled by the geometric ratio G=Apl/Alp)
P l o t s o f CD a g a i n s t o"I f o r t h e p o w e r s w e e p d a t a a r e s h o w n in F i g u r e 1.
10 4
Attempts to explain decay of persistent currents in p o r o u s media (4) h a v e c e n t r e d on t h e d e c e l e r a t i o n of the superflow, (. We a r e a b l e t o define an equivalent parameter for the ac case from the rms power dissipated by the superleak "-t
_
AP
103
_
102
_
i01
_
10 0
-
10 -1
_
I
I
[
I
10 °
101
e
o"D
plp is p l o t t e d a s a f u n c t i o n o f psp/V in F i g u r e 2. T h e d a t a a p p e a r t o lie on a common curve which strongly suggests t h a t Psp/V is t h e i m p o r t a n t variable in t h e d i s s i p a t i o n , a s w a s f o u n d in the persistent current experiments
10 - 2 _ o a
10 - 3 10 -1
__
%" 10 2
Psp / V (arbs)
(4).
FIGURE 2.
REFERENCES
1.
.
N. Mulders, R. Mehrota, Goldner, G. A h l e r s , Phys. L e t t . 67, 695 (1991). G.K.S. Wong, P.A. C r o w e l l , Cho, J.D. R e p p y , P h y s . Rev. 65, 2140 (1990).
3.
A. Tyler, H.A. Cho and J.D. R e p p y , J. L o w T e m p . P h y s . 89, 57
.
J.S. L a n g e r , J.D. R e p p y , P r o g r e s s in L o w T e m p e r a t u r e P h y s i c s , V 6. R.J. D o n n e l l y , Q u a n t i z e d V o r t i c e s in Helium II, (Cambridge U n i v e r s i t y P r e s s , 1991).
L.S. Rev. H.A. Lett.
(1992).
Physica B 194-196 (1994) 663-664 North-HoUand
M e a s u r e m e n t s of d i s s i p a t i o n of AC p r e s s u r e - d r i v e n s u p e r f l o w of 4He in Aerogel D.B. Hannon and A. T y l e r The S c h u s t e r L a b o r a t o r y , University of Manchester, Manchester M13 9PL, U.K.
Using a t w o - c h a n n e l Helmholtz r e s o n a t o r we have m e a s u r e d t h e complex conductance a s s o c i a t e d w i t h ac p r e s s u r e - d r i v e n s u p e r f l o w of liquid 4He t h r o u g h aergoel g l a s s close to the t r a n s i t i o n t e m p e r a t u r e . From t h i s we have c a l c u l a t e d a d i s s i p a t i o n f u n c t i o n which a p p e a r s to f o l l o w a power law in t h e a r g u m e n t of the s u p e r f l u i d d e n s i t y divided by the f l o w velocity.
The s u p e r f l u i d t r a n s i t i o n in aerogels is s h a r p y e t w i t h c r i t i c a l exponents t h a t d i f f e r s i g n i f i c a n t l y f r o m those of bulk helium (1,2). In t h i s work we have used a helmholtz resonator technique (3) to s t u d y the dissipation of pressure driven a.c. superflow through aerogel close to its transition at SVP to provide information about the dynamical processes o c c u r r i n g in t h e s e systems. The r e s o n a t o r (3) c o n s i s t s of two cavities of equal volume s e p a r a t e d by a baffle. Through t h i s t h e r e are two p a r a l l e l f l o w channels: an open tube -3 and a 0.287gcm silica aerogel superleak. At t h e end wall of each c a v i t y is a p i e z o e l e c t r i c t r a n s d u c e r . One is used as a s p e a k e r and the o t h e r as a microphone. The pressure f l u c t u a t i o n d e t e c t e d a t the microphone was m e a s u r e d using a lock-in a m p l i f i e r at the r e s o n a n t f r e q u e n c y , f, for which it was in q u a d r a t u r e to t h a t g e n e r a t e d by the speaker. From t h i s p r e s s u r e , we can c a l c u l a t e the r m s m a s s c u r r e n t t h r o u g h the aerogel in t e r m s of the pressure d i f f e r e n c e a c r o s s it, AP, and Q (the
ratio of pressure)
I - AAP { [ f z 1 2 2~fl fl Q
to
drive
rms
QB]I- i f[~12 - 1] }
w h e r e f l and QB r e p r e s e n t t h e open channel c o n t r i b u t i o n s to f and Q. A is t h e c r o s s - s e c t i o n a l a r e a and 1 t h e length of t h e open channel. We d e f i n e a dimensionless c o n d u c t i v i t y f o r the s u p e r l e a k w i t h dissipative and i n e r t i a l components CD and ¢I so t h a t
ApAP
I = 2nf l p where Ap superleak.
(O.D - io.i ) and
lp
refer
to
the
The e x p e r i m e n t was conducted in two ways. In t h e f i r s t , a power sweep, d a t a w a s t a k e n as the s p e a k e r drive was i n c r e a s e d and the t e m p e r a t u r e held constant. Secondly, the s p e a k e r drive w a s f i x e d and the t e m p e r a t u r e T swept slowly t h r o u g h t h e t r a n s i t i o n a t Tc.
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0912-Z
detected
664
0.4
-
03
--
-
I
I
r
I
I
I
I
"" ""
o 0 . 7 0 10 - a * 1.40
L
02
--
0.1
-
b
- 3.64
,. ~
5.82 7.04 8.06
• 0.0
--
• o
-0.1
9.20
I
I
I
I
I
I
I
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Go I FIGURE 1. P o w e r
s w e e p d a t a p l o t t e d i n t h e p l a n e of t h e c o m p l e x c o n d u c t i v i t y (Data have been scaled by the geometric ratio G=Apl/Alp)
P l o t s o f CD a g a i n s t o"I f o r t h e p o w e r s w e e p d a t a a r e s h o w n in F i g u r e 1.
10 4
Attempts to explain decay of persistent currents in p o r o u s media (4) h a v e c e n t r e d on t h e d e c e l e r a t i o n of the superflow, (. We a r e a b l e t o define an equivalent parameter for the ac case from the rms power dissipated by the superleak "-t
_
AP
103
_
102
_
i01
_
10 0
-
10 -1
_
I
I
[
I
10 °
101
e
o"D
plp is p l o t t e d a s a f u n c t i o n o f psp/V in F i g u r e 2. T h e d a t a a p p e a r t o lie on a common curve which strongly suggests t h a t Psp/V is t h e i m p o r t a n t variable in t h e d i s s i p a t i o n , a s w a s f o u n d in the persistent current experiments
10 - 2 _ o a
10 - 3 10 -1
__
%" 10 2
Psp / V (arbs)
(4).
FIGURE 2.
REFERENCES
1.
.
N. Mulders, R. Mehrota, Goldner, G. A h l e r s , Phys. L e t t . 67, 695 (1991). G.K.S. Wong, P.A. C r o w e l l , Cho, J.D. R e p p y , P h y s . Rev. 65, 2140 (1990).
3.
A. Tyler, H.A. Cho and J.D. R e p p y , J. L o w T e m p . P h y s . 89, 57
.
J.S. L a n g e r , J.D. R e p p y , P r o g r e s s in L o w T e m p e r a t u r e P h y s i c s , V 6. R.J. D o n n e l l y , Q u a n t i z e d V o r t i c e s in Helium II, (Cambridge U n i v e r s i t y P r e s s , 1991).
L.S. Rev. H.A. Lett.
(1992).