THERMAL TRANSPORT IN 3He- 4He MIXTURES IN THE REGION OF THE TRICRITICAL POINT

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THERMAL TRANSPORT IN 3He- 4He MIXTURES IN THE REGION OF THE TRICRITICAL POINT

M. Ryschkewitsch, G. Ruppeiner, H. Meyer

To cite this version:

M. Ryschkewitsch, G. Ruppeiner, H. Meyer. THERMAL TRANSPORT IN 3He- 4He MIXTURES

IN THE REGION OF THE TRICRITICAL POINT. Journal de Physique Colloques, 1978, 39 (C6),

pp.C6-186-C6-187. �10.1051/jphyscol:1978682�. �jpa-00218362�

JOURNAL DE PHYSIQUE

Colloque C6, supplkment au no 8, Tome 39, aolit 1978, page C6- 186

THERMAL TRANSPORT IN 3 ~ e - 4 ~ e EIXTURES IN THE REGION OF THE TRICRITICAL POINT

M. Ryschkewitsch, G. Ruppeiner and H. Meyer

Department of P h y s i c s , Duke U n i v e r s i t y , Durham, N . C . 27706, U.K.

RLsum6.- Des mesures du quotient de thermodiffusion

KT

et de la conductibilit6 thermique eeff en l'absence d'un flux de masse sont dlcrites. Tandis que

^{~ ~}

n'a qu'une ddpendance

^{f f}

falble en T,

KT

diverge fortement lorsqu'on approche le point tricrltique, ceci en accord avec les prddictions thgoriques.

Abstract.-Measurements of the thermal diffusivity ratio

K~

and of the thermal conductivity ceff in the absence of mass flow are reported. While

K~~~

shows only a weak temperature dependence,

KT

diverges strongly as the tricritical point is approached, in agreement with theoretical predictions.

we report preliminary results the

effec-

5 and confinned/6/its strong divergence along tive thermal conductivity

keff

in the absence of an isochore pdt.The heat conductivity Keff is mass flow and of the thermodiffusion ratio

^KT

for related to the thermal conductivity

K

in the

He - ^{4 ~ e} in the normal phase and in the region absence of a concentration gradient by the

of the tricriticA1 point. relation

These coefficients are defined by

~ ~ = f

-J/grad T

f

(1)

Keff = K-PK' ah D/T

T (2x1

^{( 6 )}

and

K~ = -T grad c/grad T (2)

where

p

is the density and D the mass diffusion.

Kawasaki and Gunton 1 have shown that the diver- where c is the mass concentration and

J

is the heat

ging parts of

K

and of the second term cancel, flow. In a He - He mixture, the relation

which causes

~ ~

to remain finite, This predic-

f f

between

c ( ~

He) and the molefraction X

(3

He) is

tion is in accord with experiments for dilute given by

mixtures 14, 7 . 1 c

=

XM3 [XM3

+

( 1 - x ) ~ ~ 1 - I

^{( 3 )}

where M3 and M4 are the molar masses of the two We have undertaken a systematic study of components and

~ ~

and

f fKT

for a number of mixtures in the

-% ^{M4 c2 grad X} neighbourhood of the tricritical point to study

- = -

- - (4) their singular behaviour along the tricritical

M3 X2

grad T

isochore and along the phase separation curve.

Along the lamdba line TX(X), KT i~ predicted

/ 1 , 3 /

M~~~~~~~~~~~

of

grad and

grad at

equilibrium to have the same singular behaviour as

C

and the for various heat flows

were

as

a

PA concentration susceptibility (a~/aA)~, where

function of X and T in the arrangement briefly A=u3-p4 is the difference chemical potentials. described below.

This singular behaviour is almost logarithmic for small X and has recently been studied experimental-

The temperature gradient is produced between ly /4,5/. However asr the tricritical point (T

=

t two horizontal copper plates of 1.9 cm diameter 0.867

K,

Xt=0.675) is approached, one expects a

separated by

2.8 mm

via a stainless steel spacer.

cross)over to a strong divergence. To each of these plates is attached a semi-transparent

-

¹

K,a(T-T

,) (5)

horizontal capacitor made of perforated stainless

1 L

steel sheets to measure the dielectric constant of along a path X=Xt (T

>

T

)

and along the phase

t the fluid. The distance between these capacitors separation curve (T

< T _).

An analysis of transient

t

is 2.2 m. Using the Clausius-Mossotti relation

effects during sound velocity measurements ~ielded

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978682

and t h e known changes of molar volume a s a f u n c t i o n of X, t h e c o n c e n t r a t i o n changes between t h e t o p and b o t t o m c a p a c i t o r a r e o b t a i n e d . Hence, assuming a l i n e a r temperature and c o n c e n t r a t i o n change w i t h h e i g h t , we c a l c u l a t e kT f o r s e v e r a l v a l u e s of J . A s t h e h e a t was s u p p l i e d from t h e bottom w h i l e t h e temperature of t h e t o p was k e p t c o n s t a n t , we observed X t o i n c r e a s e a t t h e top.

Therefore t h e c o e f f i c i e n t kT d e f i n e d by e q u a t i o n (4) i s p o s i t i v e . As Tt was approached, t h e time n e c e s s a r y t o r e a c h s t e a d y - s t a t e c o n d i t i o n s became v e r y long because t h e mass d i f f u s i o n D i s predic- t e d t o z e r o h - 3 / which h a s been conf inned by a c o u s t i c experiments /8/ We f i n d t h a t f o r X-Xt, t h e times t o r e a c h temperature and c o n c e n t r a t i o n e q u i l i b r i u m a r e approximately t h e same. Our d a t a a n a l y s i s h a s used t h e e x t r a p o l a t i o n t o t h e l i m i t J = 0 f o r a l l t h e

I$,

d a t a . Because of t h e geometry of t h e c e l l which i s complicated by t h e c a p a c i t o r s , we p l a c e a n u n c e r t a i n t y of about

*lo%

on t h e a b s o l u t e v a l u e s of K~~~ and

I$,,

w h i l e t h e i r changes c a n be measured t o a much h i g h e r accuracy.

We p l a n t o c a l i b r a t e t h e p r e s e n t c e l l by measuring

K o f pure 3 ~ e which h a s been i n v e s t i g a t e d b e f o r e / 9 /

I n F i g u r e 1, we p r e s e n t t h e d a t a f o r s e v e r a l m i x t u r e s w i t h m o l e f r a c t i o n s n e a r Xt

The r e s u l t s show c l e a r l y a s t r o n g dependence o f KT _on X and on temperature. I n p a r t i c u l a r f o r t h e m i x t u r e b e l i e v e d c l o s e s t t o X t , t h e d i v e r g e n c e i s approximately a s p r e d i c t e d by Equation / 5 / alt.hough a f i n a l f i t has not y e t been made. The d i f f i c u l t i e s mentioned above p r e v e n t e d , so f a r , o b t a i n i n g s u f f i c i e n t l y good

-

3

d a t a f o r T - T ~ / T ~ < 2 x 10 ' Considering t h e u n c e r t a i n t i e s i n t h e a b s o l u t e v a l u e of KT, t h e agreement w i t h t h e r e s u l t s o b t a i n e d by t h e t r a n s i e n t method/fj/is v e r y good. By c o n t r a s t w i t h t h e

5

r e s u l t s , k e f f i s almost independent of X and shows only a small temperature dependence, without any anomaly n e a t Tt, a s expected.

A complete a n a l y s i s and f u r t h e r measurements on o t h e r m i x t u r e s a r e planned i n t h e n e a r f u t u r e .

T h i s r e s e a r c h h a s been supported by a g r a n t from t h e U.S. A i r Force O f f i c e of S c i e n t i f i c Researchand t h e N a t i o n a l Science Foundation.

References

/ I / Kawasaki, K., and Gunton, J.D., Phys. Rev.

L e t t .

9

(1972) 1661.

/ 2 / Grover, H.K., and S w i f t , J.J.,

LOW Temp. Phys.

11

(1973) 751.

/ 3 / S i g g i a , E.D., and Nelson, D.R., Phys. Rev.

B15

(L977) 1427.

/ 4 / Tanaka, M., and Ikushima, A , , Phys. L e t t .

64A

(1978) 402.

/ 5 / Lucas, P . , and Taylor A.J., Lot. Temp. Phys.

1

(1977) 281.

/ 6 / Roe, D . , and Meyer H . J . , Low Temp. Phys.

8

(1977) 349.

r i % R e 8

/ 7 / A h l e r s , G ? , Phys. Rev. L e t t .

26

(1970) 133

0 6 7 h / 8 / Roe, D., Ruppeiner, G., and Meyer, H.J.,

c 067'1

*

0675 Low Temp. Phys.

-

27 (1977) 747.

40' 087 0 8 8 ok9 0 & 0 ok1 o k 2 / 9 / Lee, D.M., and Fairbank, H.A.,

T ( K ) Phys. Rev.

116

(1959) 1349

F i g . 1 : The thermal d i f f u s i o n r a t i o

%

and t h e e f f e c t i v e thermal c o n d u c t i v i t y K~~ f o r t h r e e m i x t u r e s n e a r t h e t r i c r i t i c a l polng. The d a t a

l a b e l l e d RM a r e t h o s e i n F i g . 4 (marked x ) of Ref. / 6 / .