THE 4He VISCOSITY NEAR THE SUPER FLUID TRANSITION UNDER PRESSURE

HAL Id: jpa-00218347

https://hal.archives-ouvertes.fr/jpa-00218347

Submitted on 1 Jan 1978

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE 4He VISCOSITY NEAR THE SUPER FLUID TRANSITION UNDER PRESSURE

L. Bruschi, M. Santini

To cite this version:

L. Bruschi, M. Santini. THE 4He VISCOSITY NEAR THE SUPER FLUID TRANSI- TION UNDER PRESSURE. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-151-C6-152.

�10.1051/jphyscol:1978667�. �jpa-00218347�

JOURNAL

DE

Colloque C6, suppigment au no 8, Tome 39, aolit 1978, page ^C6-151

THE

V I S C O S I T Y NEAR THE SUPER F L U I D TRANS I T I O N UNDER PRESSURE

L. Bruschi and M. Santini

Z s t i t u t o du F i s i c a , U n i v e r s i t d d i Padova, 35200 Padova - I t a l y U n i t 2 G.N.S.M. de.2 C.N.R. d i Padova

R6sum6.- Des mesures effectudes sur '~e liquide 1 5 pressions diffLrentes prls de la transition 1 montrentque la viscosit6 prdsente une singularitd transition. Une interprstation des r6sultats en utilisant le modlle de la singularit6 confluente donne les mzmes valeurs de l'exposant critique B des pressions diffsrentes de chaque c6td de la transition.

Abstract.- Measurements performed on liquid '~e at 5 different pressures near the 1-line show that the viscosity is singular at the transition. A description in terms of a confluent singularity gives an exponent with equal values at different pressures and on both sides of the transition.

Results of experiments on the viscosity in li- the interpolation formula of Greywall and Alhers quid 4 ~ e near T1 at saturated vapour pressure (SVP) /12/.

have been recently reported by us /1,2/. The visco- The data obtained for the viscosity at four sity resulted to be continuous at TX, and the data pressures, when fitted by the relation 3

A E ~ , were well fitted by the function

A EX, where give the A and x values shown in Table I. The SVP

n*

11 ^{- *( and}

^{I 1 -} ti. Although the values reported in Table I are those obtained in stren th A 1k differen below and above T,,, the run 25 of reference / I / .

critical exponent x has the same value, to within

the experimental errors, on both sides of the tran- TABLE I sition.

This was indeed a new result with respect to P (Atm) x A

the experiments reported by previous authors 131.

At this point is was interesting to extend the mea- surements along the 1 line, changing in a rather wide range both density and transition temperature.

As we could expect the singular behaviour to remain largely unchanged as the pressure is changed, our aim was to test such a kind of universality, in the broad spectrum of interest of dynamic critical phenomena /4,5,6/.

We performed these measurements with a vibra- ting wire viscometer along isobars at P

4.99, 10,

SVP 0.798

0.002 2.04

0.04 4.99 0.801 + 0.004 1.90 + 0.07 T>T1

20.00 0.762 + 0.005 1.72 t 0.06 25.00 0.745 + ^{0.005 1.67} + ^0.05

SVP 0.823 + ^{0.005 4.63 5 0.23}

4.99 0.808 + ^{0.005 4.53 t 0.21}

T<T1 10.00 0.804 + ^{0.006 4.47} + ^0.23

20.00 0.825 + ^{0.004 6.09}

^0.20

25.00 0.816 + 0.002 6.89 + 0.13 20 and 25 atm.

Details on the technique can be found in pre- vious papers /1,7/.

The reduced temperature

is now defined as E(P)

I ^{I- A/, where T} (P) is the transition

TX(P) X

temperature at the pressure P. The explored range

-

for

is lo-' < ^E < 10 . The temperature is mea- sured with an error AT

l ~ K and the pressure is - ~

-

kept constant within AP - ¹⁰ atm 181. The resul- ting error on E(P) is therefore AE

I O - ~ .

We see that the simple relation $ ^{= A E ~ is}

not good for the description of the full set of data, if we are looking for only one exponent, cha- racteristic of the X transition and independent on side and pressure.

Following Ahlers's idea of-a confluent sin- gularity /4/ suggested for p /p data, we tried the fitting function rf ⁼ A(P)Ex~+B(P)E~, and we found it is a good one indeed.

The total density p is calculated using in-

The best choice for y is 0.32. At T>T1 the terpolated values from experimental data /9,10,11/, mean of the four values of x is - x

0.799 * ^0.01,

and the normal density pn is then obtained through

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978667

and at T<T x

^0.815 + 0.01. The values of A(P) A

and B(P) are given in Table 11. For T<TA, x is quite independent on y indicating that B(P) is ne- gligible.

Table I1

P (Atm) A (P) B (PI

SVP 2.051

0.04 8.02 x lo-'

-

T>TA 4.99 1.925% 0.07 - 2 . 6 3 ~ 1 0 20.00 2.678 + ^{0.13 -1.404}

25.00 2.980 + ^{0.06 -1.364}

SVP 4.34k0.02 ----

4.99 4.77k0.24 ----

T<TA 10.00 4.85 + ^0.26 ----

20.00 6.85t0.12 ----

25.00 6.85k0.12 ----

-~ ~- -

In summary, the viscosity at the A transition exhibits a simple-singularity behaviour on the su- perfluid side, while on the normal side a better description is given by a confluent-singularity law.

The critical exponent x results independent on pres- sure and takes the same value on both sides of the transition.

References

111 Bruschi, L., Mazzi, G., Santini, M. and Torzo, G., J. LOW Temp. Phys. 2 (1977) 63.

/2/ Bruschi, L., Mazzi, G., Santini, M. and Torzo, G., J. Low Temp. Phys. 18 (1975) 487.

131 Biskeborn, R. and Guernsey, R.W., Phys. Rev.

Lett. 3 (1975) 455.

I41 Ahlers,

in the Physics of Liquid and Solid Helium, Edited by K.M. Bennemann and J.B.

Ketterson, Wiley - New York (I 976).

151 Hohenberg, P.C. and Halperin, B.I., Rev. Hod.

Phys. 9 (1977) 435.

I61 Ginzburg, V.L. and Sobaynin, A.A., Sov. Phys.

Uspeki 19 ^{(1 976) 773.}

I71 Bruschi, L. and,Santini, M., Rev. Sci. Inst. 46

(1975) 1560.

I81 Bruschi, L. and Santini, M., to be published.

/9/ Kerr, E.G. and Taylor, R.D., Ann. Phys. 2

(1964) 292.

1101 Kierstead, H.A., Phys. Rev. 162 (1967) 153.

1111 Elwell, D.L. and Eleyer, H., Phys. Rev. 164

(1 967) 245.

1121 Greywall, D.S. and Ahlers, G., Phys. Rev. A7

(1973) 2145.