VELOCITY AND ABSORPTION OF SECOND SOUND IN SUPERFLUID SOLUTIONS OF 3He-4 He

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VELOCITY AND ABSORPTION OF SECOND SOUND IN SUPERFLUID SOLUTIONS OF 3He-4 He

L. Dikina, G. Kotenev, E. Rudavsky

To cite this version:

L. Dikina, G. Kotenev, E. Rudavsky. VELOCITY AND ABSORPTION OF SECOND SOUND IN

SUPERFLUID SOLUTIONS OF 3He-4 He. Journal de Physique Colloques, 1978, 39 (C6), pp.C6-

146-C6-147. �10.1051/jphyscol:1978665�. �jpa-00218112�

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JOURNAL DE PHYSIQUE Colloque ^C6,suppliment au no ^8,Tome ^39,aotit ^1978,page C6-146

3 4

VELOCITY AND ABSORPTION OF SECOND SOUND IN SUPERFLUID SOLUTIONS OF

He- He

L.S. Dikina, G.Ya. Kotenev and E.Ya. Rudavsky

Physico-TechnicaZ Institute of Low Temperatures, UkrSSR Acaokmy of Sciences, 47, Lenin Prospect, Kharkov, 310164, USSR.

R6sum6.- On donne les rgsultats des mesures systgmatiques de la vitesse du second son dans des solutions, contenant jusqu'l 12,8 % de 3 ~ e et de l'indice d'absorption pour des solutions, ayant une concentration de 10 % environ dans l'intervalle de tempgrature de 1,3 l 20 K. Les rgsultats expgrimentaux obtenus pour la vitesse sont utilisgs pour l'obtention des valeurs de la ddrivge par rapport B la concentration du potentiel thermodynamique. On analyse les valeurs mesurges de l'indice d'absorption dans le but de 1'Qclaircissement de l'influence des differents processus dissi- patifs.

Abstract.- The experimental results of the second sound velocity in 12.8 % 3~e-solutions and of the absorption coefficient in 10 % 3~e-solutions are reported for the temperature range of 1.3 to 2.OK The data on velocity are used to calculate the concentration derivative of the thermodynamic potential. The absorption coefficient values are analysed to find out the effect of various dissipative processes.

The second sound propagation has been studied in detail only in superfluid 'He /I ,2/. The addition of 3 ~ e influences considerably the second sound velocity 131. and its emission intensity /4/. Experi- ments on the second sound absorption in 3 ~ e

-

^{4 ~ e}

solutions were carried out at temperatures below 1K and concentrations lower than 0.3 % 151. The temperature and concentration ranges are difficult to be extended because of the fact that as the temperature and the 3 ~ e concentration rise, the absorption coefficient and the energy generating the second sound decrease appreciably. Moreover, the experimental technique should provide maintenance of the isoto

-

pic equilibrium in the liquid during measurements.

The paper presents the experimental results of the second sound velocity in 12.8 % 3 ~ e

-

^solu-

tions and of the absorption coefficient in 10.0 % 3~e-solutions for the temperature range of 1.3

-

2.0 K and frequencies of 1-3 MHz. The experimental error in the second sound velocity is 0.5 % and that in the absorption coefficient is 5-20 2 .

The temperature dependences of the decond sound velocity for dilute solutions and 'He ard shown in figure 1. The experimental data obtained meet the lack of the literature ones and together with thd results from 131 permit the concentration

Fig. 1 : Temperature dependences of second sound ve- dependence of the second sound velocity, U

,

^{to be} locity in 3 ~ e

-

'He solutions : 1

-

'He (the curve

2

calculated exactly. In the temperature range given presents smoothed data from

111)

; 2

-

^0.5% 3 ~ e ; 3

-

^1.0^% ^{3 ~ e}^;⁴

-

^4.0% 3 ~ e ; 5

-

^7.0% 3 ~ e ; 6

-

above, the values of U have been found to be con- 12.8 % 3 ~ e ; 7

-

^10.0% 'He. (Molar concentrations

2

centration dependent and to reach the maximum at of 3 ~ e are given).

~ 7 % '~e.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978665

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Direct comparison between the experimental data on frequency independent. The second sound absorption the second sound velocity and the results calcula- in 3 ~ e

-

%e superfluid solutions is due to the ted by the hydrodynamic theory for 3 ~ e

-

^{'~e solu-} first viscosity q, thermal conductivity R, diffusion tions /6/ is quite difficult because the formula for coefficient D and second viscosity 5. Assuming the

u

involves an unknown-in general case-quantity a/aC (ZIP), where C

-

is a mass concentration of the solution, p is a total density, and the potential Z which is very important for description of the thermodynamic and kinetic quantities in solutions, is associated with the chemical potentials of 3 ~ e and +He in solution : Z = p(u3

-

^{p )}the experimental

4

values of U made it possible ot find the value of

2

a/aC (Z/p) using the expression for the second sound velocity.

The experimental data on the second sound absorption coefficient are shown in figure 2. We can see that as the 3 ~ e concentration grows, the second sound absorption, a

,

decreases'appreciably.

2

contributions from these dissipative processes to be additive, one can obtain :

a = a

(n)

⁺^{a2 (R)}⁺^a2(D>⁺^a2(C)

2 2 (1)

where the contributions have been calculated in ref.

/7/. The experimental values of a used to analyse the effect of various dissipative processes, indica- te that both in dilute solutions and in 4 ~ e the main contribution to the second sound absorption is made by the thermal conductivity of a quasi-particle gas.

For concentrated solutions (more than 4 % 3~e), the thermal conductivity contribution diminishes and be- comes comparable to that from the first viscosity and diffusion.

Fig. 2 : Temperature dependence of second sound ab- sarption coefficient divided by squared frequency.

1

-

'He (the curve presents smoothed data from 121) 2

-

^0.5^% ^{3 ~ e}^;³

-

^1.0^% ^{3 ~ e}^;⁴

-

^4.0^% ^{3 ~ e}^;

5

-

^7.0^% ^{3 ~ e}^;⁶

-

^10.0^% ^{3 ~ e .}

References

/I/ Peshkov, V.P., Zh. Eksp. Teor. Fiz.

2

⁽¹⁹⁶⁰⁾

799.

/ 2 / Hanson, W.B., Pellam, J . R . , Phys. Rev.

85

⁽¹⁹⁶⁴⁾

301.

/3/ Elliott, S.D., Fairbank, H.A., Low Temp. Phys.

Chem., Wisconsin, (1957).

/4/ Dikina, L.S., Rudavsky, E.Ya., Serbin, I.A., Zh.

Eskp. Theor. Fiz.

2

(1970) 843.

151 De Voogt, W.J., Kramers, H.C., Physica

8413

(1976) 328.

/ 6 / Khalatnikov, I.M., Zh. Eksp. Teor. Fiz.

23

(1952) 265.

/7/ Karchava, G.A., Sanikidze, D.G., Zh. Eksp. T'eor.

Fiz.

57

(1969) 1349.

Thus, for the 10 % solution a decreases almost by a factor of 100 as compared to that in 4 ~ e at T 1.5 K. The absorption measurements in the frequency range studied indicated that the value of a/w2 is sound