MANDELSHTAM-BRILLOUIN SCATTERING AND HYPERSOUND PROPAGATION IN VISCOUS LIQUIDS

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MANDELSHTAM-BRILLOUIN SCATTERING AND HYPERSOUND PROPAGATION IN VISCOUS

LIQUIDS

I. Fabelinskii, S. Krivokhizha

To cite this version:

I. Fabelinskii, S. Krivokhizha. MANDELSHTAM-BRILLOUIN SCATTERING AND HYPERSOUND

PROPAGATION IN VISCOUS LIQUIDS. Journal de Physique Colloques, 1972, 33 (C1), pp.C1-15-

C1-17. �10.1051/jphyscol:1972103�. �jpa-00214893�

JOURNAL DE PHYSIQUE

Colloque C1, suppl6ment au no 2-3, Tome 33, Fbvrier-Mars 1972, page C1-15

MANDEL SHTAM-BRILLOUIN SCATTERING

AND HYPERSOUND PROPAGATION IN VISCOUS LIQUIDS

I. L. FABELINSKII and S. V. KRIVOKHIZHA

P. N. Lebedev Physical Institute, U. S. S. R. Academy of Sciences, Moscow

Rksum6. - Dans quelques liquides visqueux la vitesse des hypersons a ete mesurke pour un grand intervalle de tem~krature var observation des sDectres de diffusion de Mandelshtam-Brillouin stimulk. Une d~iendence extraordinaire en temdkrature a kt6 observke dans la glykrine pour la vitesse des hypersons. On a montrk que tous les resultats expkrimentaux concernant la dependance ordinaire en temperature de la vitesse des hypersons dans les liquides visqueux peuvent Stre inter- prktks dans le cadre de la thkorie de Isakovich et Chaban

;

mais les bases physiques de cette thbrie demandent une Btude ultkrieure.

Abstract. -

Measurements were made of the hypersound velocity in some viscous liquids - in the wide interval of temperature by stimulated Mandelshtam-Brillouin scattering spectra. Unusual temperature dependence of hypersound velocity was observed in glycerol. It was shown that all experimental results with usual temperature dependence of velocity in viscous liquids can be described by Isakovich-Chaban theory formulas, but the physical grounds of the theory require new investigations.

The behavior of the acoustical characteristics in the are in the good agreement with experimental results region of 5-7 GHz until now can be studied in viscous received during the ultrasound velocity investigations.

liquids only by means of the light scattering [I]. The principal formulas of this theory are

:

An investigation of the ultrasound propagation into

the region 1-20 MHz in viscous liquids has shown that vm

the observed temperature dependence of ultrasound [ l + ! ~ 2 - ~ z

^{?4 y}

⁽¹⁾

velocity and absorption cannot be described with a 1m F(bdr)]

2 v;

relaxation theory that involves single or several

relaxation times. These investigations were realized 3 V: - V:

both in our laboratory and in others [3], 141. a = - Q V Re F(Qz)

;

4 v;.v: ⁽²⁾

The relaxation times spectrum is made choice of

in some works as a result of a desire t o remain at the 3

relaxation theory ground. This method is justified by F(6h)

=

Z ( l - ~ - l ) (x-tgx) ( l + t g x ) - ' ( ~ ) - ' ; convenience of comparing different experimental x = ( l - z ) & (3) results 141. However it is deprived of any physical

sense and its convenience seems doubtful to us.

On the basis of ultrasound measurements we have succeeded in formulating the principal expressions which described all the experimental results [3].

The new theory of the elastic waves propagation in viscous liquids based on these regularities was deve- loped by Isakovich and Chaban [5]. In the ground of this theory lies a hypothesis about a microinhomoge- neous structure of viscous liquids, in other words it has been supposed that it consists of ordered and disordered components with some thermodynamic parameters named 5, and t,, correspondingly. The equalization of 5, and

(,

is taking place when the elastic wave passed through such two component medium. A delay of such equalization relatively to the change of pressure leads to an absorption and dispertion of the sound velocity. Although the hypothesis about the microinhomogeneous structure of viscous liquids is unusual nevertheless the phenomenological formulas

5 v,2y 1

7

= - p -

-

, p

=

(5%)

3 v,2

^p

v,2 - v;

^{a,, sl, << 1}

where V-the sound velocity ; V, and V,-the sound velocities at zero and infinite frequency, relatively

;

a-the sound absorption coefficient

;

Q-the sound frequency

;

z-the diffusion equalization time

;

?-the viscosity ; p-the density

;

a-the sound absorption, measured far from its maximum.

The question of the description of hypersound experimental results by means of this theory arises because been has observed a good agreement bet- ween the experimental data and calculations in the ultrasound frequency range. Now known hypersound velocity data in viscous liquids obtained from the spontaneous light scattering can be described by Isakovich-Chaban theory [6].

In this work the hypersound velocity in viscous liquids has been obtained from the stimulated Man-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972103

C1-16 I. L. FABELINSKII AND S. V. KRIVOKHIZHA

delshtam-Brillouin scattering (SMBS). We used a Q-switched, 100 Mw ruby laser with light pulse dura- tion of 10-12 ns, with 0.03 cm-' wide were investi- gated the following viscous liquids

:

glycerol, triacetin, 1,2-propylene glycol. The temperature of all these liquids was altered in thz wide interval

;

the viscosity changed by ten orders of magnitude approximately.

We changed the ruby laser power to observe the SMBS at the threshold of its beginning.

As a result SMBS spectra in triacetin, 1,Zpropylene glycol and glycerol have been obtained and the hyper- sound velocity was calculated by the equation.

V = c A v A

2 n sin 012

The temperature dependence of hypersound velocity in triacetin and 1,Zpropylene glycol are given in figure 1. The points presented the results of the measu- rements of the ultrasound velocity in triacetin at frequency 3 MHz [3]. Dash dot line corresponds to calculations by Isakovich-Chaban theory formulas (I), (2), (3). As is seen from the figure all the curves have the same character of the temperature depen- dence of the velocity and both in the ultrasound and in hypersound cases, the experimental points are in the good agreement with the theoretical curve. For the theoretical calculations of hypersound velocity in the investigated liquids we used the values z-the diffusion equalization time,

-

calculated for the ultrasound range of frequency [3]. Therefor

7

has universal

FIG. 1. - Temperature dependence of the velocity of propaga- tion of elastic waves in triacetin and 1,2-propilene glycol.

: ultrasound velocity in triacetin, x : hypersound velocity in triacetin by SMBS spectra, : hypersound velocity in triacetin by thermal scattering spectra [6], A : hypersound velocity in 1,2-propylene glycol by SMBS spectra. Solid line-calculated by

Isakovich-Chaban formulas [5].

meaning. We obtained a good agreement between calculations and experimental data. The temperature dependence of

^T

for triacetin and 1,2-propylene glycol used in the calculations by Isakovich-Chaban for- mulas is represented in figure 2.

Figure

3

gives the data of ultrasound velocity at the frequency 22 MHz and the data of hypersound velocity in the glycerol.

FIG. 2.

-

Temperature dependence of diffusion equalization time : a : triacetin ; b : 1,2-propylene glycol.

FIG. 3. - Temperature dependence of ultrasound and hyper- sound in glycerol,

0

: ultrasound velocity at 22 MHz,

V

: hyper- sound velocity by thermal scattering spectra [6], : hypersound velocity by SMBS spectra, A : hypersound velocity by thermal scattering spectra [8], x : hypersound velocity by thermal

scattering spectra [9].

The data of the hypersound velocity represented by dash dot curve were received by Pesin and Fabelin- skii [6] by thermal scattering spectra. This example of glycerol kept for several years in a glass vacuum sell was utilized for hypersound measurements by SMBS spectra. Was obtained the temperature dependence of hypersound velocity in this sample glycerol in the form of a straight line (straight line with points) as a result of these measurements. The region of the rapid increasing in the velocity with the decreasing in the temperature

-

the

⁽⁽

step

⁾⁾ -

has not been observed. Data of the velocity approach to the magni- tude V,. This unexpected result made it necessary to measure ultrasound ve1ocit.y for this example of glycerol. The measurements were made and it was obtained the typical curve represented on the figure in the form of a solid line with circles.

Our numerous experiments by definition of hyper-

sound velocity by SMBS spectra for different examples

of glycerol gave the temperature dependence of hyper-

sound velocity in the form of a. straight line.

MANDELSHTAM-BRILLOUIN SCATTERING AND HYPERSOUND PROPAGATION C1-17 It was found out by the investigation of the hyper-

sound velocity in triacetin by SMBS spectra that in the triacetin cleared by means of distillation more than a year before it was observed the temperature depen- dence of the hypersound velocity in the form of a

<(

step

))

((Fig. 4). It was found that the

<<

step

⁾⁾

has been

smoothed essentially, when the triacetin example was distillated once more and immediately after the distil- lation the investigation of hypersound velocity by SMBS spectra was made.

v "-

-1

FIG. 4. -

Dependence of ultrasound and hypersound velocity in triacetin,

^:

ultrasound velocity,

:

hypersound velocity

^by

thermal scattering spectra,

x :

hypersound velocity by SMBS

spectra immediately after

^the

distillation.

The reason for such hypersound velocity dependence remains not clear enough. If together with Isakovich and Chaban one considers that the viscous liquid is essential microinhomogeneous medium, then shortly after distillation microinhomogeneous perhaps have no time to form themselves sufficiently. Such a fantas- tical ideas of explanation is need of a strong experi- mental examination.

Rank

et

al. [7], [8] have carried out experiments by the investigation of hypersound temperature depen- dence by thermal scattering spectra in glycerol. At first work it was observed the temperature dependence of hypersound velocity in the form of the straight line [7] ; in the second work

-

in the form of the strongly smoothed step with little difference from the straight line. In these experiments glycerol was cleared by means of distillation.

In all experiments where the hypersound velocity was investigated by SMBS spectra, the data of velo-

city are somewhat smaller than the data received by thermal scattering spectra (Fig. 5). As it is shown in [9]

this is connected with the appearance of stimulated temperature scattering (STS-11). The STS-I1 was caused by light absorption in the liquid. The SMBS components shift is smaller in that region of tempe- rature where the hypersound absorption is small and so the intensity of scattered light is great and the STS-I1 appears (I,, > 4 I,). The shift of the SMBS components coincides with the spontaneous scattering component shift in that region of temperature, where the hypersound absorption is large and so the intensity of the SMBS components is essentially smaller (IMB < 4 I,) therefore the STS-I1 did not begin. This leads to a coincidence of the hypersonic velocity measured by SMBS spectra and measured by thermal scattering spectra in that temperature interval where hypersound absorption increases.

FIG.

5. -

Temperature dependence of hypersound measured

^by

SMBS spectra

(X)

and measured

^by

thermal scattering spectra (0)

in

1,Zpropylene glycol - - - dependence of absorption coefficient of hypersound calculated

by

Isakovich-Chaban formulas

[S].

A systematic investigation of hypersound propaga- tion has been begun just recently and the strange behaviour of the velocity, when the viscosity changed in many orders, was found in this work for the first time. The whole field of the problems needs careful investigations.

References

F A B E L ~ N S K ~ ~

(I.),

Molecular Scattering of light,

1968,

Plenum Press

N. Y.

ZLATIN (I.), KRIVOKHIZHA (S.), FABELINSKII (I.),

Soviet Phys. JETP, 1969,56,1186.

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Soviet Phys. JETP, 1966, 50, 3.

((

Physical Acoustic

⁾⁾

Edited

by

Mason

W. 1965,

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A

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(M.),

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