SHIFT OF THE ANGULAR SPEED OF COLLECTIVIZATION OF VORTEX OSCILLATIONS IN ROTATING HELIUM II UNDER HIGH PRESSURE

(1)

HAL Id: jpa-00218361

https://hal.archives-ouvertes.fr/jpa-00218361

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.

SHIFT OF THE ANGULAR SPEED OF

COLLECTIVIZATION OF VORTEX OSCILLATIONS IN ROTATING HELIUM II UNDER HIGH

PRESSURE

Z. Nadirashvili, J. Tsakadze

To cite this version:

Z. Nadirashvili, J. Tsakadze. SHIFT OF THE ANGULAR SPEED OF COLLECTIVIZATION OF

VORTEX OSCILLATIONS IN ROTATING HELIUM II UNDER HIGH PRESSURE. Journal de

Physique Colloques, 1978, 39 (C6), pp.C6-182-C6-183. �10.1051/jphyscol:1978681�. �jpa-00218361�

(2)

JOURNAL DE PHYSIQUE

Colloque C6, suppl@ment au no 8, Tome 39, aotit 1978, page C6-182

SHIFT OF THE ANGULAR SPEED OF COLLECTIVIZATION OF VORTEX OSCILLATIONS IN ROTATING HELIUM I 1 UNDER HIGH PRESSURE

Z.Sh. Nadirashvili and J.S. Tsakadze

I n s t i t u t e o f P h y s i c s , Academy o f S c i e n c e s o f t h e Georgian SSR, B i Z i s i , U.S.S.R.

Rdsumd- Dans 1'He I1 en rotation sous pression, nous avons mis en dvidence un dCcalage de la vitesse correspondant B l'amortissement maximum.

Abstract.- In rotating He I1 under pressure, a shift in the angular speed of collectivization of vor- tex oscillations is reported.

With the purpose of investigating the elastic- 4

plasticproperties of helium I1 under high pressures we have used the method of oscillating disk, repea-

tedly used earlier for the investigation of rota-

I

1

ting helium (see for example /

1

/) . The disk making twisting oscillations around its axis participated also in a regular rotation of the apparatus. The speed dependence of the damping logarithmic decre- ment of the "heavy" disk oscillation was measured

(the frequency of which is independent of the amount of liquid interacting with it). Schematic drawing of the appzratus is presented in figure

1.

Disk

1

and rotating glass 2 were placed into hermetic ca- sing 3 made of stainless steel, which was designed for high pressure. Casing 3 has plexiglas cover 4, 30

mm

thick with polished faces. Condensation of helium into a working volume proceeded through the high pressure line. Gaseous helium flowing from voluue 5 of high pressure was purified in carbon

adsorber 6, cooled down to nitrogen temperature u

and passed into the apparatus. The pressure was measured wiht high precision gauge 7. The high pres-

Fig.

1 :

Arrangement of the unit. I-oscillating sure line was provided with valve 8, connecting the disk, 2-rotating glass of stainless steel, 3-herme- system with a return line by valJe 9, connecting tic casing, 4-transparent plexiglas cover, 5-volu- me for helium storage under high pressure, 6-angu- the high pressure line with initial vacuum pump and lar adsorber, 7-high precision pressure gauge, 8-9 -10-communication fittings of the high-pressure li- valve 10, cutting off the apparatus from the rest ne .

of the high pressure line. Measurements of the lo- garithmic decrement of oscillation damping were carried out using chronometric method/2/.

In the course of the experiment constant tem- perature (with accuracy of K) and pressure (with accuracy of 0.16 atm) were maintened.

A curve of oscillation damping logarithmic decrement-versus-rotation speed was obtained at pressure P

=

27.7 atm, T

=

1.76 K (see figure 2, curve 1). For comparison, a curve obtained at sa-

turated vapour pressure (curve 2) is given in the same figure. From the comparison of these curves it becomes clear

:

first, that curve I maximum is shif- ted towards high speeds and secondly, that curve I is below curve 12.

As it is known131 the position of the maxi- mum on the curve

6 =;

f(2wo/i2) is determined by the angular speed of collectivization of vortex oscil- lations

:

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978681

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Fig. 2

:

Speed dependence of logarithmic decrement of disk oscillation damping in rotating helium I1 at

T =

1.76 K. &-logarithmic decrement of disk os- cillation damping in rotating state, 6 ~ - the same in non-rotating helium 11, &-the same in vacuum, wo-rotation angluar speed, R

=

2r, 9-oscillation

-K

period. Curve 1 P

=

27.7 atm, Curve 2 - ^saturated

vapor pressure.

where b

=

'x, wo-rotation angular speed, R-cyclic

ml,, --.

frequency of disk oscillation, m--mass of helium atom, a -vortex stem radius.

On the other hand, according to Mamaladzel41

And assuming that relation betweed

p

and

a

is maintained at high pressures, than the following expression can be obtained for

a

5

4 x I O - ' ~ sm (2)

s

Using the table data (at P

=

27.7 atm and T

=

1.76 K) 16-7-81 by formula (2) it is possible to obtain values

a %

1.5 x

10-

7cm, which gives 2wO/R

1

0.25 for the maximum on curve of 6

=

f (2wo 10).

Taking into account the roughness of the esti- mate formulae

(1)

and (2) it can be assumed that experimental data obtained by us are in good agre- ement with the theoretical conclusions.

General lowering of the curve 6= f (2wo/R) un- der pressure can also be explained. As it is known 131, additional damping of the disk in rotating helium I1 is due to its interaction with the vor- tices, the tension of which is proportional to

p

.

In the conditions of the above experiment ps de- creases by a factor of 2, which should cause a cor-

responding weakening of this interaction and hence, the decrease of 6. The experiment agrees with this estimate.

The authors express their sincere gratitude to E.L. Andronikashvili for the stimulating inte- rest to this work and to Y.G. Mamaladze for valua- ble discussions.

References

/l/Andronikashvili,E.L., Tsakadze,J.S., J. Eksp.

Teor. Fiz. 37 ^{(1959) 8}

121 Andronikashvili,E.L., Mamaladze,Yu.G., Tsaka- dze,G.S., Papers of the Institute of Physics AN GSSR, 1 (1960) 59

131 Andronikashvili,E.L., Mamaladze,Yu.G., Rev.

Mod. Phys. 2 (1966) 567

141 Mamaladze,Yu.G.,

J.

SHIFT OF THE ANGULAR SPEED OF COLLECTIVIZATION OF VORTEX OSCILLATIONS IN ROTATING HELIUM II UNDER HIGH PRESSURE

HAL Id: jpa-00218361

https://hal.archives-ouvertes.fr/jpa-00218361

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.

SHIFT OF THE ANGULAR SPEED OF

COLLECTIVIZATION OF VORTEX OSCILLATIONS IN ROTATING HELIUM II UNDER HIGH

PRESSURE

Z. Nadirashvili, J. Tsakadze

To cite this version:

Z. Nadirashvili, J. Tsakadze. SHIFT OF THE ANGULAR SPEED OF COLLECTIVIZATION OF

VORTEX OSCILLATIONS IN ROTATING HELIUM II UNDER HIGH PRESSURE. Journal de

Physique Colloques, 1978, 39 (C6), pp.C6-182-C6-183. �10.1051/jphyscol:1978681�. �jpa-00218361�

Colloque C6, suppl@ment au no 8, Tome 39, aotit 1978, page C6-182

SHIFT OF THE ANGULAR SPEED OF COLLECTIVIZATION OF VORTEX OSCILLATIONS IN ROTATING HELIUM I 1 UNDER HIGH PRESSURE

Z.Sh. Nadirashvili and J.S. Tsakadze

I n s t i t u t e o f P h y s i c s , Academy o f S c i e n c e s o f t h e Georgian SSR, B i Z i s i , U.S.S.R.

Rdsumd- Dans 1'He I1 en rotation sous pression, nous avons mis en dvidence un dCcalage de la vitesse correspondant B l'amortissement maximum.

Abstract.- In rotating He I1 under pressure, a shift in the angular speed of collectivization of vor- tex oscillations is reported.

With the purpose of investigating the elastic- 4

plasticproperties of helium I1 under high pressures we have used the method of oscillating disk, repea-

tedly used earlier for the investigation of rota-

ting helium (see for example /

/) . The disk making twisting oscillations around its axis participated also in a regular rotation of the apparatus. The speed dependence of the damping logarithmic decre- ment of the "heavy" disk oscillation was measured

(the frequency of which is independent of the amount of liquid interacting with it). Schematic drawing of the appzratus is presented in figure

Disk

and rotating glass 2 were placed into hermetic ca- sing 3 made of stainless steel, which was designed for high pressure. Casing 3 has plexiglas cover 4, 30

thick with polished faces. Condensation of helium into a working volume proceeded through the high pressure line. Gaseous helium flowing from voluue 5 of high pressure was purified in carbon

adsorber 6, cooled down to nitrogen temperature u

and passed into the apparatus. The pressure was measured wiht high precision gauge 7. The high pres-

Fig.

of the high pressure line. Measurements of the lo- garithmic decrement of oscillation damping were carried out using chronometric method/2/.

In the course of the experiment constant tem- perature (with accuracy of K) and pressure (with accuracy of 0.16 atm) were maintened.

A curve of oscillation damping logarithmic decrement-versus-rotation speed was obtained at pressure P

27.7 atm, T

1.76 K (see figure 2, curve 1). For comparison, a curve obtained at sa-

turated vapour pressure (curve 2) is given in the same figure. From the comparison of these curves it becomes clear

first, that curve I maximum is shif- ted towards high speeds and secondly, that curve I is below curve 12.

As it is known131 the position of the maxi- mum on the curve

f(2wo/i2) is determined by the angular speed of collectivization of vortex oscil- lations

Fig. 2

Speed dependence of logarithmic decrement of disk oscillation damping in rotating helium I1 at

1.76 K. &-logarithmic decrement of disk os- cillation damping in rotating state, 6 ~ - the same in non-rotating helium 11, &-the same in vacuum, wo-rotation angluar speed, R

2r, 9-oscillation

period. Curve 1 P

27.7 atm, Curve 2 - saturated

vapor pressure.

where b

'x, wo-rotation angular speed, R-cyclic

frequency of disk oscillation, m--mass of helium atom, a -vortex stem radius.

On the other hand, according to Mamaladzel41

And assuming that relation betweed

and

is maintained at high pressures, than the following expression can be obtained for

a

4 x I O - ' ~ sm (2)

s

Using the table data (at P

27.7 atm and T

1.76 K) 16-7-81 by formula (2) it is possible to obtain values

1.5 x

7cm, which gives 2wO/R

0.25 for the maximum on curve of 6

f (2wo 10).

Taking into account the roughness of the esti- mate formulae

and (2) it can be assumed that experimental data obtained by us are in good agre- ement with the theoretical conclusions.

General lowering of the curve 6= f (2wo/R) un- der pressure can also be explained. As it is known 131, additional damping of the disk in rotating helium I1 is due to its interaction with the vor- tices, the tension of which is proportional to

.

In the conditions of the above experiment ps de- creases by a factor of 2, which should cause a cor-

responding weakening of this interaction and hence, the decrease of 6. The experiment agrees with this estimate.

The authors express their sincere gratitude to E.L. Andronikashvili for the stimulating inte- rest to this work and to Y.G. Mamaladze for valua- ble discussions.

References

/l/Andronikashvili,E.L., Tsakadze,J.S., J. Eksp.

Teor. Fiz. 37 (1959) 8

121 Andronikashvili,E.L., Mamaladze,Yu.G., Tsaka- dze,G.S., Papers of the Institute of Physics AN GSSR, 1 (1960) 59

131 Andronikashvili,E.L., Mamaladze,Yu.G., Rev.

Mod. Phys. 2 (1966) 567

141 Mamaladze,Yu.G.,

Eksp. Teor. Fiz. 52 (1967)

27.7 atm, Curve 2 - ^saturated

Teor. Fiz. 37 ^{(1959) 8}

Eksp. Teor. Fiz. 52 ⁽¹⁹⁶⁷⁾