DISSIPATION IN THE SUPERFLUID HELIUM FILM AT VARIOUS TEMPERATURES

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DISSIPATION IN THE SUPERFLUID HELIUM FILM

AT VARIOUS TEMPERATURES

G. Arajs, R. Harris-Lowe, R. Turkington

To cite this version:

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JOURNAL DE PHYSIQUE _Colloque_{C6, supplPment au no 8, Tome 39, aozit 1978, page C6-304}

DISSIPATION IN THE SUPERFLUID HELIUM

FILM

AT VARIOUS TEMPERATURES

G.A. Arajs, R.F. Harris-Lowe and R.R. Turkington

Royal M i l i t a r y CoZlege, Kingston, h t a r i o

R6sumL.- Nous avons mesurd le taux de dissipation d'dnergie dans l'dcoulement d'hdlium suprafluide

sous forme d~ film 1 diverses tempdratures afin de verifier une thdorie selon laquelle le taux de

dissipation Q pour les vitesses 16gSrement supdrieures 1 la valeur critique v est donne par

c'

6

= Les resultats de nos experiences concordent avec cette predict~on dans la g a m e de

tempdratures enfre 1,2 et 1,8 K .

Abstract.- We have measured the rate of energy dissipation in superfluid helium film flow at various temperatures to test a theory which predicts that for superfluid velocities vs which just exceed a

critical value vc, the rate of dissipation Q is given by Q = A(v

-

v,)~/~. This prediction is con-

sistent with our experimental results in the temperature range 1S2 to 1.8 K.

In a recent paper Harris-Lowe / 1 / developed

a theory for an extrinsic dissipative mechanism in superfluid helium film transport involving pinned vortex lines. This theory predicted that the dissi-

pation Q should start to build up at supercritical

velocities v > v in accordance with the equation

s - C

6

= A(v -vc)3/2 (1

The parameter A and the critical velocity v

cannot be determined from the theory because they are expected to vary with the film substrate condi-

tion. However, the 312 power is anexact asymptotic prediction of the theory, and Turkington and Harris- Lowe 121 have reported that this prediction is consistent with their experimental results at a temperature of 1.33 K. According to the theory equation

1 should describe the film dissipative buildup at

all temperatures in the extrinsic region, which is

expeceed.to extend up to within 1ess:than 100 mK of

the A-transition /3,4/. The present work describes some experiments designed to test the applicability

of the theory over the temperatuxe range 1.2 K to

1.8 K.

In their paper Turkington and Harris-Lowe have described a technique whereby they could deter mine the functional form of the dependence of dissipation upon superfluid velocity by the observation of level changes in a simple beaker which resulted

from the application of resistive heater-power to

the interior of the beaker. We have employed the same technique in the present experiments to esta- blish the dissipative functional dependence at va-

rious temperatures. Figure 1 presents a selection of

the data 151 taken at six different temperatures

plotted in a manner such that the ordinate and absci-

ssa are linearly proportional to In Q and ln(vs

-

vc)

respectively.

Fig. 1 : Log-Log plot of the dissipation rate ver-

sus v S v c at various temperatures. The solid lines were plotted with a slope of 312 employing values for vc and the intercept obtained by a least squares fit to the data. Superfluid velocities shown fall in the range v c L v s 5 1 . 0 7 ~ ~ .

According to equation 1, the data plotted in this

manner should fall on a straight line with a slope of 312. The solid lines in the figure have been drawn with the theoretically predicted slope, with values for the critical velocity and y intercept obtained from a weighted least squares fit to the data. As cai be seen these results are consistent

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with the theoretical prediction over the temperature range tested to date.

It is our intention to proceed with experimtnts of this type in an attempt to achieve an actual measurement of the exponent m when the data is fitted to an equation of the form

m

6

= A(v

s

-

vC) (2)

This type of measurement could come from a three parameter least squares fit. However, because of the particular nature of equation 2 it turns out thar better data is required over a more extended range in order to achieve well-defined values from this type of fit. Another approach might be to determi- ne the critical velocity from an independent measurement, and use this value in conjunction with a two parameter fit of the data to equation 2. At present the latter method appears to be the more attractive, although we are in the process of improving the cry- ostat in order to improve the quality of the data.

References

/I / Harris-Lowe, R.F., J. Low Temp. Phys.

8

( 1 977)

489

/2/ Turkington, R.R. and Harris-Lowe, R.F., J. Low

Temp. Phys.

8

(1977) 513

/3/ Ahlers,J., J. Low Temp. Phys. L(1969) 159

/4/ Clow,J.R. and Reppy,J.D., Phys. Rev. Lett.

19

(1967) 291