SEARCH FOR EXPONENTIALLY DAMPED SURFACE SOLUTIONS GENERATED BY HEAT FLOW AT AN INTERFACE WITH He II

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SEARCH FOR EXPONENTIALLY DAMPED

SURFACE SOLUTIONS GENERATED BY HEAT

FLOW AT AN INTERFACE WITH He II

M. Twerdochlib, W. Kirk

To cite this version:

JOURNAL D E PHYSIQUE

Colloque

C6,

supplement au n°

8,

Tome

39,

aoUt

1978,

page

C6-250

SEARCH FOR EXPONENTIALLY DAMPED SURFACE SOLUTIONS GENERATED BY HEAT FLOW

AT AN INTERFACE WITH He II

M. Twerdochlib and W.P. Kirk

Physios Deparment, Texas ASM University, College Station, Texas 77845, USA

Résumé.- Une expérience pour découvrir des solutions de surface, exponentiellement amorties, de l'équation de transport de Boltzmann, pour la transmission de chaleur dans une interface cuivre-li-quide He II est décrite. La conduite d'un thermomètre de résistance carbone film qu'on pouvait dé-placer en rapport avec l'interface a été mesurée par deux techniques différentes. On n'a trouvé au-cune évidence pour les solutions de surface dans toutes les mesures en descendant jusqu'à 100 mK. Abstract.— An experiment to detect exponentially damped surface solutions of the Boltzmann transport equation, for heat transfer at a copper-liquid He II interface, is described. The behaviour of a carbon film resistance thermometer which could be displaced with respect to the interface was measu-red by two different techniques. No evidence for the surface solutions was found in any of the mea-surements down to 100 mK.

It has been noted /l,2/ that heat flow across an interface gives rise to a set of surface solu-tions to the Boltzmann transport equation which damp out exponentially with characteristic decay lengths, 6. and further depend strongly on the tem-perature as <5. 1/ T 9. It was suggested that

experi-mentally the decay lengths could be studied near an interface where there is heat flow by measuring the spatial dependence of s suitable thermometer loca-ted in a medium such as He II at about 0.1 K or in rarefied gases /3/. A carbon resistance thermome-ter, for example, would be a type of detector in which its thermometric property, the resistance of a resistor in the proximity of an interface at some distance z would experience the effect of the surfa-ce solutions via the phonon density. In particular the resistance, R(z), would be expressed as

R(z) = R + I A.e

0 i-1 X

-z/6.

(O

o

The quantities A. depend on details of the surface solutions and the boundary conditions at the inter-face, and are proportional to the heat current. The S.'s depend on properties of the medium alone and could, in principle, provide information about pho-non-phonon scattering and phonon dispersion in He II. The longer length 5.'s were shown to be separa-ted from the shorter ones. (At 0.1 K, & = 3.41 x 103 cm and &2 = 3.44 X 102 cm in He II.)

We report the first attempt to search for these predicted exponentially damped surface solu-tions in He II generated by heat'flow at an inter-face Ikl. A resistor, in the form of a carbon film could be moved in a container of He II that had heat flowing from a nearly planar interface. Measu-rements were made at several temperatures down to

100 mK and for several heat flows up to 0.25 mW. A cross sectional view of the apparatus is shown in figure 1. A cylindrical pancake shaped cell was desirable to approximate a planar geome-try of the copper - He II interface, and to mini-mize wall effects. Heat flow from plate H to C was accomplished by attaching the upper plate C to the mixing chamber of a dilution refrigerator. The lo-wer plate H was heated by a bismuth heater which was evaporated on to a thin (~0.1 mm) single quartz

crystal. The small carbon film resistor shown as R in figure 1 could be displaced with respect to the hot surface H. It was made on a small quartz fiber

(~0.127 <mn dia.) using a carbon suspension (Dag 154). To avoid a moveable superfluid tight joint, magnetic levitation was used to translate the

re-sistor. The resistor could'be brought within 0.3mm of the interface.

Two methods were used to measure the resis-tance of the moveable resistor. In the first method the copper end plates of the cell were held at a fixed temperature difference, AT, and the resistan-ce of the moveable resistor was measured with a conventional 4-terminal AC resistance bridge. For AT as large as 180 mK, the resistance (or "tempe t This work has been supported in part by the

Na-tional Science Foundation under Grant No DMR-76-09807

rature") of the moveable resistor always remained constant with displacement to within 452 (or -l&).

The 452 resolution was limited primarily by tempe- rature drifts of the whole sample cell.

cients

.

CMN Thermometer

Supenonducting

Fig. 1 : Cross-sectional view of sample cell. H and C are copper plates ; sides are stainless steel with 0 . 2 5 m wall by 7 6 . 2 mm

ID.

In order to reduce temperature drift effects, a second detection method was used which enabled a higher resolution measurement. This method consi- sted of phase locking the response of the resistor to the variation of the bismuth heater power. In this case, the bismuth heater current was modula- ted at frequencies between 3 and 10 Hz. The modu- lation caused the temperature to vary by AT. The results, using the improved second method, are shown in figure 2, and again within the resolution there is no dependence on distance from the inter- face.

In conclusion, no evidence was found for ex- ponentially damped surface solutions which would produce spatially dependent temperature variations greater than 1 mK at 100 mK or variations greater than 0 . 0 1 mK at 250 mK. These experiments do not disprove the existence of the surface solutions, but they do set upper limits on the values for the A. coefficients in eq. ( 1 ) . So far, no calculations have been made to provide values for the A. coeffi-

toward ~nterfme

-

I

Fig. 2 : Change in resistance, AR, of carbon film resistor vs displacement. (A) mixer temperature, T = 256 mK ; heater power, P = 0 . 0 9 uW, error bars

=

+

error bars = f 0 . 0 2 3 mK.

References

/ l / Saslow,W.M., Phys. Rev. B

11

/ 2 / Saslow,W.M., Phys. Rev. B

0

rarefied gases are relatively large. For rare- fied gas phenomena see : Springer,G.S., Advan- ces in Heat Transfer, Vol V11 (Academic Press, New York, 1970)

/ 4 / More details to appear in Phys. Rev. B(-May