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Submitted on 1 Jan 1978
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TIME DEPENDENCE OF THE ANOMALOUS
KAPITZA CONDUCTANCE OF COPPER
K. Rawlings, J.C.A. van der Sluijs
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C6,
supplement au n°
8,
Tome
39,
aout
1978,
page
C6-254
TIME DEPENDENCE OF THE ANOMALOUS KAPITZA CONDUCTANCE OF COPPER
K.C. Rawlings and J.C.A. Van der SluijsSchool of Physical and Molecular Sciences, UCNW, Bangor, LLS7 2 UW, Great Britain.
Résumé.- Nous avons trouvé dans la conductance de Kapitza anormale du cuivre /1,2/ des temps de mise en équilibre allant jusqu'à 1000 s, accompagnés parfois de fluctuations persistantes, indiquant une différence systématique entre la conductance de Kapitza mesurée en régime stationnaire et celle ob-tenue à partir de mesures de 21ème son.
Abstract.- We report on new transients in the anomalous Kapitza conductance of copper/1,2/ of up to 1000s, at times accompanied by persistent fluctuations, suggesting a systematic difference bet-ween a.c. and d.c. Kapitza conductance.
The anomalous Kapitza conductance was described by Cheeke et al.in 1974 /1/and the enhanced effect by the present authors in 1977 HI For experimental details of the present experiment the reader is re-ferred to elsewhere /3,7/. The experiment consists of measuring the temperature difference across the copper to "*He interface as a function of the time, by increasing the heat flux density Q in discrete steps, and to wait for establishment of the steady state, as shown by the recorder traces in figures 1 and 2. The following remarks may be made.
Fig.l : Time dependence of the temperature difference across a copper to ''He interface after a change in heat flux density : demonstration of fluctuations in power on state. Numerical date see text.
1) There exists a critical heat flux Q above which the anomalous Kaptiza conductance may be observed /1,2/.
2) For Q < Q the delay time till a steady state has been reached is not more than about 20 s, compatible with the known heat capacity and heat resistance of
the system.
3) For Q > Q the delay time is very large in the power on mode, of the order of 1000 s, one or two orders of magnitude above that observed for 0 < Q (figure 2,C)
1
x10-Fig.2 : Time dependence of the temperature differen-ce across the interfadifferen-ce after a change in heat flux density: demonstration of fluctuations after a re-duction in power. Numerical data see text.
4) The steady state reached in the power on mode is not always a true steady state, but may show large variations with a period of the order of a few hun-dred seconds (figure 1).
5) In reducing power the heat present in the sys-tem may flow off very slow slowly, fluctuations per-sisting untill quite a low temperature has been r reached (figure 2 ) . This behaviour is not general and the temperature may drop fairly fast, although more slowly than in the subcritical case. However even in this case ten decay curve is not exponen-tial, but shows an increasing negative slope with time, indicating that the heat resistance falls with decreasing temperature difference. The arrows-in the figures arrows-indicate a change arrows-in heater power.
Figure 1 : A down to 1 .57 = 2 mw/ cm2
.
= power up to 2.34 mw/cm2, B = power mw/cm2
,
C = power off,
T = 1.66 K, QC Figure 2 : A = power up to 1.6 mw/cm2, B = power down to 1.1. mw/cm2, C =power off, T = 1.95 k, QC = 1.5 mw/cm2.No direct precedents exist for the observed behaviour. It is unlikely that solid effects are responsible, solid dealy times being much shorter usually. Long delay times have been found before /8,9/ in heat transfer in supercritical 4He and it seems plausi- ble that an explanation associated with such effects will have to be sought. It has been shown that the
anomalous effect may be explained in terms of super- critical heat flow through "hot spots", small loca- lised areas on the interface /2/, which is consis- tent with an impurity based heat transfer model for the Kapitza conductance /S/. At present no quanti- tative model for transient heat flow in supercriti- cal 4 ~ e near an interface is available, but a qua- litative and somewhat speculative picture may be sketched as follows.
Let a steady heat flow near an interface cor- respond to a certain structure of vortex lines, con- centrated nearhot spots. Such a structure may be relatively stable when the heat flux density is low or when the energy-barrier between different structures is high. Transitions between different structures may occur in the following cases.
a) When the surface density of hot spots is low, the energy barrier may be low due to overlap. In such a case small variations in the Kaptiza conductance may beintroduced readily, and reproducibility will be
poor 161.
b)For low hot spot density transitions may be made for high heat flux density, which plausibly drives the transitions. The energy carried is large and the resistance againts change is large, leading to long delay times.
The observed effects have some relevance to the com- paribility of Kapitza conductance results obtained by different experimental methods.
When the literature is investigated on Kapitza con- ductance results for copper, the results for the d.c.methods are significantly lower than those obtained by a.c. methods, in this case second sound 171. The present results show that there exits a "vortex line barrier" with a relaxation time of the order of seconds or more. Second sound experi- ments, and also heta pulse experiments are carried
out at frequencies of lkHz and above so the vortex line barrier will not respond and no anomalous ef- fectwill be found. Therefore results on the a.c. and d.c. Kapitza conductance are not directly com- parable.
The above interpretation is somewhat specula- tive and a direct proof is needed. This would be ob- tainable from an experiment on the anomalous Kapit- za conductance in 3 ~ e .
It should be stressed that the above effects can be observed only when due care has been taken in preparing the samples /3,4/.
Further proof of this will be published elsewhere shortly 171. The effects depend on a suf- ficiently small surface density of impurities. For larger densities the transients vanish and the sta- tic effect changes into that observed by Cheeke et al. /l/
The authors acknowledge with thanks support from the Science Research Council and from Oxford Instruments Ltd.
References
/I/ Cheeke,J.D.N., Hebral,B.,Richard,J., and Turkington,R.P., Phys. Rev. Lett.
32
(1974)658 /2/ Rawlings,K.C.andPan der Sluijs,.T.C.A. Solid. State Commun.2
(1977)509/3/ Van der Sluijs,J.C.A. and Alnaimi,A.E., Cryo- genics
5
(1976) 161/ 4 / Alnaimi,A.E. and Van Der Sluijs,J.C.A.,Cryoge- nics
13,
(1973) 722/5/Van der Sluijs,J.C.A., Jones,E.A. and Alnaimi, A.E
.
,
Cryogenics3
( 1974) 95/6/ Jones E.A. and Van der Sluij s ,J.C .A. ,cryogenics 13 (1973) 535
171 Rawlings K.C. and Van der Sluijs J.C.A., to be published.
/8/ Vinen,W.F., Pr0c.R. Soc.
