Mutual friction and the thermal conductivity of superfluid helium near T?

Leiderer, Paul; Pobell, F.

doi:10.1007/bf00628335

Cited by 23 publications

(3 citation statements)

References 17 publications

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“…They demonstrated that their results can be described by a simple expression consistent with earlier measurements made by Leiderer and Pobel [33], much farther from the transition and at higher Q. These results were also verified in DX measurements [34] at temperatures very near the transition, using an engineering model of the DX instrument.…”

Section: Thermal Counterflow and Mutual Frictionsupporting

confidence: 84%

The CQ experiment: Enhanced heat capacity of superfluid helium in a heat flux

Lee

Duncan

Harter

et al.

Proceedings, IEEE Aerospace Conference

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Absti-uct-CQ will exploit the superfluid transition of pure liquid 'He, in a microgravity environment, in order to study a critical point phase transition under non-equilibrium conditions. It will be conducted in conjunction with the DYNAMX experiment (Critical Dynamics in Microgravity) on board the ISS, using the same hardware and electronics, and on the same mission. We call the combined mission DWCQ.It is expected on very general grounds that superflow will break down along a curve on the superfluid side of the Q (heat flux) -T (temperature) plane, and it has been shown that the heat capacity at constant Q, CQ, should diverge along that same curve, which we refer to as Tc(Q). The fundamental purpose of the CQ experiment is to measure C, as close as possible to Tc(Q). Earthbound measurements to determine Tc(Q) have given results that disagree with theory. Our own laboratory measurements of CQ [ 11 yield a much larger enhancement of the heat capacity than is predicted by theory, provided that the theoretical value of Tc(Q) is used in the data analysis. However, for a variety of gravity-related reasons, these measurements could not be made close to Tc(Q). The CQ experiment will make use of the microgravity environment on board the ISS to resolve these discrepancies, and should result in the first highly quantitative measurement of dynamical effects on a critical point phase transition.

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Section: Thermal Counterflow and Mutual Frictionsupporting

confidence: 84%

The CQ experiment: Enhanced heat capacity of superfluid helium in a heat flux

Lee

Duncan

Harter

et al.

Proceedings, IEEE Aerospace Conference

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“…*> We estimate lm starting from ( 13 ). Not far from the interface Vs is nearly constant, so that we define cs=(m/h)vs~ where ~=~o(l _ T/T=)-213= ~o(A=IT=)-213Q-112.…”

Section: Coexisting Phasementioning

confidence: 99%

“…Following a phenomenological approach of Gorter and Mellinkn we assume (13) where p is the mass density and A is a phenomenological constant dependent on T. We are assuming that the heat is flowing in the negative x direction. Vinen related A to a dimensionless parameter B associated with the vortex motion in flow using intuitive arguments.…”

Section: Superfluid Phasementioning

confidence: 99%

Nonlinear Temperature Profiles near the Superfluid Transition

Ōnuki

1983

Progress of Theoretical Physics

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Temperature profiles are calculated near the superftuid transition in the.presence of a heat flow in the normal, superftuid and coexisting phases. In particular, in the neighborhood of the Hei-Heii interface, vortices on the superftuid side give rise to a temperature gradient much smaller than that on the normal fluid side by a factor c: m( ~ 10-3). As a result the predicted temperature depression T,-T on the superftuid side is measurable only when the size of a thermometer is smaller than ~clcm~ 10-'Q-112 em with Q in mW /em', ~c being the interfacial thickness of order 3 X 10-5 Q-' 12 cm. Therefore, the mutual friction can have a significant effect in measurements of temperatures near the interface, which appears to explain the discrepancy between the theory and Bhagat and Lasken's measurement. § 1. Introduction 935Near the superfluid transition the thermal resistance depends on T-T;. strongly, where T is the temperature and T;. is the critical temperature. As a result the gradient VT can be strongly inhomogeneous in the presence of a constant heat flowQ. In this paper we examine the resultant nonlinear temperature profiles in three possible phases under heat flow, namely, the normal fluid phase, the superfluid phase and the coexistence phase. 1 > The coexistence of the two phases has been investigated recently. 2 >,a> The interfacial thickness is of order ~c=kc -\where kccx:. Q 112 . A flat interface is at rest only when the temperature on the superfluid side T satisfies T;.-T=A,,Q 314 where A""~ 10-5 deg with Q in mW/cm 2 • In this case the superfluid density Ps and the superfluid velocity Vs(cx:.Q/ps) are both proportional to Q 112 . We find that Vs well exceeds the critical velocity Vsc associated with the vortex generation for any value of Q. 2 >,a> (Note that Vsccx:.Ps. 4 >) Vortices thus produced give rise to only a relatively small VT far from the interface and do not affect the interfacial structure. § 2. N orrnal fluid phase Let Tr and T2 be the temperatures at the cooler and warmer ends of the cell. The linear response theory holds only when T2-Tr ~ T2-T;.. In the region where the reduce temperature t = ( T-T;.) / T;. (which should not be confused with the time variable) is greater than a characteristic reduced temperature tc, the inhomogeneity is weak and T obeys ;..dT =Q dx 'where (2) at

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