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Behavior of the thermal conductivity of dilute -43He mixtures in the superfluid phase

Physical Review B, ISSN: 0163-1829, Vol: 40, Issue: 7, Page: 4306-4315
1989
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We present a new solution to the Khalatnikov two-fluid hydrodynamic equations which suggests that thermal conduction experiments in superfluid -43He mixtures measure the diffusive conductivity. This implies that for small He3 concentrations the measured conductivity approaches a constant. The singular behavior predicted by Khalatnikovs original solution can be eliminated using a constraint imposed by the tight coupling of concentration and temperature gradients. Microscopically, we find that diffusive mass transport in bulk superfluid is limited by the ability of the diffusing atoms to get rid of the thermodynamic diffusion energy they carry, leading to an apparent diffusivity which can be much smaller that the isothermal mass diffusivity. We also describe a preliminary experiment to observe two effects predicted by our analysis. In agreement with our predictions, we find that (1) the thermal relaxation time in dilute mixtures is very long and (2) the temperature gradient in a superfluid mixture is caused by He3 mass diffusion. The latter observation gives rise to a new technique for measuring the effective thermal conductivity which avoids the main difficulties encountered by the previous method. © 1989 The American Physical Society.

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