AC Thermal Conductivity Measurements in Dilute Mixtures of 3 He in Superfluid 4 He

Abstract

In Part III of a three-part study, we report measurements of the thermal response, ΔT(ω), of 3 He-superfluid- 4 He mixtures to an ac heat flux, Q(t)=Q0eiωt. These data are for dilute concentrations, X, and they show the presence of three separate thermal resistances. One of these is the bulk-fluid resistance predicted by Khalatnikov and associated with the effective conductivity, κ eff . Results for this component of the resistance are in quantitative agreement with the Khalatnikov predictions. With parallel work by Murphy and Meyer, these experiments resolve a long-standing conflict between theory and experiment. One of the remaining resistances is the ordinary boundary resistance Rb. The third resistance, R 0 , is independent of the fluid layer height, d. This resistance is presumably the same as that seen in earlier dc measurements. Both the temperature and concentration dependences of this anomalous resistance differ from that of either R fluid or Rb. It has been ascribed recently by Murphy and Meyer to effects associated with the narrow gaps usually present in cryogenic thermal conductivity experiments. We use an ad hoc model as a convenient way to parameterize the extra thermal resistance. The present studies have been carried out with an apparatus which permits us to vary d continuously and in situ from zero to 3 mm. This feature and the ac technique are important for separating the various components of the thermal resistance. In two preceeding studies, we considered related aspects of the ac thermal response of liquid helium. Part I addresses the response of normal liquid helium. Part II, provides the theoretical backdrop for the present experimental study.