Thermal response of a³He-superfluid-⁴He mixture

Abstract

The response of a layer of superfluid mixture to an ac heat source,Q(t)=Q ₀ exp(iωt), is determined. In the low-frequency regime, the temperature response at the heated side of a superfluid layer is essentially identical to that of an ordinary fluid having a thermal conductivity κ_eff and a thermal diffusion coefficient Γ ₀ /2. Here κ_eff is the effective conductivity of Khalatnikov, and Γ ₀ is the diffusion coefficient of Griffin. At much higher frequencies, the results are more complicated. The low-frequency regime is defined in terms of the second sound velocityu ₂ by ω≪u ² ₂ /Γ ₀ . The ac response function is valuable in a number of ways. It can be used to obtain the system response to more complicated time-dependent variations inQ such as step changes inQ. A knowledge of the response function in the low-frequency regime provides a mechanism for directly determining the Kapitza resistance in mixtures. Finally, a knowledge of the response function provides an additional opportunity to test two-fluid hydrodynamics. Alternative tests of superfluid hydrodynamics are of particular interest in light of recent experiments that show anomalous values for κ_eff in the low³He concentration limit