In the cooling concept by adiabatic melting, solid 4 He is converted to liquid and mixed with 3 He to produce cooling power directly in the liquid phase. This method overcomes the thermal boundary resistance that conventionally limits the lowest available temperatures in the helium fluids and hence makes it possible to reach for the temperatures significantly below 100 μK. In this paper we focus on the thermodynamics of the melting process, and examine the factors affecting the lowest temperatures achievable. We show that the amount of 3 He− 4 He mixture in the initial state, before the melting, can substantially lift the final temperature, as its normal Fermi fluid entropy will remain relatively large compared to the entropy of superfluid 3 He. We present the collection of formulas and parameters to work out the thermodynamics of the process at very low temperatures, study the heat capacity and entropy of the system with different liquid 3 He, mixture, and solid 4 He contents, and use them to estimate the lowest temperatures achievable by the melting process, as well as compare our calculations to the experimental saturated 3 He− 4 He mixture crystallization pressure data. Realistic expectations in the execution of the actual experiment are considered. Further, we study the cooling power of the process, and find the coefficient connecting the melting rate of solid 4 He to the dilution rate of 3 He.

In pure superfluid 3 He-B at ultra-low temperatures, quartz tuning fork oscillator response is expected to saturate when the dissipation caused by the superfluid medium becomes substantially smaller than the internal dissipation of the oscillator. However, even with small amount of 4 He covering the surfaces, we have observed saturation already at significantly higher temperatures than anticipated, where we have other indicators to prove that the 3 He liquid is still cooling. We found that this anomalous behavior has a rather strong pressure dependence, and it practically disappears above the crystallization pressure of 4 He. We also observed a maximum in the fork resonance frequency at temperatures where the transition in quasiparticle flow from the hydrodynamic to the ballistic regime is expected. We suggest that such anomalous features derive from the superfluid 4 He film on the oscillator surface.

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We studied a novel cooling method, in which 3 He and 4 He are mixed at the 4 He crystallization pressure at temperatures below 0.5 mK. We describe the experimental setup in detail and present an analysis of its performance under varying isotope contents, temperatures, and operational modes. Further, we developed a computational model of the system, which was required to determine the lowest temperatures obtained, since our mechanical oscillator thermometers already became insensitive at the low end of the temperature range, extending down to (90 ± 20) μK ≈ T c (29±5) (T c of pure 3 He). We did not observe any indication of superfluidity of the 3 He component in the isotope mixture. The performance of the setup was limited by the background heat leak of the order of 30 pW at low melting rates, and by the heat leak caused by the flow of 4 He in the superleak line at high melting rates up to 500 μmol/s. The optimal mixing rate between 3 He and 4 He , with the heat leak taken into account, was found to be about 100..150 μmol/s. We suggest improvements to the experimental design to reduce the ultimate achievable temperature further.

Riekki, Tapio; Manninen, M. S.; Tuoriniemi, Juha Decoupling of first sound from second sound in dilute 3He-superfluid 4He mixtures Bulk superfluid helium supports two sound modes: first sound is an ordinary pressure wave, while second sound is a temperature wave, unique to superfluid systems. These sound modes do not usually exist independently, but rather variations in pressure are accompanied by variations in temperature, and vice versa. We studied the coupling between first and second sound in dilute 3 He -superfluid 4 He mixtures, between 1.6 and 2.2 K, at 3 He concentrations ranging from 0% to 11%, under saturated vapor pressure, using a quartz tuning fork oscillator. Second sound coupled to first sound can create anomalies in the resonance response of the fork, which disappear only at very specific temperatures and concentrations, where two terms governing the coupling cancel each other, and second sound and first sound become decoupled.