The study of quantum media through observation of oscillating bodies immersed in helium has always been a powerful tool for revealing unique properties of these substances. In recent years, quartz tuning forks have gained particular popularity as universal probes for studying liquid helium at low temperatures. Quartz tuning forks are highly reliable, allowing for long–term experiments without the risk of failure or the need for frequent calibration.
To fully utilize the advantages of quartz tuning forks in studying the fundamental properties of superfluid helium isotope solutions, it is necessary to thoroughly investigate their resonance characteristics in liquid helium both theoretically and experimentally.
The main goal of this work is to investigate the physical mechanisms determining the interaction of hydrodynamic modes (first and second sounds, viscous, diffusion, and thermal waves) with bodies oscillating in liquid helium. In particular, the processes of energy emission and absorption in superfluid solutions are considered; sound resonances in critical helium are studied, and resonance features of first and second sounds in superfluid helium and its isotope solutions are analyzed.
Special attention in the dissertation is paid to the study of superfluid helium isotope solutions and the development of a theory of the full system of hydrodynamic modes of these solutions.
The relevance of these tasks is driven by a significant number of new experimental results obtained by immersing an oscillating quartz tuning fork in superfluid ³He–⁴He solutions with various ³He concentrations — from small amounts up to 15%.
Experimental results have shown that second sound in solids and liquids can no longer be considered a rare or purely academic phenomenon. In particular, phonon hydrodynamics may affect the performance of graphene and graphite as heat–conducting materials in microelectronics, opening new possibilities for efficient thermal flow management in nanoscale systems.
The dissertation analyzes the fundamental possibility of using second sound for efficient heat removal and its prospects for cooling computing devices.
For the theoretical description of observed phenomena in pure helium and superfluid solutions over a wide temperature and concentration range, the relaxation problem was solved based on the full system of hydrodynamic equations for ³He–⁴He solutions. Using Fourier transform, non–Hermitian matrix formalism, and Green’s functions, the solution of this system was obtained for an instantaneous point heat source or an initial concentration disturbance. The solution is expressed through Green’s functions describing two main relaxation mechanisms: dissipative (due to thermal conductivity, diffusion, and thermodiffusion) and wave–like (due to second sound propagation
Oscillations of density, temperature, concentration, and pressure were studied to determine the conditions under which solid wall oscillations excite first and second sounds, as well as the dissipative diffusion wave in superfluid helium and acoustic waves in supercritical helium. Calculations of contributions of these processes to resonance formation during oscillations of closed tuning forks were performed.
As a result of these studies, a model describing the physical properties of resonance phenomena observed experimentally was created.
To compare with experimental data within the framework of a gas–kinetic model describing a weakly interacting gas mixture of quasiparticles — phonons and impurities — and based on a system of kinetic equations for these particles, the dissipative properties of both liquid and solid ³He–⁴He solutions were studied.
The phenomena of mass and spin diffusion, self–diffusion, and thermal conductivity were considered over a wide range of temperatures and concentrations. As a result of the calculations, explicit expressions were obtained for the coefficients of spin and mass diffusion, as well as for the thermal conductivity coefficient. To verify the constructed model, comparisons were made with experimental data, particularly analyzing the dependencies observed in experiments on spin relaxation and phase separation of solutions.
Theoretical studies were conducted on the mechanisms of energy dissipation manifesting in experiments with quartz tuning forks oscillating in superfluid ³He–⁴He solutions with high concentrations of ³He impurities. Specifically, the possibility and efficiency of tuning fork radiation not only of the second sound wave but also of the diffusive dissipative wave, which is characteristic of helium isotope solutions, were studied.
During the analysis, relationships between the amplitudes of temperature and concentration oscillations in these waves were found, as well as their relative intensities.
