The transition between laminar and turbulent flows around a quartz tuning fork vibrating with frequency ω in superfluid 4He and concentrated solutions (5 and 15% 3He in 4He) in the temperature range 0.3–2.3 K has been studied. The temperature dependences of the amplitude of the critical transition velocity vcr are obtained. The relationship vcr ∼ √(ηω/ρ) is shown to be applicable for the description of these dependences in concentrated solutions of 3He in 4He with density ρ and viscosity η, but this formula does not hold for the temperature dependence of vcr in pure 4He over the entire temperature range explored. It is also shown that in contrast to pure 4He temperature has virtually no effect in concentrated 3He–4He solutions on the drag coefficient in both laminar and turbulent regimes. The concentration dependences of the drag coefficient in the laminar regime normalized to the effective cross section of the vibrating body are plotted in the temperature range 0.5–1 K. The calculated dependences show that for low concentrations of a solution with x3 < 1% 3He the normalized drag coefficient weakly depends on the concentration of 3He and can be qualitatively described by the formula λ/S∼ρηω. In the x3 > 1% 3He concentration range, this coefficient increases sharply, and the reason for such a growth is currently not clear. Overall, the results of the study show that an increase in the 3He concentration in the solution enhances its stability with respect to the development of turbulence as the exciting force of a quartz tuning fork increases.

The amplitude–frequency characteristics of tuning forks immersed in superfluid 3He–4He solutions were measured in the temperature range of 0.1–2.5 K. The tuning fork resonance frequency and the resonance width were measured as functions of temperature for 5% and 15% concentrations of 3He and, for comparison, for pure 4He. The experimental results for the key dissipation mechanisms, that is, viscous friction and first and second-sound emission of a tuning fork, were analyzed. For separation and evaluation of the contributions of viscous damping and first and second-sound waves, “closed” (in a factory capsule) and “open” (without a capsule) tuning forks were used. The resonance width, which is a measure of dissipation of tuning fork vibrations, was found to be higher in solutions than in pure 4He, and to increase with increasing 3He concentration. It was shown that the existing analytical expression for the contribution of viscous friction provides a good description of the experimental data for 4He only in the hydrodynamic region. For the solutions, the viscosity contribution is consistent with the experiment only at high temperatures (above 1.4 K). For the “open” tuning fork, the contribution of the first-sound is consistent with the calculation results only for 4He, whereas for the solutions, the calculated values are underestimated compared to the experiment. The possible contribution of the second-sound to the dissipation of the tuning fork vibrations in solutions was estimated using experiments with the “closed” tuning fork. This contribution was found to vary non-monotonically with a maximum at temperatures of ≈ 0.6–0.8 K. The ratio of the tuning fork energy loss due to the thermal diffusion wave versus the loss due to the radiation flux of the second-sound wave in superfluid solutions was calculated using literature data with an accuracy of 10–3–10–4.

The possibility has been investigated for measuring the viscosity of concentrated superfluid mixtures of 3He in 4He in the temperature range 0.4−2.2 K using commercial quartz tuning forks with a resonance frequency of ≈ 32 kHz. It was found that the temperature dependence of the viscosity coefficient in a mixture with a concentration of 5% of 3He in 4He is in good qualitative agreement with the data obtained using other experimental techniques in the entire temperature range of the research. The same dependence of a mixture with 3He concentration of 15% agrees with the previously obtained data only at temperature T > 1.4 K, and at lower temperatures a difference appears that grows with decreasing temperature. The experimental temperature dependences of the viscosity coefficient obtained by different methods are compared with those calculated within the framework of the kinetic theory for the quasiparticles in superfluid 3He−4He solutions, developed by Landau, Khalatnikov, and Zharkov for the temperature range T > 0.6 K and by Baym, Saam, and Ebner for lower temperature.