The critical velocity of transition to turbulence in 3He–4He liquid solutions

Abstract

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.