The turbulent drag force in superfluid 3He−4He mixtures under oscillations of a quartz tuning fork

Abstract

We have studied the resonance curves of a quartz tuning fork of the fundamental frequency 32 kHz immersed in superfluid 4He and mixtures 3He–4He with 3He concentration of 5 and 15% in the temperature range of 0.35–2.5 K at saturated vapor pressure. Two types of experiments have been carried out, with a tuning fork both not covered by a bulb and coated by a bulb, i.e., in the restricted geometry. In both cases, the velocity-force dependences for the tuning fork showed a linear damping force at low peak velocities and extra drag due to the appearance of vortex lines accompanying the transition to turbulence under increasing peak velocity. These dependencies are mainly determined by the density of the normal helium component. There is a pronounced difference between superfluid 4He and mixtures of 3He in 4He, where 3He impurity particles provide a constant temperature-independent contribution to the normal component of the mixture. The extra contribution to the damping force, so-called “turbulent drag force”, decreases with concentration increase at the same peak velocity of the tuning fork that can be explained by the extension of the range of laminar flow with an increase in the concentration of 3He. We found that the drag coefficient in superfluid 4He and mixtures 3He–4He reaches a plateau at different peak velocities and different exciting forces and explained this fact by different conditions for vortex formation, depending on the different thickness of the near-wall viscous layer. The comparison between the data obtained in restricted and unrestricted geometries shows that there is an excessive dissipation of the tuning fork motion associated with the emission of the first sound wave in unrestricted geometry.