Oscillating objects such as discs, piles of discs, spheres, grids and wires have been widely used in cryogenic fluid dynamics and in quantum fluids research since the discovery of superfluidity. A new addition are quartz tuning forks, commercially available frequency standards. We review their use as thermometers, pressure- and viscometers as well as their potential as generators and detectors of cavitation and turbulence in viscous and superfluid He liquids.

Vibrating Quartz Fork—A Tool for Cryogenic Helium Research

We report on experimental investigations of acoustic emission by quartz tuning forks resonating at frequencies 32 kHz, 38 kHz, 77 kHz and 100 kHz immersed in cold gaseous 4He and its normal and superfluid liquid phases. Frequency dependence of the observed low-drive-linewidth at 350 mK together with the temperature and pressure dependences (1.3 K < T < 4.2 K, 0 < p < 25 bar) of the observed damping of the high frequency (77 and 100 kHz) resonators measured in normal liquid 4He and its superfluid phase provide strong and direct evidence of the importance of sound emission by these tuning forks. Three analytical models of acoustic emission by vibrating tuning forks are developed and compared with the experimental results. We also discuss the importance of sound emission for experiments with the commonly used 32 kHz tuning forks as well as other oscillating structures—spheres, wires, grids and various micromachined sensors. We compare the relative importance of dissipative losses due to laminar viscous/ballistic drag and acoustic emission in liquid and superfluid 4He.

Acoustic Emission by Quartz Tuning Forks and Other Oscillating Structures in Cryogenic 4He Fluids

We present measurements of the drag forces on quartz tuning forks oscillating at low velocities in normal and superfluid ${}^{4}$He. We have investigated the dissipative drag over a wide range of frequencies, from 6.5 to 600 kHz, by using arrays of forks with varying prong lengths and by exciting the forks in their fundamental and first overtone modes. At low frequencies the behavior is dominated by laminar hydrodynamic drag, governed by the fluid viscosity. At higher frequencies acoustic drag is dominant and is described well by a three-dimensional model of sound emission.

/pdf/crossover-from-hydrodynamic-to-acoustic-drag-on-quartz-4offqd2kkl.pdf

Crossover from hydrodynamic to acoustic drag on quartz tuning forks in normal and superfluid 4 He

A study of the drag on the prongs of a number of quartz forks vibrating in the superfluid phase of $^{4}\text{H}\text{e}$ is reported, and particular attention is paid to the transitions from laminar to turbulent flow over a wide range of temperature. Behavior in the normal phase is consistent with that for a classical fluid, as has already been reported [Phys. Rev. E 75, 025302 (2007)]. Behavior in the superfluid phase is compared to that of other structures vibrating in superfluid $^{4}\text{H}\text{e}$, and similarities and differences are noted. We focus on the observed behavior of the drag coefficient as a function of velocity, and the problems posed by this behavior are explored. There is evidence for a sharp critical velocity at which significant turbulence starts to be generated in the superfluid component. At high velocities the drag coefficient tends to that observed in a classical fluid, suggesting that the two fluids, strongly coupled by mutual friction, are then behaving like a single classical viscous fluid. Behavior in the intermediate region seems to vary from one case to another. Evidence is presented that in the case of some structures the transition to single-fluid behavior takes place rather abruptly at a velocity that is only slightly greater than the sharp superfluid critical velocity, but that in other structures the transition is more gradual. Observed values of both the superfluid critical velocity and the effective viscosity of the fully coupled fluids are presented and discussed. It is suggested that the critical superfluid velocity is always closely similar to that at which the coupled fluids would be expected to undergo a classical transition between a flow that is strictly laminar and one that displays the first instability, and a possible reason is discussed.

Generation of turbulence by vibrating forks and other structures in superfluid H 4 e

Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of macroscopic quantum systems, while topology and broken symmetries determine allowed TDs. Taking advantage of the symmetry-breaking patterns in the phase diagram of nanoconfined superfluid 3He, we show that half-quantum vortices (HQVs)-linear topological defects carrying half quantum of circulation-survive transitions from the polar phase to other superfluid phases with polar distortion. In the polar-distorted A phase, HQV cores in 2D systems should harbor non-Abelian Majorana modes. In the polar-distorted B phase, HQVs form composite defects-walls bounded by strings hypothesized decades ago in cosmology. Our experiments establish the superfluid phases of 3He in nanostructured confinement as a promising topological media for further investigations ranging from topological quantum computing to cosmology and grand unification scenarios.

/pdf/half-quantum-vortices-and-walls-bounded-by-strings-in-the-kt6t0u3v0e.pdf

Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid 3He

Commercial quartz oscillators of the tuning-fork type with a resonant frequency of ∼ 32 kHz have been investigated in helium liquids. The oscillators are found to have at best Q values in the range 105–106, when measured in vacuum below 1.5 K. However, the variability is large and for very low temperature operation the sensor has to be preselected. We explore their properties in the regime of linear viscous hydrodynamic response in normal and superfluid 3He and 4He, by comparing measurements to the hydrodynamic model of the sensor.

Quartz Tuning Fork: Thermometer, Pressure- and Viscometer for Helium Liquids

Commercial quartz oscillators of the tuning-fork type with a resonant frequency of ~32 kHz have been investigated in helium liquids. The oscillators are found to have at best Q values in the range 10^5-10^6, when measured in vacuum below 1.5 K. However, the variability is large and for very low temperature operation the sensor has to be preselected. We explore their properties in the regime of linear viscous hydrodynamic response in normal and superfluid 3He and 4He, by comparing measurements to the hydrodynamic model of the sensor.

https://arxiv.org/pdf/cond-mat/0608385.pdf

P. Skyba

Papers

Quartz Tuning Fork: Thermometer, Pressure- and Viscometer for Helium Liquids

Quartz Tuning Fork: Thermometer, Pressure- and Viscometer for Helium Liquids