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

Abstract

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 3 He and 4 He, by comparing measurements to the hydrodynamic model of the sensor.

Probing Liquid $$^4$$ 4 He with Quartz Tuning Forks Using a Novel Multifrequency Lock-in Technique

“…The physical parameters of the fork such as force and velocity can be determined from the applied voltage and measured current [2]. The force experienced by the fork prong is determined by the applied voltage V and is given by F = aV /2, where the coefficient a is termed the fork constant.…”

“…To quantitatively explain our results, we follow the approach and annotation described by Blaauwgeers et al [2] and Bradley et al [10] by assuming that the viscous penetration depth (∼1 µm for both forks) is much smaller than the fork dimensions and that acoustic damping is negligible at resonance frequencies below 100 kHz. In such case, it is possible to employ the two-fluid model of the superfluid and to obtain the fork resonance frequency and resonance width using the hydrodynamic contributions to the effective mass and Stokes' drag.…”

“…Quartz tuning forks were relatively recently introduced for probing quantum liquids [1] and were quickly adopted for low temperature thermometry [2][3][4], the generation and detection of quantum turbulence [5][6][7][8] and studies of acoustic emission [9][10][11] and cavitation [12]. The popularity of quartz tuning forks is driven by their availability, high quality factor and ease of use.…”

“…In this paper, we compare the measurements of the tuning forks by the conventional technique, using a Stanford Research Systems SR830 Lock-in Amplifier, with the multifrequency approach using an Intermodulation Products Multifrequency Lock-in Analyser (MLA) [19]. 2 We demonstrate that new technique is applicable even when the fork is immersed in liquid helium as the interactions of the fork with the fluid remain linear at small fork velocities. In the future, if non-linear effects are observed at high fork velocities the mixing effects can be attributed solely to the interaction of the fork with the fluid and should help to understand the nature of arising non-linearities.…”

A Quasiparticle Detector for Imaging Quantum Turbulence in Superfluid $$^3$$ 3 He-B

“…Quartz tuning forks have very high quality factors, of order 10 5 , making them sufficiently sensitive to study the mechanical properties of helium fluids at low temperatures. They have found many applications in superfluids research including measurements of viscosity [5][6][7], quantum turbulence in 4 He [8][9][10], cavitation [11], Andreev scattering in 3 He-B [12,13] and acoustic modes [14][15][16]. Here we describe their use as sensitive probes of ballistic quasiparticles in superfluid 3 He-B.…”