Crossover from hydrodynamic to acoustic drag on quartz tuning forks in normal and superfluid4He

Abstract

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.

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

“…The resonant frequency of each fork could be quite accurately predicted from the ideal cantilever model which predicts [4,15]:…”

“…There are several single forks which have fundamental resonant frequencies in the range 6-32 kHz and an additional array with forks having resonant frequencies in the range 20-160 kHz. These were used to study frequency dependent properties in superfluid 4 He such as sound emission [15] and turbulent drag [4]. Each array is attached to the frame of the wafer by two small tabs at one end next to the contact pads.…”

“…where I r and V r are the current and voltage amplitudes at the resonant frequency, Δf 2 is the frequency width of the resonance and the effective mass can be assumed to be equal to one quarter of the prong mass [15] m eff = ρ LT W/4 where ρ is the density of quartz. Direct optical measurements of the fork motion [3,4] show that the fork constant given by Eq.…”

“…For each fork, the amplitude of the driving voltage was held at a relatively low level whilst the frequency was swept through the fundamental resonance. Each resonance was fitted to the ideal Lorentzian lineshape [4,15] to obtain the resonant frequency f 0 , the frequency width Δf 2 and the resonant signal from which we could infer the fork constant using Eq. 3.…”

“…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.…”