Extension of the torsional crystal viscometer to measurements in the time domain

Abstract

This paper reports the first wide-ranging application of the free-mode measurement technique to a torsional crystal viscometer. The viscous damping of the fluid on the surface of the crystal is detected in the time domain by observing the freely decaying torsional oscillation of the crystal. Previously, the torsional crystal viscometer was used exclusively in a forced mode of measurement, where the response of the crystal is determined in the frequency domain by scanning through the resonance. The free-decay measurement mode has many advantages over the previous technique. It enables a better characterization of the sensor because the torsional displacement of the crystal can be observed directly. Measurements can be carried out at smaller displacements as well as at constant amplitude in fluid and in vacuo. Direct control over the crystal displacement is an important extension (especially at low external damping of the crystal as in gases or in vacuo), because the measurements can be limited to the linear regime of the crystal vibration and the nonlinear regime can be avoided. In addition, this extension allows for a more complete characterization of the transducer by validating the consistency of its operation in the time and frequency domains. Finally, free-decay measurements are much faster than resonance scans, thus eliminating medium and large time constant variables that can affect the measurement. With these advantages, a second metrological approach has been added to the utilization of torsional crystal viscometers. Sulfur hexafluoride (SF 6) was used as a test fluid to compare the two measurement modes in the presence of external damping. The results of both methods are consistent up to a (viscosity × density) of 0.020 (Pa s)(kg m −3). With improved signal conditioning this limit can be increased substantially. Both measurement techniques were also compared to determine the internal damping of the crystal in vacuo. Nonlinear crystal oscillations were observed which can be interpreted in terms of Duffing and Van der Pol nonlinearities with displacement-dependent stiffness and damping respectively. This insight represents a substantial advance in our understanding of torsional crystal viscometers.

Measurement of Newtonian fluid slip using a torsional ultrasonic oscillator

“…Similar derivations have considered damping of other torsional oscillators by viscoelastic fluids under the NSBC, yielding similar functional forms [41,43,56]. For the oscillator of specimen rod radius a δ described by Fig.…”

Torsional piezoelectric fiber for viscosity measurement of Newtonian fluids

“…The working equation for absolute viscosity measurements of torsional rod resonator has been presented for crystal viscometer [17]:…”

High-Frequency Shear Viscosity of Low-Viscosity Liquids

“…Torsional crystal viscometers (B) detect the viscous effect of the fluid on the torsional oscillations of the cylindrical rod. Highly viscous samples with viscosity up to 2 × 10 2 Pa·s [24] have been measured using this method as well as gases with viscosity as small as 10 −5 Pa·s [26]. On account of the small sizes needed, however, the range of operation is restricted to frequencies smaller than 300 kHz.…”

“…We thus used a thickness shear resonance method (D) to measure the complex shear viscosity of liquids with low η s in the frequency range from 6 MHz to 130 MHz [30]. [9,14,22,23]; (b) torsional crystal viscometer [24][25][26]; (c) oscillating plate viscometer [27]; (d) thickness shear resonator technique [28][29][30]: 1, liquid sample; 2, BT-cut quartz crystal; 3, fusedquartz rod; 4, cylindrical torsional quartz transducer; 5, cuvette; 6, oscillating plate; 7, thickness shear vibrating AT-cut quartz disk…”