Thomas Voglhuber-Brunnmaier

Miniaturized sensors for the viscosity and density of liquids-performance and issues

This paper reviews our recent work on vibrating sensors for the physical properties of fluids, particularly viscosity and density. Several device designs and the associated properties, specifically with respect to the sensed rheological domain and the onset of non-Newtonian behavior, are discussed.

Methods for the robust measurement of the resonant frequency and quality factor of significantly damped resonating devices

For many applications, resonating sensors can be designed which exhibit excellent sensitivity of the resonant parameters (resonant frequency and quality factor) to the wanted physical parameters. When the resonant parameters are to be derived from measured data, the utilized signal processing algorithm significantly affects the precision of the obtained results, in particular, when the resonance is impaired with spurious contributions. In particular, for systems with low Q-factors (e.g., electromechanical resonators in viscous liquids with Q < 100), the measurement precision suffers from various unwanted spectral components induced by parasitic effects of the resonator and measurement errors. In order to separate the adverse effects from the ideal second-order characteristics, three related methods for estimating the parameters of second-order resonant systems are introduced in this paper extending established methods. To this end, the spectrum is separated into a component induced by a second-order resonant system and an unknown background spectrum.

Resonance parameter estimation from spectral data: Cramér–Rao lower bound and stable algorithms with application to liquid sensors

A recently introduced method for robust determination of the parameters of strongly damped resonances is evaluated in terms of achievable accuracy. The method extracts and analyzes the locus of the resonant subsystem of noisy recorded complex spectra, such that the interfering influences of many environmental factors are eliminated. Estimator performance is compared to the absolute lower limit determining the Cramer–Rao lower bound (CRLB) for the variance of the estimated parameters. A generic model that is suitable for representation of a large class of sensors is used and analyzed. It is shown that the proposed robust method converges to the CRLB for low measurement noise.

Experimental and theoretical evaluation of the achievable accuracies of resonating viscosity and mass density sensors

Electrodynamically driven resonators upon immersion in a sample liquid which can be used as viscosity and mass density sensors are presented. The most promising concepts for such resonant sensors include devices which are fabricated in technologies involving clamped wire and plate structures. In this contribution, achievable accuracies for these types of resonating sensors are considered and investigated by means of long term measurement series. As a suitable reference for such devices, a steel tuning fork is used, which serves as a frequency standard in low frequency applications (440 Hz). Such tuning forks can serve as viscosity and density sensors themselves if they are immersed in a liquid. In order to make their frequency response electronically accessible, an electromagnetic driving and readout setup has been devised to compare their performance to the wire-and plate-based sensors.

Miniaturized viscosity and mass density sensors combined in a measuring cell for handheld applications

Miniaturized viscosity sensors are attractive devices for condition monitoring applications involving fluid media. Previously introduced devices utilize vibrating resonant mechanical structures interacting with the fluid where the resonance frequency and the quality factor are affected by the fluids viscosity and mass density. The investigation of many of these devices showed instabilities in their resonance frequencies and high cross-sensitivities e.g., to temperature. To overcome these drawbacks, we designed new resonant sensor principles based on U-shaped electrical conductors interacting with the sample liquid, which are presented and discussed in this contribution. For measuring the viscosity with resonant principles, it is necessary to know the liquids mass density. Hence, we integrated a separate mass density sensor in our measuring cell. We present first measurement data obtained with these devices and discuss their sensitivity to viscosity and mass density.

Double membrane sensors for liquid viscosity and mass density facilitating measurements in a large frequency range

A resonating double membrane based sensor for viscosity and mass density facilitating measurements at different frequencies and two adjustable modes of vibration is presented. The sensor is designed to be suitable, e.g., for low cost handheld devices with inline capabilities and disposable sensor elements. In the sensor, a sample liquid is subjected to time harmonic shear stress induced by two opposed vibrating polymer membranes, placed in an external static magnetic field. These membranes carry two conductive paths each. The first path is used to actuate the membranes by means of Lorentz forces while the second acts as a pick-up coil providing an induced voltage representing the movement of the membrane. From the measured frequency response the liquids viscosity and mass density can be deduced. This double membrane based setup allows to examine the test liquid at adjustable frequencies in the low kilohertz range from 1 kHz to 15 kHz. Two different designs are presented and the results obtained by experimental investigation are compared to previous theoretical findings.

Modeling of piezoelectric tube resonators for liquid sensing applications

A model for the electrical impedance of a fluidic piezoelectric tube sensor, resonating in thickness-wall-mode, is presented. The tube is mechanically loaded with acoustic impedances which represent the fluid properties. It is shown that the electrical impedance of a plane resonator model yields results very close to the tube model, if the static capacitance of the tube is used with the plane impedance expression. Therefore, the common transmission line models may furthermore be used with minor changes. Measurement results are compared with the cylindrical model and with the plane approximation.

Characterization of Viscous and Viscoelastic Fluids Using Parallel Plate Shear-Wave Transducers

We introduce a recently devised approach for viscosity and viscoelasticity measurement using a device based on the excitation of acoustic shear waves in fluids, which opens up opportunities for rheological applications in the low kilohertz range. Two in-plane plate resonators, which are driven and read out electromagnetically, are aligned in parallel and are separated by a well-defined gap filled with the fluid sample. The lower plate is actuated, generating a shear wave in the viscous or viscoelastic fluid. The response on the second side is recorded in a frequency range, where intrinsic resonances of this setup are observed. The coupling of the two resonators increases with viscosity, yielding a, for resonator viscosity sensors unprecedented, high viscosity measurement range (measured up to 17.6 Pa · s). Analytical modeling and experimental results are presented.

Concept study on an electrodynamically driven and read-out torsional oscillator

In this contribution a concept study for an electrody-namically driven and read-out torsional oscillator is presented. The fundamental mechanical and electrodynamical theory is explained in detail and measurements results obtained with first prototypes are discussed.

Application of resonant sensors for magnetic flux density measurements

This contribution discusses the influence of the magnetic flux density on Lorentz force driven resonant sensors. A closed form model describing the physical behavior of the resonating wire shows the quadratic influence of magnetic flux density on the readout signal, which in our case is the motion induced voltage in the oscillating wire. It is furthermore shown that the resonating wire sensor is well suited for magnetic field measurements, even at high temperatures.