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In this work, a resonant quartz tuning fork sensor based measurement system is employed to study the settlement of small particles in suspension as they pass the sensing element. The resonator features varying sensitivity to fluid parameter changes along its length, with the tip being most sensitive. The spatial averaging effect is analyzed theoretically and measured by passing the sensor through a fluid–fluid interface. Subsequently, the averaging function is used for particle distribution determination from recorded resonance frequency and quality factor measurements. The associated inverse problem is of Fredholm type and is solved numerically. Based on the system specifications, detection limits, required temperature stability and expected precision are assessed and particle distribution functions of defined test dispersions are measured.

A design for a high quality factor photonic crystal ring resonator (PCRR) is presented. The PCRR is based on pillar type photonic crystals, which consist of a hexagonal array of silicon rods. The cavity is created by removing elements from the regular photonic crystal (PhC) grid. Achieving strong confinement of light intensity in the low index region is the advantage of this PCRR. In that manner, the interaction of light and analyte, which can be a liquid or a gas, will be enhanced. The high quality factor of the cavity ( Q = 1.0229 × 10 5 Q=1.0229\times {10}^{5} ), along with strong overlap between the field of the resonant mode and the analyte as well as the low group velocity of PCRR modes yield enhanced light-matter interaction. An enhancement factor of γ = 2.127 × 10 4 \gamma =2.127\times {10}^{4} compared to the bulk light absorption in a homogenous material provides the potential for highly sensitive gas detection with a photonic crystal ring resonator.

In this work we report on a computational study regarding the enhancement of the absorption of mid infrared (MIR) light for gas sensing applications. In order to address this goal, a photonic crystal ring resonator (PCRR) with a quality factor of more than 3.85 × 10 5 was designed. The considered PCRR is based on 2D pillar type photonic crystals, which consist of a hexagonal array of silicon rods. The high quality factor of the cavity, along with strong overlap between the field of the resonant mode and the analyte (0.76) and low group velocity of PCRR modes consequence into enhance sensitivity for gas sensing.

We present a concept for a resonant absorber structure featuring high compatibility with CMOS technology in a slab design, which is suitable for integration with slab waveguides. Finite-element simulations were used together with the Transfer-Matrix Method and genetic-algorithm optimization in order to model the optical resonators. These absorbers are based on so-called slab Tamm plasmon (STP) structures. Depending on the slab thickness relative absoptances up to 70 % were achieved for an incident guided slab waveguide mode. Only silicon based materials are used in the design of the STP absorbers. This facilitates the fabrication process, as metals are omitted in the components of the structure.

The goal of this work is the analysis of viscoelastic properties of complex liquids like synovial fluid (i.e. the lubricant in joints), where the available volume is in the range of microliters. Viscosity and shear modulus as a function of frequency carry important information about the physiological condition. Our approach utilizes an electrodynamically excited, mechanically balanced inplane resonator, where the resonance frequencies and quality factors of several modes are evaluated under liquid loading. The balanced "tuning fork" design ensures minimal suspension losses which, together with the advanced rapid readout technique, implements unprecedented features paving the way for shear-wave spectroscopy of soft materials.

We investigated the vibration characteristics of the torsional oscillation mode of an earlier proposed resonant viscosity sensor based on vibrating pipes. To do so, the sensor housing is opened, so that half of the resonator is freely accessible. The actuation and readout of the sensor is realized with electromagnetic coils on the remaining part of the housing and the oscillation velocity is measured on different positions on the uncovered sensor surface. We demonstrate the feasibility and suitability of the electromagnetic readout principle and identified an additional spurious oscillation. All measurements were performed with an air filled resonator to minimize the damping and maximize the oscillation amplitudes.

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 $17.6~\textrm {Pa} \cdot \textrm {s}$ ). Analytical modeling and experimental results are presented.

In modern light-duty Diesel vehicles the particulate filters in the exhaust system require periodic regeneration to prevent plugging. The regeneration procedure is a major cause of dilution of engine oil with diesel fuel. In order to investigate the effect of the operation conditions of the engine on the fuel content in the oil, a precise and fast in-line measurement system is required. In this contribution a resonant sensor system for determination of diesel content by measuring the viscosity of the oil is tested. A commercial off-the-shelf quartz tuning fork resonator is used as sensor element and evaluated using a universal analyzer for resonant sensors developed for fast and precise acquisition of resonant sensor responses. The experiments presented in this paper show that fuel concentration in the range of 0.2 % can be determined within seconds. The obtained results are compared to that obtained with an accurate lab bench viscosity and mass density meter.

Electromechanical resonators are used as viscosity sensors where the effect of the fluid loading on the resonance parameters is evaluated. A complete numerical analysis is often unrealistic due to the large computational effort. We introduce a reduced-order fluid impedance model valid for a large class of geometries. The fluid structure interaction is characterized by three parameters, an effective volume, an effective interaction surface, and an effective length. For idealized geometries these parameters can be derived analytically. We derive scaling laws for rectangular cross sections which are relevant for quartz tuning fork resonators.

A design for enhancing the quality (Q) factor of a photonic crystal ring resonator (PCRR) for gas sensing in the mid infrared (MIR) region is introduced. The PCRR is based on 2D pillar type photonic crystals, which consist of a hexagonal array of silicon rods. The high quality factor (390000) of the cavity, along with strong overlap between the field of the resonance mode and the analyte (0.76) was calculated.

In this contribution, we present a symmetric arrangement of electromagnetically actuated, resonating plates for viscosity and density measurement. Regarding the oscillation mode, the design resembles a tuning fork and is based on previously introduced resonating plate designs. It exhibits similar sensitivity to viscosity as previously characterized single plate resonators, while having two shear modes at different frequencies, that can be both actuated with the same setup allowing a multi-frequency analysis of viscoelastic liquids. We introduce the new design and present the results of FE simulations in order to determine the associated eigenmodes. We investigate the effects of the actuation method on the sensors performance by actuating with two different magnetic field configurations and by trying different configurations of the actuation and readout circuit, from which we show that with a particular configuration, Q-factors of up to 5000 can be reached for the symmetric shear mode. From these results we then proceed to suggesting a simplified lumped mechanical oscillator model explaining the dependence of the resonator’s Q-factor while operated in air on induced eddy currents damping. Measurement results are presented which show the general dependence of the new design’s actuated modes, the anti-symmetric and symmetric mode, on viscosity and density. We apply two different models to our data: a newly developed generalized model and a simplified version of that model which better describes the observed relation of our measurements to the square root of the product viscosity density. We then proceed to perform an estimated error analysis on viscosity, density, and the square root of their products based on the above mentioned applied models. From this error analysis several conclusions are drawn, mainly that the symmetric mode is more accurate than the anti-symmetric one, the sensor is generally more accurate for lower viscosity liquids, and lastly that the square root of the viscosity density product is a more suited value for the description of the sensor's behavior than the viscosity or the density alone.

In this contribution a conceptual study for torsional oscillators, which are electromagnetically driven and read out, is presented. The aim is to experimentally investigate the basic feasibility of a torsional resonator with application to viscosity and mass density sensing in liquids. Such a device is particularly interesting as cylindrical, torsional resonators for fluid sensing applications are hardly reported but unlike many other devices, yield pure shear wave excitation in the liquid. The design of first conceptual demonstrators for measurements in air as well as in liquids and their benefits and disadvantages are discussed in detail. A closed form as well as a reduced order model and measurement results obtained with first demonstrators are presented.

The synovial fluid is found in joints of vertebrates and contains a high molecular weight polysaccharide (hyaluronan) acting as a modifier to ensure proper lubrication. Both, its concentration and molecular weight are subject to pathological alterations in certain diseases. Laboratory analysis of physical properties is difficult because of the limited amount of sample volume (usually below 100 μl). We present a sensor platform which requires volumes below 10 μl to measure the viscoelastic properties in the kilohertz range and the electrochemical impedance spectrum (EIS) from 102 to 106 Hz. Two electrodynamic acoustic shear wave transducers are used to measure both the single-sided viscoelastic shear impedance and the transmission of shear waves. The same elements are used as electrodes for measuring the EIS with a precision impedance analyser. The device is supposed to be used for clinical diagnosis and therapy tracking.

A piezoelectric tuning fork sensor is evaluated as a physical excitation and sensing device aiming at the detection of crystals and their nucleation behavior in joint fluids, as observed in gout. This device allows to study the crystallization tendency at varying temperatures or at increased uric acid concentrations as predominant in real human joints. In this work, a tuning fork resonator is characterized to enable spatially resolved viscosity and density measurements by calculating the mode shape of the vibration from resonance frequency measurements when immersed in test liquids.

We introduce an analysis platform for the viscoelastic properties of biological fluids such as the synovia found in articular joints. Small sample volumes are available for diagnostic purpose. Our approach uses a thickness shear mode quartz crystal integrated in an electrodynamically actuated spring structure. This combines the sensitivity of the quartz resonator operating at several overtones in the MHz range with previously introduced low kHz frequency multimode resonators. The latter is not only advantageous for characterizing viscoelastic fluids but is also used as an acoustic streaming actuator. Particulate matter in the sample thus can be resuspended and their settling is observed by tracking the resonance frequencies and Q-factors of both the quartz and electrodynamic resonator sensors.

In this work we present a design to enhance absorption of infrared light by a fluid analyte being in contact with a slot photonic crystal ring resonator (slot-PCRR). For this purpose, we propose a new PCRR design facilitating higher interaction between guided mode and analyte. These types of PCRRs are based on two-dimensional photonic crystals, which consist of an array of holes in a silicon slab being arranged in a hexagonal lattice. The holes will be filled with liquid analyte. A slot is embedded in this hexagonal ring cavity to create a slot-PCRR. The strong confinement of light in the low index region, occupied by the analyte, is the key advantage of the slot- PCRR. We also calculate the relative intensity change in the transmission spectrum due to the absorption in the analyte. The maximum change obtained is given by a mode which has most of the electromagnetic field energy in the region the region filled with the analyte. Furthermore, this mode is well separated from neighboring bands, which has the advantage that impinging light with specified frequency is less likely to spuriously couple to other modes with the same frequency, which would decrease the amount of energy coupled to desired mode. The slot-PCRR yields a higher relative change due to absorption compared to the PCRR without a slot. In this work, the radii of six rods at the outer PhC were tuned to enhance the quality factor of slot-PCRR. Using these optimum values of radii, the Q-factor rises up to 80000.

A design for a high Q factor photonic crystal ring resonator (PCRR) is presented. The PCRR is based on 2D pillar type photonic crystals, which consist of a hexagonal array of silicon rods. The cavity is created by removing elements from the regular PhC grid. Achieving strong confinement of light intensity in the low index region (filled with the gaseous analyte) is the advantage of this PCRR. In that manner, the interaction of light and analyte, which can be a liquid or a gas, will be enhanced. The high quality factor of the cavity (Q=1.2×104 ), along with strong overlap between the field of the resonant mode and the analyte as well as the low group velocity of PCRR modes yield enhanced light-matter interaction. An enhancement factor of 1.149×105 compared to the bulk light absorption in a homogenous material provides the potential for highly sensitive gas detection with a photonic crystal ring resonator.

A resonant sensor for a fluid's viscosity and mass density, employing an out-of-plane vibrating U-shaped tungsten wire is presented. The motivation for such a design is based on four major aspects, which are: operation in the low kilohertz range, circular cross-section of the resonator, electrodynamic actuation and read-out by means of Lorentz forces and low cross-sensitivity of the device's resonance frequency to temperature. The setup is described in detail, an analytical model is presented and results from experiments using acetone–isopropanol and DI-water–glycerol solutions are discussed to show the sensor's performance.

Most recently introduced viscosity and mass density sensors utilize vibrating resonant mechanical structures interacting with the sample fluid where the resonance frequency and the quality factor are affected by both, the fluid's viscosity and its mass density. Unlike singly clamped beams, straight, doubly clamped structures are advantageous when using electromagnetic excitation and read-out based on Lorentz forces which allow high excitation forces and read-out signals. However, classical straight beams such as bridges are subjected to high cross-sensitivities of their resonance frequencies to ambient temperature. To overcome high spurious temperature dependencies but to benefit from the straight doubly clamped approach, a spiral spring resonator applicable as viscosity and mass density sensor has been designed.

The principle of using steel tuning forks for viscosity and mass density measurements is investigated. From recorded frequency responses of fully immersed tuning forks, resonance frequencies and quality factors are evaluated and related to the liquids mass densities and viscosities. The benefit of these resonators is their mechanical rigidity which allows the application in harsh environments and mechanical cleaning processes without detuning or damaging the device. The setup was particularly devised that only the resonator itself but no excitation or read-out mechanisms get wetted by the sample liquid. The results obtained with a circular cross-sectioned tuning fork in different liquids are shown and discussed.

In this contribution we discuss a generalized, reduced order model for resonant viscosity and mass density sensors which considers also the devices’ cross sensitivities to temperature. The applicability of the model is substantiated by experimental results from measurements obtained with a circular steel tuning fork in various liquids and temperatures. Advantages of this model are its simplicity, its general applicability for resonant mass density and viscosity sensors which furthermore facilitates the comparison of different sensors.

Miniaturized resonating viscosity sensors operating at frequencies in the low KHz-range, offer portability and measurement results comparable to existing lab viscometers. In this paper, we present a viscosity measurement cell, based on a concept that we proposed earlier utilizing electrodynamic-acoustic resonator sensors, with a novel design based on interchangeable resonator cards. Experimental results obtained with the new resonator cards show the dependence of the resonance frequency and Q-factor on viscosity. We obtained repeatability errors in the order of a few percent for a range of Newtonian liquids. We discuss the related errors in viscosity measurement based on deviations in the determination of the Q-factor and resonance frequency. In addition, experiments were made aiming at increasing the initial Q-factor of the sensor by varying the distance separating the two magnets of the viscosity measurement cell and investigating different bonding techniques of the resonator card. Based on these results, design rules for the magnetic circuit and the mounting are derived.

For many applications the viscosity of a complex fluid sample is interesting to control the process and reactions. These fluids can for instance be suspensions of different types of microorganisms, e.g., bacteria or fungi. Macroscopic viscosity measurement systems would only be able to measure the global, averaged viscosity. Miniaturized TSM resonators, however, are probing only a very thin fluid film (typically only a few μm thick, depending on frequency and viscosity) on their surface. Earlier investigations with water-in-oil micro-emulsions have shown that the influence of water droplets in oil is dependent of their size. In this paper we focus on a similar effect, i.e. the influence of the surface roughness. It turns out that the sensor behaves differently if the dimension of the inclusions or particles is in the order of the surface roughness.

We demonstrate the operation of a digital microfluidic lab-on-a-chip system utilizing Electro Wetting on Dielectrics (EWOD) as the actuation principle and a High Fundamental Frequency (HFF; 50MHz) quartz crystal microbalance (QCM) resonator as a mass-sensitive sensor. In a first experiment we have tested the reversible formation of a phosphor-lipid monolayer of phospholipid vesicles out of an aqueous buffer suspension onto a bio-functionalized integrated QCM sensor. A binding of bio-molecules results in an altered mass load of the resonant sensor and a shift of the resonance frequency can be measured. In the second part of the experiment, the formation of a protein multilayer composed of the biomolecule streptavidin and biotinylated immunoglobulin G was monitored. Additionally, the macroscopic contact angle was optically measured in order to verify the bio-specific binding and to test the implications onto the balance of the surface tensions. Using these sample applications, we were able to demonstrate and to verify the feasibility of integrating a mass-sensitive QCM sensor into a digital microfluidic chip.

Resonant mechanical sensors are powerful tools for measuring, e.g., physical properties of fluids. Suitable systems for real-time monitoring of a sensor’s resonance behavior are, e.g., oscillator circuits and phase-locked loop circuits. In this contribution, we present a novel specific digital phase-locked loop circuit with the ability to determine damping, as well as resonance frequency, and providing automatic compensation of spurious parallel capacitances of the sensor. Instead of a phase-frequency detector, the system measures phase and amplitude of the sensor signal with a 16-bit ADC and uses this information to control a numerically-controlled oscillator. Due to the used 4-channel digital synthesizer, the sensor can be excited with up to three frequencies at the same time facilitating enhanced performance in terms of simultaneous measurement of higher order resonances and compensation of spurious capacitances.

Miniaturized physical sensors for precise density and viscosity measurement are required as supplement or replacement for complex and expensive laboratory instruments. Utilizing miniature mechanical resonators as transducers, one can greatly reduce the necessary liquid volume, measurement time, and complexity of the experimental setup. In this contribution, we describe the development of a miniature, modular measurement setup for a large viscosity range. We devised and fabricated an inexpensive flow-through cell using milling technology of multiple PCB layers and Parafilm or Teflon sealing for easy assembly and disassembly. The mechanical resonator is designed as a suspended plate using electrodynamic Lorentz force excitation and movement induction detection. Quality factor and frequency shift of the resonator are evaluated and related to the density–viscosity product of different test liquids at multiple resonant modes of vibration at low operating frequencies for different temperatures and over a wide range of different viscosities.

Piezoelectric fluid sensors with an LFE electrode arrangement (LFE: lateral field excitation — both electrodes are placed on one side of the disc) show unique differences compared to common thickness field excited (TFE) resonators, due to the additional lateral field components produced. In this contribution the LFE sensor setup is modeled as a layered structure in the spectral domain utilizing a semi-numerical approach. In particular the interaction of the piezoelectric disc and the sample liquid, which is too complex for analytical methods or too comprehensive for FEM, is efficiently modeled by the method. The calculation of the frequency responses as well as the electrical and the mechanical fields are illustrated. The simulation results are compared to results obtained from the Christoffel–Bechmann formalism, and sensitivities to fluid parameters like viscosity, density, and conductivity are shown. Furthermore, the sensitivity to viscosity is compared to experimental data.

Resonating sensors are commonly used for various measurement tasks, e.g., as microbalances as well as for viscosity and density measurements of viscous or viscoelastic media. The resonance frequency and the quality (Q) factor of these sensors is typically determined electrically and can be disturbed by parasitic effects caused by the sensor or the interface circuit. To achieve high accuracy the resonator behavior is recorded in vicinity of the resonant frequency and the desired parameters are calculated from this spectral information. For the determination of resonance frequency and Q–factor the use of estimator algorithms which are insensitive to parasitic effects is preferable. We demonstrate advantageous estimator strategies and assess the performance of the specific estimators by evaluating the spectral data of a strongly damped resonant sensor evaluated with two different analyzer instruments.

We investigate a gas density sensor based on quartz crystal resonators for high pressure ( 2.5 × 1 0 6 Pa ) and high temperature ( 340 K ) application. The suitability of tuning fork resonators for density measurement in pure gases has been demonstrated. Furthermore, thickness shear-mode resonators are commonly used for viscosity and density measurement in liquids. In our contribution, these devices are compared with respect to their sensitivity to gas density for the target application in a polymerization reactor, involving high ambient pressures. It was confirmed, that tuning fork resonators are mainly sensitive to density, whereas shear-mode resonators are more suitable for viscosity measurement. Moreover, a density sensor for density measurements in unknown gases and gas mixtures, based on two tuning forks, is presented. At high pressures, an additional pressure-dependent frequency shift has to be considered.

Piezoelectric discs excited by lateral fields (LFE; both electrodes are placed on one side of the disc) show unique differences compared to common thickness field excited (TFE) resonators, in particular when they are used for liquid sensing. In this contribution the LFE-sensor setup is modeled as a layered structure in the spectral (wavenumbers) domain utilizing a semi-numerical approach. In particular the interaction of the piezo-disc and the sample liquid, which is too complex for analytical methods and too comprehensive for FEM, is effciently modeled by the method. The calculation of frequency responses as well as electrical and mechanical fields are illustrated for a simulated setup. The simulation results are compared to results obtained from the Christoffel–Bechmann formalism, and sensitivities to fluid parameters like viscosity and conductivity are shown.

We demonstrate the operation of an Electro Wetting on Dielectrics (EWOD) hybrid lab-on-a-chip system by utilizing a High Fundamental Frequency (HFF; 50MHz) Quartz Crystal Microbalance (QCM) resonator as masssensitive sensor. In a first experiment we have tested the reversible formation of a phosphor-lipid monolayer out of an aqueous buffer suspension of phospholipid vesicles onto the integrated sensor, coated by a Self-Assembled Monolayer (SAM) of 1-octadecanethiol on a gold-covered surface. The altered mass load resulted in a shift of the resonance frequencies. In the second experiment, the formation of a protein multilayer composed of streptavidin and biotinylated immunoglobulin G was monitored. The original resonance frequency was recovered by the complete lipid removal by the detergent octyl-D-glucopyranoside. Using these sample applications, we were able to demonstrate and verify the feasibility of our prototype combining a mass-sensitive QCM sensor with digital microfluidics based on EWOD.

We present a novel micromachined sensor for the viscosity of liquids. The sensor operates at frequencies in the kHz range and consequently its measured values are better comparable to conventional laboratory equipment as those of microacoustic sensors vibrating at several MHz. The sensor utilizes Lorentz force excitation and piezoresistive readout. The first mode of vibration is an in-plane mode with low damping, whereas the overall mass is high. The sensor design is intended to achieve higher quality factors than, e.g., clamped-clamped beams. For the interpretation of the measurement results we take a simple phenomenological model that allows the simultaneous measurement of both viscosity and mass density of liquids.

Liquid level measurement is a key aspect for many applications in the processing industry, chemistry, and pharmaceutical industry to determine, e.g., the exact liquid volume in a reaction chamber. A large variety of measurement principles exist for these applications, ranging from mechanical, electrical, and optical methods to ultrasonic and radar measurements. However, many of these principles are not suitable for sensing very small amounts of liquid volume and liquid levels. Ultrasonic transducers allow for very precise measurements, where the sensitivity can be improved by increasing the operating frequency. In this contribution we introduce the concept of electromagnetic-acoustic resonators as the ultrasonic transducer. Here, we measure the changed frequency shifts and damping characteristics due to interference effects instead of the time-of-flight measurements usually employed. Our experiments show, that by using continuous, resonant excitation the achievable resolution is not limited by the wavelengths of the ultrasonic waves radiated into the liquid. We introduce an experimental setup consisting of a simple resonating element placed inside the fluidic chamber, which is remotely excited by a planar coil. We present an analytical model for the operation of these devices based on finite element simulations of the excited resonant mode shapes. The ability of electromagnetic-acoustic excitation to easily generate many different modes of vibration is also an advantage to simultaneously measure liquid level and other liquid properties.

A quartz disc resonator operating in thickness shear mode was used for the in situ monitoring of the viscosity during zeolite crystal formation.

Electromagnetic excitation of miniaturized acoustic resonator sensors is a novel approach with distinct advantages over piezoelectric resonators. A much wider range of transducer materials can be utilized, and remote excitation of resonant vibrations in a wide variety of different mode shapes is possible. These resonant modes display similar quality factors and characteristics as those in piezoelectric transducers and can be applied for mass detection as well as liquid phase sensing. In this contribution, we focus on the electromagnetic excitation of acoustic face shear mode (FSM) resonators for liquid property sensing. A variety of non-piezoelectric transducer materials has been investigated. For liquid phase sensing, we have found circular face shear mode resonators to be most sensitive to fluid properties, e.g., density and viscosity, while radial flexural plate modes excite compressional waves and are thus most sensitive to fluid volume, or rather the distance to the liquid surface, i.e. liquid level. Experimental results have been compared with an FEM eigenmode analysis and equivalent circuit models providing a better understanding of the generation and detection mechanisms.

Miniaturized liquid sensors are essential devices in online process or condition monitoring. In case of viscosity and density sensing, microacoustic sensors such as quartz crystal resonators or SAW devices have proved particularly useful. However, these devices basically measure a thin-film viscosity, which is often not comparable to the macroscopic parameters probed by conventional viscometers. Miniaturized cantilever-based devices are interesting alternatives for such applications, but here the interaction between the liquid and the oscillating beam is more involved. In our contribution, we describe a measurement setup, which allows the investigation of this interaction for different beam cross-sections. We present an analytical model based on an approximation of the immersed cantilever as an oscillating sphere comprising the effective mass and the intrinsic damping of the cantilever and additional mass and damping due to the liquid loading. The model parameters are obtained from measurements with well-known sample liquids by a curve fitting procedure. Finally, we present the measurement of viscosity and density of an unknown sample liquid, demonstrating the feasibility of the model.

For fluid analysis applications, such as oil condition monitoring, fuel quality, or gas concentration measurements, resonant sensors deliver an outstanding performance when signal processing is optimized and the fluid-mechanical model of the electromechanical resonator is suitable and accurate for the particular resonator. By combining recent advancements, significant improvements in accuracy, measurement speed, dynamic range, and suppression of cross-sensitivities could be achieved. These features enable the development of new solutions for a variety of measurement issues in industry and bio technology. In this contribution the performance of a highly universal evaluation system is demonstrated using a commercially available quartz crystal tuning fork resonator as sensing element for liquid viscosity and mass density. The obtained results are quantified with respect to an accurate lab bench viscosity and mass density meter. A significant advantage of this system is that it operates reliably and accurately even for strongly damped resonators. Therefore, the sensor elements can be used in a larger viscosity range than with alternative evaluation methods.

In this paper, a readout circuit for a thickness shear-mode (TSM) resonator is presented which can be used for sensing applications in liquids such as viscosity sensing. The system features compensation of both spurious capacitances and conductances in parallel to the resonator. This allows measurements even in conductive liquids without the need for an elaborate sealing of the sensor. The influence of the spurious elements is determined by means of two orthogonal synchronous detectors and eliminated by active compensation using voltage-controlled amplifiers (VCAs). Furthermore, the circuit is robust against possible phase errors. The basic concept is discussed in detail, and a readout circuit is developed. A prototype is presented, and sample results are given, demonstrating the feasibility of the approach

Sensors for fluid viscosity and density based on mechanical resonators are commonly modeled as linear systems, allowing a lumped element description as second order harmonic oscillators. To increase the signal-to-noise ratio it is advisable to maximize the oscillation amplitude. As a side effect, this leads to flow rectification known as acoustic streaming. To model this phenomenon we start with a harmonic analysis of the linearized fluid-structure interaction problem. From this solution the time-averaged rectification stresses (Reynolds stresses) are calculated and used as volume forces in a time-dependent laminar flow analysis. This method is applied to in-plane plate resonator structures and tuning fork resonators and compared to experimental investigations using high-speed flow visualization.

In this paper, a novel purely analog electronic readout circuit for sensors based on thickness shear-mode (TSM) resonators is introduced. This system can, e.g., be used for viscosity sensing of liquids, even if the liquid shows a comparatively high viscosity. In contrast to conventionally utilized oscillator circuits, the present circuit eliminates the disturbing influence of the static capacitance of the sensor by means of a dedicated synchronous detector circuit. The sensor is externally driven by a voltage-controlled oscillator (VCO), which is tuned to the resonator's fundamental frequency by means of a control circuit utilizing a frequency modulation of the VCO signal. When the control loop has settled, either the obtained resonance frequency or the damping of the sensor, which is indicated by means of a DC output voltage, can be used as the output signal providing a measure for the viscosity.

In this article we investigate the spurious excitation of compressional waves by thickness-shear-mode resonators, which are commonly used for chemical sensing and viscosity sensing. In particular, we consider the excitation mechanism due to the nonuniform shear displacement present at the sensitive surface of the resonator. To illustrate the basic mechanism we analytically develop a general solution for a two-dimensional model describing the displacement and the pressure distribution in the liquid obtained in terms of Fourier integrals. We discuss these solutions and derive a useful approximation for the far field representing said compressional modes. We finally illustrate the results considering a practical example and associated numerical results.

In this contribution, U-shaped resonators used for viscosity and mass density sensing are presented. These devices were especially designed to reduce and overcome spurious instabilities, which were observed in previous sensor designs. Five sensor designs are presented and their sensitivities to viscosity and mass density are examined. The setups are discussed regarding their working principle, sensitivity, cross-sensitivity to temperature and repeatability. The measurement results in liquids featuring different viscosities and mass densities are shown and the theory necessary to relate the measured data to viscosity and mass density is outlined.

Ultrasonic sensors are well suited for the determination of physical fluid parameters like e.g. mass density, sound velocity and (longitudinal) viscosity. In this contribution we present the recently devised concept of a sensor setup utilizing resonant pressure waves to determine the so called longitudinal viscosity of fluids. Due to a novel cylindrical geometry, spurious diffraction effects are intrinsically avoided so that a computational correction is superfluously. Beside the basic sensor concept we present an according 1D-model of the whole sensor setup and compare simulation results to measurement results obtained with a first prototype device.

Piezoelectric and electrostatic excitation are the standard transduction methods of ultrasonic sensors. However, electromagnetic-acoustic transduction has been demonstrated as a suitable alternative with unique advantages of noncontact excitation and multi-mode vibration in inexpensive materials, such as thin metal plates. We have also demonstrated the use of high-Q silicon membranes as resonator elements. Here, we report on the utilization of these devices as liquid phase sensors for density and viscosity measurements.

In this contribution a concept for a torsional oscillators which is electromagnetically driven and read-out is presented. The aim is to experimentally investigate a principle feasibility for a torsional resonator with application for viscosity and mass density sensing. Such a device is particularly interesting as cylindrical torsional resonators for fluid sensing applications are hardly reported but unlike other devices, would yield pure shear wave excitation in the liquid. The design of first conceptual prototypes and measurement results obtained with these devices are presented.

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.

Acoustic streaming in a sessile droplet can be achieved, e.g., by surface acoustic wave transducers or piezoelectric actuators. We present a novel method using a plate resonator, which is electrodynamically actuated. The liquid droplet rests on a round plate, which is suspended by spring structures and oscillates in its own plane at a resonance frequency around 1 kHz. The resonator loading depends on mass density and (complex) viscosity of the liquid in the vicinity of the contact surface. Actuating the oscillation at the resonance frequency yields high displacement amplitudes, which consecutively leads to acoustic streaming capable of effective stirring within the droplet. The method is used to quantify the stability of two-phase systems such as emulsions and suspensions. After a defined stirring period, the resonator loading is measured every few seconds. Resonance frequency shift and bandwidth are evaluated to derive the viscosity of the liquid two-phase system and monitor the phase-separation.

Resonators are sensitive to their external loading. When a surface is exposed to a liquid, rheological properties can be measured. In contrast to laboratory methods, resonator sensors feature high sensitivity at low viscosity and applicability for online monitoring tasks. On the other hand, the accuracy decreases significantly at higher viscosities. Here, the concept and theory is investigated with the example of an electrodynamic resonator sensor where a sessile droplet of sample liquid is deposited on the sensitive area. The in-plane motion leads to a dominant shear-wave interaction between the fluid and the oscillating structure.