Martin Heinisch

Comparison and experimental validation of two potential resonant viscosity sensors in the kilohertz range

Oscillating microstructures are well established and find application in many fields. These include force sensors, e.g. AFM micro-cantilevers or accelerometers based on resonant suspended plates. This contribution presents two vibrating mechanical structures acting as force sensors in liquid media in order to measure hydrodynamic interactions. Rectangular cross section microcantilevers as well as circular cross section wires are investigated. Each structure features specific benefits, which are discussed in detail. Furthermore, their mechanical parameters and their deflection in liquids are characterized. Finally, an inverse analytical model is applied to calculate the complex viscosity near the resonant frequency for both types of structures. With this approach it is possible to determine rheological parameters in the kilohertz range in situ within a few seconds. The monitoring of the complex viscosity of yogurt during the fermentation process is used as a proof of concept to qualify at least one of the two sensors in opaque mixtures.

A study on tunable resonators for rheological measurements

In this contribution a feasibility study on resonating sensors for rheologic properties such as e.g., viscosity facilitating measurements at tunable frequencies is presented. For the concepts presented in this work, sample liquids are subjected to time harmonic shear stresses induced by a resonating wire and a suspended resonating platelet, respectively. From the resulting frequency response the liquids rheological properties can be deduced by fitting the parameters of an appropriate closed-form model representing the physical behavior of the sensors. To allow large penetration depths of the shear waves being imposed by the resonating mechanism into the test liquid, it is desired to have oscillators with resonance frequencies in the low kilohertz range. Large penetration depths become important when examining complex liquids such as multi-phase systems as, e.g., emulsions. For the investigation of liquids showing shear thinning (or thickening) or viscoelastic behavior, it is necessary to record the liquids characteristics not only at one single frequency but in a range of different frequencies, which in the best case should cover several decades of resonance frequencies. For this purpose, especially in the case of resonating microsensors, it is desired to have devices, which can be operated at tunable frequencies without changing their geometries. For the two concepts presented in this work, the ability of tuning the sensors resonance frequency is based on varying the normal stresses within tungsten wires. The use of appropriate materials and different micro-fabrication techniques are discussed and the applicability of the devices for rheological measurements are outlined. The models are compared to measurement results and the capability of the particular resonator for accurate and reliable sensing is discussed.

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.

Efficient numerical modeling of oscillatory fluid-structure interaction

We present a method to calculate the complex-valued coefficients of fluid loading of immersed mechanical resonators, used as sensors for density, viscosity, and viscoelastic properties. Based on the eigenmode decomposition of structures of arbitrary geometry, the linearized Navier-Stokes equations in the surrounding fluid are used. A complete numerical solution with finite elements is computationally very expensive for most real cases. The critical part is the fine discretization in the boundary layer. In domains away from the oscillating structure, the velocity field can be well approximated by potential flow. We introduce a novel reduced-order model for the fluid interaction which is based on the definitions of an effective added fluid volume, an effective area of shear-wave interaction, and an effective length of viscous interaction. These LAV-parameters are characteristic for a specific resonator geometry and eigenmode, and only weakly dependent on the fluid properties and frequency, so they can be used as the sensors calibration factors.

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.

Droplet mixing and liquid property tracking using an electrodynamic plate resonator

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.

Modeling and data analysis of a multimode resonator sensor loaded with viscous and viscoelastic fluids

In this contribution, we present a novel data-analysis scheme for resonant sensors loaded with viscous and viscoelastic fluids. The suspended-plate resonator has integrated electrodynamic excitation and readout, exhibiting three well-defined modes of vibration below 1 kHz - one uniformly out-of-plane, one translational in-plane, and one out-of-plane wagging, identified by stroboscopic microscopy. Measurements were performed with 20 μl of water, ethanol and silicone fluids with up to 98 mPa.s steady-shear viscosity, resulting in sufficiently high Q-factors. The interaction of the liquid droplet with the resonator is modeled by finite elements analysis (FEA). The dependence of the resonance parameters on the mass-density and viscoelastic moduli is investigated. The material parameters of small sample volumes can be measured with this fast and sensitive method.

Density sensitive driving mode of a double membrane viscometer

This contribution shows the applicability of the double membrane sensor presented earlier for high sensitivity mass density sensing. The sensor is based on two opposed membranes vibrating in parallel in a sample liquid. Excitation and read-out of the membrane vibration are based on Lorentz forces induced in a static magnetic field. Each membrane carries three conductive paths for excitation which can be separately connected to the excitation currents. This possibility allows for switching between viscosity or mass density sensitive driving mode, which is analyzed in this contribution. Measurements with various test liquids show, that the frequency of the fundamental mode strongly decreases with increasing mass density. Comparing the results with measurements achieved with earlier designs indicates an increased sensitivity on density featuring a reasonably sustained quality factor for increasing viscosities.

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.