Erwin K. Reichel

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.

Characterizing Vibrating Cantilevers for Liquid Viscosity and Density Sensing

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.

A suspended plate viscosity sensor featuring in-plane vibration and piezoresistive readout

Miniaturized viscosity sensors are often characterized by high-resonance frequencies and low-vibration amplitudes. The viscosity parameter obtained by such devices is therefore not always comparable to those probed by conventional laboratory equipment. We present a novel micromachined viscosity sensor with relatively low operating frequencies in the kHz range. The sensor utilizes Lorentz force excitation and piezoresistive readout. The resonating part consists of a rectangular plate suspended by four beam springs. The first mode of vibration is an in-plane mode. Thus, the contribution of the moving plate to the device damping is low, whereas the overall mass is high. This principle improves the quality factor and gives additional freedom to the device designer. This paper presents the device concept, the fabrication process and a prototype of the viscosity sensor. Measurement results demonstrate the feasibility of the device and show that the damping of the device is an appropriate measure for the viscosity.

A micromachined doubly-clamped beam rheometer for the measurement of viscosity and concentration of silicon-dioxide-in-water suspensions

In this contribution we demonstrate the feasibility of a sensor system for viscosity and concentration measurement of complex liquids, in particular suspensions of silicon dioxide particles in water. The sensor system is based on a doubly clamped micromachined beam vibrating in the sample liquid, and an optical readout utilizing a DVD player pickup head. The vibrating beam features resonance frequencies in the range of several 10 kHz, and higher mechanical amplitudes than microacoustic sensors, e.g., quartz thickness shear mode (TSM) resonators or surface acoustic wave (SAW) devices. We show that the damping of the beam is dominated by the viscosity of the liquid, and that this relation also holds for the considered complex liquids, whereas a TSM resonator sensor fails to detect the steady state shear viscosity of the suspensions.

A Novel Sensor System for Liquid Properties Based on a Micromachined Beam and a Low-Cost Optical Readout

For the measurement of liquid parameters like viscosity and density vibrating micromachined structures offer useful alternatives to bulky conventional measurement equipment. Evaluating the shift of the resonance frequency and the change of the damping factor of such devices allows the simultaneous determination of viscosity and density. Furthermore, these sensors can even be used for complex liquids like emulsions where other microacoustic sensors like TSM quartz resonators, in comparison to conventional laboratory viscometers, measure in a different rheological domain. In our contribution we present a novel implementation of a viscosity and density sensor system utilizing a doubly-clamped vibrating micromachined beam. The beam deflection is determined by means of a laser pickup head as it is used, e.g., in DVD drives, yielding high sensitivity and a low-cost setup at the same time. The measured damping factor correlates well with the viscosity of the respective liquid, whereas the resonance frequency is also influenced by the liquids density.

A Novel Combined Rheometer and Density Meter Suitable for Integration in Microfluidic Systems

In this contribution we present a combined rheometer and density meter based on two vibrating membranes carrying electrically conductive paths for excitation and readout. The liquid is contained in a 100 mul volume between the rectangularly clamped membranes. The vibration is excited by Lorentz forces arising from a static magnetic field provided by a permanent magnet and the current through the excitation path going back and forth on the vibrating part of the membrane. The sensor element is designed in such a way that the viscous liquid is subjected to shear stress. Additional conductive loops on the membrane perform the sensor readout by means of the induced voltage due to motion in a static magnetic field. The measured frequency response in a range from 500 Hz to 15 kHz allows the determination of the fluids mass density and viscosity. This novel sensor design is well suited for miniaturization and the integration in microfluidic platforms.

Phase contrast method for measuring ultrasonic fields

Pulsed acoustic waves in water generated by ultrasonic transducers with power levels in the medical diagnostic range are characterized by analyzing the optical diffraction patterns of short laser pulses due to the pressure waves to be analyzed. The diffracted laser light is filtered in the Fourier plane of an optical system and projected onto a charge-coupled-device camera to be grabbed and further processed. Using this technique, it is possible to measure and characterize the ultrasound field in minutes time, which would otherwise last hours or days using the standard method of measuring the intensity on a fine three-dimensional grid with a hydrophone. In addition, the phase information of the ultrasonic wave is acquired easily.

Characterizing Resonating Cantilevers for Liquid Property Sensing

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 macroscopic measurements. 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 by a curve fitting procedure.

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.