Analysis and experimental verification of a metallic suspended plate resonator for viscosity sensing
Introduction
In a wide range of applications, such as oil condition monitoring [1], ink mixing, medical analysis [2], or materials research [3], [4], sensors for measuring the deformation properties of liquids directly in a process or as part of fluidic analysis systems, are required.
The viscoelastic properties of liquids with complex flow behavior can be analyzed in the lab by oscillatory methods, where the frequency-dependent loss and storage mechanisms are measured at frequencies up to a few hundred hertz [5]. On the other hand, common viscosity sensors operate at much higher frequencies, a few Megahertz in the case of TSM resonators [6], or above hundred Megahertz in the case of surface acoustic wave (SAW) devices [7]. The probed rheological regime turns out to be essentially different [8], [9], [10]. Therefore, state-of-the-art online microacoustic sensors are mainly applicable to simple (Newtonian) liquids, where a single, constant viscosity parameter is sufficient for a wide range of shear rates and frequency.
Structured liquids, like suspensions, emulsions and some polymer solutions, are usually characterized by long thermodynamic relaxation time constants compared to molecular processes [11]. The parameter of interest often is the steady-shear viscosity, hence a low frequency regime is preferable to measure viscosity.
Some new concepts use low-frequency Lorentz-force excited resonators [12], [13], [14]. These devices mainly exhibit out-of-plane motion, generating rather non-uniform velocity fields. This results in high fluid damping even in moderately viscous liquids, caused by spurious compressional waves and dominating boundary effects [15].
In [9], a cantilever with a resonance frequency in the range of kilohertz was utilized to measure the viscosity of non-Newtonian liquids, where a TSM-quartz sensor measures different values. Recent experiments with suspensions of SiO2 (20–22 nm) in water emphasize the requirement for low-frequency devices [10]. In our approach, the dominating effect is the excitation of a shear-wave with rather uniform amplitude distribution (except for boundary effects) [16], [17]. The presented concept of an in-plane resonator operates in the low kilohertz range. This way, the deformation regime comes closer to that used in laboratory methods. Additionally, the gap between the low-frequency data obtained using oscillatory shear-flow methods and data obtained using acoustic methods is closed.
Section snippets
Sensor principle
The sensor element consists of a 0.1 mm thick plate suspended on four springs, structured using lithography and wet-etching as shown in Fig. 1. The element is fully metallic (nickel–brass) which has the advantage of a high electric conductivity, and a relatively high mass density kg m−3. Optional gold plating improves the surface properties so that it can withstand corrosive environments. The sensor element is mounted on a printed circuit board (PCB) centered above a 6 mm diameter hole,
Numerical approach
The sensor modeling starts from a numerical finite elements analysis (FEA). The commercial software package COMSOL multiphysics 3.5 is used. Using this method, the mechanical and electrical behavior of the device can be modeled at once, including a good approximation of the fluid-structure interaction. The two-dimensional geometry is shown in Fig. 5, together with exemplary results. The electrical AC analysis module is used together with the mechanical plane stress module. The FEA approach is
Experimental verification
For the measurements, a differential excitation signal is applied as shown in Fig. 1 to terminals 1 and 2. The voltage is measured between terminals 3 and 4, assuming that the measurement current is zero: , see Fig. 7. Using the electrical equivalent model, the component parameters of the RLC parallel resonance circuit are derived by a least squares algorithm. Spurious electrical coupling is incorporated by allowing arbitrary complex values for . The results of this fit algorithm
Conclusions
We introduced a novel resonant sensor for liquid properties, featuring low-frequency (i.e. around 5 kHz) in-plane fluid–structure interaction with Lorentz-force actuation and inductive readout. The characteristics of the device qualifies this sensor concept for the analysis of complex liquids with frequency-dependent material properties. Viscosity and mass density both influence on the frequency response of the fully immersed resonator. The primary effect is the excitation of a shear wave in the
Acknowledgements
The authors would like to thank Bernhard Mayrhofer (IME, JKU Linz) for manufacturing the devices. This work was supported by the Austrian Science Fund (FWF) Project L103-N07, the Austrian Center of Competence in Mechatronics (ACCM), and ESA (Belgian PRODEX programme).
Erwin K. Reichel was born in Linz, Austria, in 1979. He received the Dipl.-Ing. (M.Sc.) degree in mechatronics from Johannes Kepler University, Linz, Austria, in 2006. From 2006 to 2009 he was working at the Institute for Microelectronics and Microsensors of the Johannes Kepler University, Linz. In 2009 he obtained his doctoral (Ph.D.) degree and started a post-doctoral position at the Centre for Surface Chemistry and Catalysis, KU Leuven, Belgium. The main research fields are the modeling,
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Erwin K. Reichel was born in Linz, Austria, in 1979. He received the Dipl.-Ing. (M.Sc.) degree in mechatronics from Johannes Kepler University, Linz, Austria, in 2006. From 2006 to 2009 he was working at the Institute for Microelectronics and Microsensors of the Johannes Kepler University, Linz. In 2009 he obtained his doctoral (Ph.D.) degree and started a post-doctoral position at the Centre for Surface Chemistry and Catalysis, KU Leuven, Belgium. The main research fields are the modeling, design, and implementation of sensors for liquid properties.
Christian Riesch was born in Feldkirch, Austria, in 1979. He received the Dipl.-Ing. (M.Sc.) degree in electrical engineering from the Vienna University of Technology (VUT), Vienna, Austria, in 2005. From 2005 to 2009 he worked at the Institute of Sensor and Actuator Systems of VUT, and obtain his doctoral (Ph.D.) degree in 2009.
Franz Keplinger studied electrical engineering at the Vienna University of Technology (VUT) and received his MS degree in 1986. In 1987, he joined the group of sensors and biomedical microsystems at the Institute for Electrical Engineering and Electronics and worked in the field of electrochemical microsensors and sensor systems. He developed miniaturized thin-film ion sensors and methods for their characterization. In 1995, he received his Ph.D. degree in electrical engineering (Thesis: “Miniaturized ion-selective electrodes”). Current research issues are micromechanical magnetic field sensors and thermal flow sensors. In 2007, he received his Venia docendi for sensors (Vienna University of Technology: “Contributions to miniaturized sensors”).
Christine E.A. Kirschhock Christine Kirschhock obtained her Dipl.-Ing. in Physical Chemistry and her doctoral degree in Material Sciences from the Technical University Darmstadt, Germany, in 1990 and 1995, respectively. From 1996 she worked as Research Assistant in the Department for Structure Analysis and Crystallography of the faculty of Material Sciences in Darmstadt and joined in 1997 the Center for Surface Chemistry and Catalysis of the Katholieke Universiteit Leuven, Belgium, where she became Assistant Professor in 2003 and full professor in 2005. Throughout her career Christine Kirschhock studied structure and formation of catalysts based on porous materials and in this context also is involved in development of hardware and diagnostics. Currently she is the coordinator of the international Topical Team of ESA for zeolite crystallization and consultant for the European Science Foundation and the Research Foundation—Flanders.
Bernhard Jakoby obtained his Dipl.-Ing. (M.Sc.) in Communication Engineering and his doctoral (Ph.D.) degree in electrical engineering from the Vienna University of Technology (VUT), Austria, in 1991 and 1994, respectively. In 2001 he obtained a Venia legendi for Theoretical Electrical Engineering from the VUT. From 1991 to 1994 he worked as a Research Assistant at the Institute of General Electrical Engineering and Electronics of the VUT. Subsequently he stayed as an Erwin Schrödinger Fellow at the University of Ghent, Belgium, performing research on the electrodynamics of complex media. From 1996 to 1999 he held the position of a Research Associate and later Assistant Professor at the Delft University of Technology, The Netherlands, working in the field of microacoustic sensors. From 1999 to 2001 he was with the Automotive Electronics Division of the Robert Bosch GmbH, Germany, where he conducted development projects in the field of automotive liquid sensors. In 2001 he joined the newly formed Industrial Sensor Systems group of the VUT as an Associate Professor. In 2005 he was appointed Full Professor of Microelectronics and Microsensors at the Johannes Kepler University Linz, Austria. He is currently working in the field of liquid sensors and monitoring systems.
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