On the modeling of a piezoelectrically actuated microsensor for simultaneous measurement of fluids viscosity and density Ghader Rezazadeh ⇑ , Mina Ghanbari, Iraj Mirzaee, Aliasghar Keyvani Mech. Eng. Dept., Faculty of Eng., Urmia University, Urmia, Iran article info Article history: Received 13 October 2009 Accepted 31 August 2010 Available online 8 September 2010 Keywords: MEMS Fluid Viscometer Densitometer Piezoelectric actuation abstract This paper deals with the analysis of a novel micro–electro-mechanical (MEM) fluid den- sity and viscosity sensor. The proposed sensor consists of a micro-beam and a sensing micro-plate immersed in a fluid. In order to actuate longitudinally the micro-beam and micro-plate, the sensor includes a pair of piezoelectric layers bonded to the upper and lower surfaces of the micro-beam and subjected to an AC voltage. The coupled governing partial differential equations of longitudinal vibration of the micro-beam and fluid field have been derived. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions. The enhanced equations have been discretized over the beam and fluid domains using a Galerkin based reduced order model. The dynamic response of the sensing plate for different piezoelectric actuation voltages and different exciting frequen- cies has been investigated. The effects of viscosity and density of fluids and geometrical parameters of the sensor on the response of the sensing plate have been studied. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Physical systems and applications as diverse as the flow of fluids in pipes, the flow of blood, lubrication of engine parts, and pharmaceutical and petroleum industries are all involved in fluid viscosity and density. Various mechan- ical vibration-based viscosity–density sensors are available for measuring liquid viscosity and density by sensing the force required to induce motion. Magneto restrictive wave guide viscometers are used to measure viscosity. It is based upon the retardation of the transmission of a torsion sound wave through a solid by the surface interaction of the transmitted wave with the viscous fluid in contact with the solid [1]. Oscillating cylinder viscometers and densi- tometers are the other kind of sensors for viscosity and density measurement. It is based on oscillations of a hol- low cylinder in its longitudinal direction. This device can be immersed in the tank of liquid of interest and send nec- essary information via wireless communications back to the operator [1]. Quartz crystal resonator [2] and ultrasonic plate wave [3] are also used to measure fluid viscosity. MEMS-based technologies enable the fabrication of small, low power, fast response times sensors in order to measure the fluid properties. Properly designed and packed MEMS sensors can easily withstand the extreme temperature (200 °C) and pressure (100 MPa). Various MEMS-based sensors as micro-cantilever sen- sors have found utility in a variety of fields, especially those for sensing applications. Many groups have studied such systems for their applications to atomic force microscopy (AFM) which is based on the resonant of a cantilever fabri- cated with micro–electro-mechanical systems (MEMS), to analyze surface with nanometer resolution [4,5]. Another application of micro-cantilevers is measuring physical properties of fluids such as their viscosity and density [6–9]. Also several mathematical modeling studies have been done on effect of excitation voltage on micro-cantile- ver sensors, including the deflection properties of piezoelec- tric materials [10,11]. As one of the methods, viscosity 0263-2241/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2010.08.022 ⇑ Corresponding author. Tel.: +98 914 1451407; fax: +98 441 2777022. E-mail address: g.rezazadeh@urmia.ac.ir (G. Rezazadeh). Measurement 43 (2010) 1516–1524 Contents lists available at ScienceDirect Measurement journal homepage: www.elsevier.com/locate/measurement