Calibration procedure for piezoelectric MEMS resonators to determine simultaneously density and viscosity of liquids

Abstract

The main objective of this work is the assessment of a calibration method for piezoelectric MEMS resonators for simultaneous density and viscosity sensing. A device designed to resonate with the 2nd order out-of-plane modal vibration (13-mode) was immersed in several test liquids (i.e. D5, N10, N35, PAO8, olive oil, ester oil, DITA and N100). Two important parameters were estimated from the electrical impedance characterization: the quality factor and the resonant frequency. Once these two parameters are known, the viscosity and density of the liquids under test were determined following different calibration models. An advanced calibration model, based on a Taylor series of the hydrodynamic function, was established as a suitable method for determining the density and viscosity with the lowest calibration error. Our results demonstrate that the calibration coefficients, obtained in the calibration process, are valid in a temperature range between 20 and 40 °C in liquids with viscosities up to 300 mPa s. Furthermore, the estimated density and viscosity values with the MEMS resonator were compared to the values obtained with a commercial density–viscosity meter, reaching a mean calibration error in the best scenario of around 0.4% for the density and 2.8% for the viscosity.