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J. Toledo, V Ruiz-Díez, G. Pfusterschmied, U. Schmid, J.L. Sànchez-Rojas:
"Calibration procedure for piezoelectric MEMS resonators to determine simultaneously density and viscosity of liquids";
Microsystem Technologies - Micro- and Nanosystems - Information Storage and Processing Systems, 24 (2018), 1423 - 1431.

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-ofplane
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.

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-ofplane
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.

http://dx.doi.org/10.1007/s00542-017-3536-0