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E. Benes, H. Nowotny, S. Braun, S. Radel, M. Gröschl:
"Analytical sensor response function of viscosity sensors based on layered piezoelectric thickness shear resonators";
Physics Procedia, 70 (2015), 236 - 240.

Resonant piezoelectric sensors based on bulk acoustic wave (BAW) thickness shear resonators are promising for the inline measurement
of fluid viscosity, e.g., in industrial processes. The sensor response function can be derived from the general rigorous
transfer matrix description of one-dimensional layered structures consisting of piezoelectric and non-piezoelectric layers of arbitrary
number. This model according to Nowotny et al. provides a complete analytical description of the electrical and mechanical
behaviour of such structures with two electrodes and arbitrary acoustic termination impedances (Rig-1d-Model). We apply this
model to derive the sensor response functions and the mechanical displacement curves of the following configurations appropriate
for viscosity sensors:
(a) An AT cut quartz crystal plate in contact with vacuum at the backside plane and with the liquid under investigation at the
front side plane (QL).
(b) An AT cut quartz crystal in contact with the liquid under investigation at both sides (LQL).
It is shown that in the QL case the originally only heuristically introduced and well established sensor response function according
to Kanasawa can be derived from the Rig-1d-Model by introducing minor approximations. Experimental results are presented for
the LQL configuration using an N1000 viscosity reference oil as test fluid.

http://dx.doi.org/10.1016/j.phpro.2015.08.144