Analytical 3D-analysis of compressional wave excitation by thickness-shear-mode resonators

Piezoelectric thickness-shear-mode resonators are well established as viscosity and chemical liquid sensors. When immersed in the sample liquid, the resonator excites a strongly damped shear-polarized wave as well as spurious compressional waves in the liquid. The latter are scarcely damped, which can lead to disturbing interferences if they are reflected by obstacles close to the sensor. In order to analyze the spurious compressional wave excitation, we developed a three-dimensional mathematical model utilizing solutions of the linearized Navier-Stokes equation in the spatial Fourier-domain, which govern the acoustic field in the liquid. Finally, we discuss the solutions and illustrate the results by considering practical examples.