Equivalent circuit model and impedance analysis for the fine response characteristics to liquid viscodensity for a piezoelectric quartz crystal sensor with longitudinal wave effect

In this work, the resonance behavior of a piezoelectric quartz crystal (PQC) operating in the thickness-shear model to solution viscodensity was investigated using the electroacoustic impedance analysis method. It was shown that a slight variation in liquid density caused unexpected large impedance responses of the PQC. The fine structures of the responses of the resonant frequency shift (ΔfS) and motional resistance (Rm) as a function of the density (ρ) and viscosity (η) of the liquid deviated from the linear relationships of ΔfS versus (ρη)1/2 and Rm versus (ρη)1/2. Detail analysis of the correlation between ΔfS and Rm versus (ρη)1/2 showed periodic waveforms, revealing the presence of longitudinal wave. The properties of the longitudinal wave could be integrated with the thickness shear wave with a modified BVD equivalent circuit model. The validity of the equivalent circuit was supported by the experimental observations, and the fitting of experimental data with the equivalent circuit simulation was further improved with the consideration of the second and third harmonics of the longitudinal waves. While the longitudinal wave effect has been regarded as a source of error in the PQC measurements, our study demonstrated that it is possible to control the periodicity and intensity of the longitudinal wave and to generate additional information on the solution properties utilizing the longitudinal wave effect.