Prediction ability of a lumped-element equivalent-circuit model for thickness-shear mode resonators in liquids

The viscosity-density prediction ability of a lumped-element equivalent-circuit model for a thickness-shear mode resonator operating in Newtonian liquids is examined. The model is a Butterworth-Van Dyke equivalent-circuit modification that describes the near-resonance electrical characteristics of a liquid-loaded resonator. By comparing the relative significance of different Toad contributions, a simplified liquid-phase lumped-element model is introduced. This model is calibrated with an admittance measurement on a resonator in contact with water. With the calibrated model, the liquid viscosity-density product is predicted from measurements made in aqueous glycerol solutions. These predictions are found to be accurate compared to the literature values. In addition, the predicted value for the average surface roughness of the resonator is consistent with the presented SEM micrographs.