Impedance analysis of thickness-shear mode quartz crystal resonators in contact with linear viscoelastic media

An electromechanical description of the impedance response of thickness-shear mode quartz crystal resonators in contact with linear viscoelastic media is presented. Explicit assignments for equivalent circuit parameters (resistances, inductances, and capacitances), are derived in terms of the properties of the resonant piezoid and damping fluid medium. The calculation shows that the effect of fluid elasticity is a reduction in both the equivalent resistance and inductance relative to a corresponding viscous bulk. The lower inductance is due to a reduced decay envelope for shear wave propagation into the liquid; in effect, a smaller mass of liquid is “dragged” by the crystal. The lower equivalent resistance is due to the combined effect of lower energy dissipation and enhanced recoverable energy storage within the mechanically active fluid layer near the crystal surface. Comparison of model predictions with published results on a variety of undamped, viscously damped, and viscoelastically damped crystals shows very good agreement.