Fluid impedance model for resonator viscosity sensors

Electromechanical resonators are used as viscosity sensors where the effect of the fluid loading on the resonance parameters is evaluated. A complete numerical analysis is often unrealistic due to the large computational effort. We introduce a reduced-order fluid impedance model valid for a large class of geometries. The fluid structure interaction is characterized by three paramete rs, an effective volume, an effective interaction surface, and an effective length. For idealized geometries these parameters can be derived analytically. We derive scaling laws for rectangular cross sections which are relevant for quartz tuning fork resonators.