Reduced order models for resonant viscosity and mass density sensors

A generalized reduced order model for resonant viscosity and mass density sensors is presented and experimentally verified. The reduced expressions for the resonance frequency and quality factor, respec- tively, are mathematically valid for in-plane oscillating plates, oscillating spheres and laterally oscillating cylinders. However, as shown for measurements obtained with a tuning fork resonator with rectangular cross-section, the model can also be applied for resonating structures, for which closed form solutions of the fluid structure interaction are not available. Benefits of the presented model are amongst others first, its simplicity, which requires no more than three calibration measurements for parameter identification and second, its general applicability for resonant mass density and viscosity sensors which furthermore facilitates the comparison of different resonant mass density and viscosity sensors in terms of sensitivity and measurement noise propagation.