Higher Order Models for Resonant Viscosity and Mass Density Sensors

Advanced fluid models relating viscosity and density to resonance frequency and quality factor of vibrating structures immersed in fluids are presented. The numerous established models which are ultimately all based in the same approximation are refined, such that the measurement range for viscosity can be extended. Based on the simple case of a vibrating cylinder and dimensional analysis, general models for arbitrary order of approximation are derived. Furthermore, methods for model parameter calibration and the inversion of the models in order to determine viscosity and/or density from measured resonance parameters are shown. One of the two presented fluid models is a viscosity-only model, where the parameters of it can be calibrated without knowledge of the fluid density. The models are demonstrated for a tuning fork based commercial instrument, where maximum deviations between measured and reference viscosities of approximately ±0.5% in the viscosity range from 1.3 to 243~mPas could be achieved. It is demonstrated that these results show a clear improvement over the existing models.