A Viscosity and Density Measurement Scheme without Using Q-factor and Parameter Calibration

The measurement of viscosity and density in liquid is crucial for industrial production, healthcare, and petrochemical industries. Cantilever-based viscosity-density sensors are widely studied due to their fast response, high sensitivity and high resolution. Although a single cantilever is used for measuring viscosity and density, the decoupling model necessitates quality factor (Q-factor) as an input variable, and parameter calibration with a known viscosity-density. In this paper however, a viscosity and density measurement scheme without using Q-factor and parameter calibration, but utilizing two resonant frequencies of double-cantilever configuration, is proposed via establishing a theoretical model and validating with a prototype. Compared to that of measured data with the viscometer and the densitometer, the relative error with double-cantilever configuration is 1.10-2.53% for viscosity and 0.82-1.64% for density, with a measurement range of 55.3 mPa·s -91.1 mPa·s and 1217 kg/m³-1223 kg/m³, respectively. Compared to that with single cantilever, the measurement accuracy with double-cantilever configuration is numerically improved by 5% for viscosity and 36% for density, with a measurement range of 10 mPa·s -100 mPa·s and 700 kg/m³-1300 kg/m³, respectively. The proposed viscosity and density measurement scheme are both size-free and geometry-free, and applicable to various processes from micro-nano fabrication to precision manufacturing.