Precision density and viscosity measurement using two cantilevers with different widths

Abstract

We introduce a novel method for fast measurement of liquid viscosity and density using two cantilevers with different geometries. Our method can be used for real-time monitoring in lab on chip systems and offer high accuracy for a large range of densities and viscosities. The measurement principle is based on tracking the oscillation frequencies of two cantilevers with a phase-locked loop (PLL) and comparing with reference measurements with a known fluid. A set of equations and a simple algorithm is developed to relate the density and the viscosity to the frequency shifts of the cantilevers. We found that the effect of the density and the viscosity can be well separated if cantilevers have different widths. In the experiments, two Nickel microcantilevers (widths 25 μm and 100 μm, length: 200 μm, thickness: 1.75 μm) were fully immersed in the liquid and the temperature was controlled. The actuation was using an external electro-coil and the oscillations were monitored using laser Doppler vibrometer. Thus, electrical connections to the cantilevers are not required, enabling measurements also in conductive liquids. The PLL is used to set the phase difference to 90° between the actuator and the sensor. Calibration measurements were performed using glycerol and ethylene glycol solutions with known densities and viscosities. The measurement error with the new method was lower than 3% in density in the range 995–1150 kg/m3 and 4.6% in viscosity in the range 0.935–4 mPa.s. Based on the signal-to-noise ratio, the minimum detectable difference in the viscosity is 1 μPa.s and the density is 0.18 kg/m3. Further improvements in the range and the accuracy are possible using 3 or more cantilevers with different geometries.