Simultaneous liquid viscosity and density determination with piezoelectric unimorph cantilevers

We have examined both experimentally and theoretically a piezoelectric unimorph cantilever as a liquid viscosity-and-density sensor. The fabricated piezoelectric unimorph consisted of a PbO⋅ZrO2⋅TiO2 (PZT) layer on a thin stainless-steel plate. In addition to a driving electrode, a sensing electrode was placed on top of the PZT layer, permitting the direct measurement of the resonance frequency. The cantilever was tested using water–glycerol solutions of different compositions. In all three of the tested modes, the resonance frequency decreased while the width of the resonance peak increased with increasing glycerol content. To account for the liquid effect, we consider the cantilever as a sphere of radius R oscillating in a liquid. By including the high and low frequency terms in the induced mass and the damping coefficient of the liquid, we show that for a given liquid density and viscosity the oscillating-sphere model predicts a resonance frequency and peak width that closely agree with experiment. Furthermore, the viscosity and the density of a liquid have been determined simultaneously using the experimentally measured resonance frequency and peak width as inputs to the oscillating-sphere model. The calculated liquid viscosity and density closely agreed with the known values, indicating that our cantilever-based sensor is effective in determining viscosity and density, simultaneously. We also show that scaling analysis predicts an increase in the width of the resonance peak with decreasing cantilever size, an observation in agreement with the large peak widths observed for microcantilevers.