Measurement of the viscosity of liquids using a longitudinally vibrating PZT ceramic and electric impedance measurements

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Abstract
A simple and very accurate method for measuring the viscosity of liquids is presented. A vibrating lead zicronate titanate (PZT) ceramic polycrystalline resonator is totally immersed in a liquid and the oscillation behavior is studied both analytically and experimentally. The vibrating ceramic generates a shear wave traveling in the surrounding fluid normal to the surface of the resonator with heavy damping. The PZT is modeled as a vibrating thin plate. The resulting 1D governing equation of motion, which includes the effect of damping, is solved with the appropriate damped boundary conditions using impedance methods. The resonance frequency of a PZT immersed in a fluid is shown to be a function of the PZT parameters and the product of the fluid density and viscosity. Fluid loading is shown to lower the resonance frequency of the ceramic and both diminish and broaden the impedance plot near resonance. Unlike previous methods utilizing crystal shear-mode resonators, this method is valid for both low and high viscosity values. The proposed method provides viscosity values within 10 percent accuracy compared to tabulated values. The current study also provides an equivalent circuit model for the PZT in fluid loading. Immersing the PZT in a liquid increases both the inductance and the resistance of the unperturbed ceramic. The calculated elements of the equivalent circuit compare well with the values obtained using a best-fit statistical model.

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