Simple frequency-based sensing of viscosity and dielectric properties of a liquid using acoustic resonators

The effects of a finite polarizability of a liquid sample onto the series resonance frequency of a piezoelectric resonator are described within the small-load approximation. It is found that the sample's electrical capacitance (the ratio of surface potential and surface polarization at the crystal surface) enters the motional branch of the equivalent circuit, thereby shifting the series resonance frequency. This effect is caused by piezoelectric stiffening. Using a conventional quartz crystal with small hole in the front electrode and exposing this crystal to a variety of different liquids, we demonstrate that derived equation describes the experiment reasonably well. Electric and dielectric effects are particularly strong for torsional resonators, which operate at a frequency of around 56 kHz. These are in commercial use for determination of the viscosity of engine oils. We propose a simple method to in situ switch the strength of piezoelectric stiffening. It allows separation of the viscoelastic parameters from the electric polarizability. It could, for instance, be used to differentiate between gasoline and water being accidentally admitted to the lubricant reservoir. The instrument requires a single resonator and is based on the determination of only 2 frequency shifts.