Characterization of the behaviour of a quartz crystal resonator fully immersed in a Newtonian liquid by impedance analysis

The response in resonance frequency and dissipation of a quartz crystal resonator totally immersed in a liquid medium was theoretically and experimentally studied as a function of overtone number along a wide overtone range. In the experimental part it was observed that parasitic effects caused by finite crystal size and interference with inharmonic modes reduce the experimental valid overtone domain. In particular, it was shown that the fundamental mode significantly deviates from other harmonics trend. In the valid working domain, it was observed that the dissipation and resonance frequency follow a regular behaviour versus overtone number. A model that accounts for the interfacial factors through two parameters in addition to viscous damping was developed to reproduce the experimental behaviour observed as a function of overtone order. One parameter represents the thickness of a virtual viscoelastic layer deposited onto the crystal surface whereas another parameter takes into account the contribution of interfacial effects on the dissipation. The proposed model leads to an excellent agreement with experiments of both resonance frequency and bandwidth despite the presence of only one parameter in each expression. Moreover, carrying out comparison with various liquids having an electrical conductivity below 10−6 S/m and covering a wide range of viscosity-density product shows that the parameter occurring in the expression of dissipation only depends on the quartz resonator characteristics whereas the other coefficient is linked to both quartz oscillator and liquid behaviours.