Mechanical response of thickness-shear mode quartz-crystal resonators to linear viscoelastic fluids

A mechanically based description of the response of thickness-shear mode quartz-crystal resonators to contact with linear viscoelastic fluids is presented. The calculation describes the effect of viscoelasticity in terms of a dimensionless correction to the Newtonian result, χ which is primarily dependent on the product of the dominant relaxation time of the overlying medium and the oscillation frequency of the resonator. The results show that the effect of a finite relaxation time is a lower frequency shift compared to a viscous reservoir with identical density and a viscosity matching the low-frequency limit of the viscoelastic reservoir. This is due to reduced viscous dissipation in the boundary layer adjacent to the crystal surface and an effectively smaller inertial load on the resonator. The model is shown to reduce appropriately to previously published results in the low- and high-frequency limits, in addition to predicting correctly experimental results for polymeric fluids assuming Rouse-like behaviour.