The oscillation frequency of a quartz resonator in contact with liquid

Abstract

A simple relationship is derived which expresses the change in oscillation frequency of a quartz crystal in contact with a fluid in terms of material parameters of the fluid and the quartz. The relationship is Δf = -f 3 20(ηLρ{variant}L/πμQρ{variant}Q) 1 2, where f0 is the oscillation frequency of the free (dry) crystal, ηL and ρ{variant}L are the absolute viscosity and density of the liquid, respectively, and μQ and ρ{variant}Q are the elastic modulus and density of the quartz. This relation is obtained from a simple physical model which couples the shear wave in the quartz to a damped shear wave in the fluid. Quantitative comparisons with two test cases, aqueous solutions of glucose and ethanol at various concentrations, demonstrate the accuracy of this model. © 1985.