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 Δ f = - f 3/2 0(η Lϱ L/πμ Qϱ Q) 1/2 , where f 0 is the oscillation frequency of the free (dry) crystal, η L and ϱ L are the absolute viscosity and density of the liquid, respectively, and μ Q and ϱ 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.
- Publication:
-
Analytica Chimica Acta
- Pub Date:
- 1985
- DOI:
- 10.1016/S0003-2670(00)82721-X
- Bibcode:
- 1985AcAC..175...99K