Abstract
A hydrodynamic model of using quartz tuning forks (QTFs) for density and viscosity sensing, by measuring the resonance frequency and quality factor, has been established based on the cantilever beam theory applied to the atomic force microscope (AFM). Two examples are presented to verify the usability of this model. Then, the Sobol index method is chosen for explaining quantitatively how the resonance frequency and quality factor of the QTFs are affected by the fluid density and viscosity, respectively. The results show that the relative mean square error in viscosity of the eight solutions evaluated by the hydrodynamic model is reduced by an order of magnitude comparing with Butterworth–Van Dyke equivalent circuit method. When the measured resonance frequency and quality factor of the QTFs vary from 25,800–26,100 Hz and 28–41, the sensitivities of the quality factor affected by the fluid density increase. This model provides an idea for improving the accuracy of fluid component recognition in real time, and lays a foundation for the application of miniaturized and cost-effective downhole fluid density and viscosity sensors.
Highlights
The measurement of fluid density and viscosity is essential in petrochemical, food, automotive and textile industries
In order to estimate the density and viscosity of a liquid at the same time, the hydrodynamic model based on the work of Sader, J.E. [35] for the atomic force microscope (AFM) is established, and two examples are verified by using this model
The hydrodynamic model, as shown in Equations (13) and (14), is used to reverse the density and viscosity of the fluid according to the resonance frequency and quality factor of the quartz tuning forks (QTFs)
Summary
The measurement of fluid density and viscosity is essential in petrochemical, food, automotive and textile industries. For more than a decade, tuning fork sensors have been used to detect the density and viscosity of fluids in complex downhole environments [4,5,6,7,8,9]. The Butterworth–Van Dyke equivalent circuit is an important method to study the measurement of liquid density and viscosity [12,13,14,15,16,17]. In this method, a tuning fork resonator can be seen as a series connection of resistor, capacitor and inductor. In order to estimate the density and viscosity of a liquid at the same time, the hydrodynamic model based on the work of Sader, J.E. [35] for the atomic force microscope (AFM) is established, and two examples are verified by using this model
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