Modeling-free evaluation of resonant liquid sensors for measuring viscosity and density

Abstract

A performance estimation method for resonant viscosity and density sensors is described. The ultimate sensor precision and the separability of density and viscosity from measured frequency spectra are estimated. The approach relies on using recently introduced models which are flexible enough to describe a large class of sensors. It is therefore not required to develop a specific sensor model and a parameter extraction method for each newly devised sensor. With the method introduced in this contribution, it is sufficient to adjust and validate a general model using at least three test liquids. Then, the error propagation and the error bounds for viscosity and density can be estimated and consequently the required signal-to-noise ratio (SNR) or the amount of required data points can be determined. This method enables direct comparison of different sensor setups as will be demonstrated for piezoelectric tuning fork sensors, electrodynamic platelet sensors and steel tuning forks.

Fluid Sensing Using Quartz Tuning Forks—Measurement Technology and Applications

“…Due to several advantages of using QTFs for fluid sensing, sophisticated setups have been proposed e.g., by [12,13] prior to our work. With this work, we extend the discussions from [11] to QTFs and compile the key findings of our own work from [14,15,16,17,18,19,20,21,22] into one consistent manuscript and demonstrate that accurately measured fluid parameters facilitate numerous applications, some of which are demonstrated in this paper.…”

“…The propagation of measurement noise on current i(t) and voltage V(t) signals to resonance parameters f0 and Q is considered in [41]. Based on Equation (4), the propagation of noise to ρ and η can be determined [17,20]. As a rule of thumb, measurement noise provokes relative deviations which are typically more than ten times higher on viscosity than on density.…”

Higher-Order Models for Resonant Viscosity and Mass-Density Sensors

“…Consequently, the model from Heinisch et al, yields lower deviations between the fluid reference values and the measured values, as is also outlined in [ 26 ]. For the above mentioned models, the closed form solutions for the fluid force of vibrating cylinders have been approximated by a power series in the Reynolds number, where a low order of approximation was chosen in order to obtain models which can be rearranged yielding simple expressions for and [ 29 ].…”

“…As the exact hydrodynamic function is only known for some special cases, the conventionally used fluid models derived, e.g., by [22][23][24][25][26] are all based on an approximation of the hydrodynamic function of a vibrating prismatic beam featuring a cylindrical cross-section by means of a truncated power series. A remarkable fact, shown by a many researchers in experimental work [22][23][24][25][26][27][28][29][30][31], is that the resulting reduced order models with adjustable parameters are suitable for representing various different types of fluid loaded vibrating structures, including cantilevers of different cross-sections, large steel and miniaturized quartz tuning forks, spiral springs, platelets, U-shaped wires, piezo buzzers in fluids, etc. However, the limitations of the approximation being made to obtain models of manageable complexity, narrows the accurately measurable range of fluid parameters.…”

Electromechanical resonators for sensing fluid density and viscosity—a review

“…Using the respective definitions for series and parallel RLC quality factors, it can be shown (see, e.g. [218]) that the circuit representations of piezoelectric sensors featuring an electrical fluid load and the electrodynamic sensors with series components caused by cross-talk or wire resistance and inductance are represented by the dual circuits in figure 14. Group delay of cables, and phase errors or phase changes in the readout circuit due to calibration errors, thermal effects, or aging are accounted for by a phase shift in figure 14.…”