# Fluid Sensing Using Quartz Tuning Forks—Measurement Technology and Applications

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## Abstract

**:**

## 1. Introduction

#### 1.1. Benefits of Using Tuning Fork Sensors for Fluid Sensing

#### 1.2. Viscosity and Density Sensing Using QTFs

## 2. Measurement System

## 3. Applications

#### 3.1. Real Time Monitoring of Biodiesel Content

^{3}. Figure 8 also shows the results with $\alpha =0$ and $\beta =0$ as dash-dotted lines, which indicate that in the low mass fraction range, reasonably good results without fitting for $\alpha $ and $\beta $ can be obtained. Figure 9 shows the time series of each measurement consisting of 300 consecutive raw measurements. It is emphasized that these data points are completely independent. No a priori knowledge of previous data is used to calculate the actual data point. This means that there is no filtering or averaging being used, which leaves plenty of headroom for more sophisticated signal processing. Given the low noise of the measured data, the standard deviations of the mass fraction calculated from density (${\sigma}_{\phi ,\rho}$) and viscosity (${\sigma}_{\phi ,\eta}$) are approximately given for the three temperatures in the low mass fraction range of 0 to 10% by

#### 3.2. Diesel and Soot Determination in Engine Oil

#### 3.3. Particle Characterization by Monitored Sedimentation

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**

**Left**: Dimensions of the tuning forks (µm) used in the described applications.

**Right**: The fundamental in-plane mode shape of the vibration simulated using finite element analysis. The eigenfrequency is 32.7 kHz.

**Figure 2.**The processing of the data follows the measurement chain. A data acquisition system gives the frequency spectra which are processed by a resonance estimation algorithm. The resonance parameters are related to density and viscosity values $\rho $ and $\eta $ by a sensor model with predictable error propagation from measurement noise on the time signals.

**Figure 3.**

**Left**: Butterworth–Van Dyke equivalent circuit model for the unloaded quartz crystal tuning fork (QTF). The electro-mechanical resonance is modeled by the series resonant circuit termed motional branch with shunt capacitance ${C}_{0}$ in parallel accounting for the capacitance formed by electrodes and quartz material.

**Right**: Liquid mass-loading and viscous drag are modeled by ${L}_{\mathrm{f}}$ and ${R}_{\mathrm{f}}$. The conductivity and permittivity of the liquid in contact with the electrodes are modeled by ${R}_{\mathrm{e}}$ and ${C}_{\mathrm{e}}$.

**Figure 4.**Frequency spectra of measured and fitted admittance signals for a silicone oil at varying liquid temperatures in the range from 5 °C to 80 °C are shown in the left two plots. The signals are dominated by the linear slope of ${C}_{0}$ in the magnitude, and only the small phase shifts indicate resonances. The above middle figure shows the associated Nyquist plots. In the lower middle figure, the background signals were subtracted, leaving only the motional branch admittance, which resemble circles. The solid lines are results of the resonance estimation algorithm, and the markers show the data points recorded using the system in Figure 6. On the right, the liquids corresponding to the labels (1–5) and the measured resonance parameters are listed.

**Figure 5.**

**Left**: The fluid model in Equation (4) is adjusted using three fluid standards (filled dots No. 4, 5, and 9). The calibration is verified for eight additional fluids.

**Right**: Relative deviations due to measurement noise. Error ellipses showing three times the standard deviation are plotted for fluid standards (N7.5, N14, N44, and S200 from Cannon) at three different temperatures each. Units of density and viscosity are kg/m

^{3}and mPas, respectively.

**Figure 6.**Schematic of the measurement system. The viscosity-density cell VDC100 is connected to the universal resonance analyzer MFA200. The graphical user interface suite of the MFA200 is used for test cycle automation and post processing.

**Figure 7.**Viscosity-density diagram of fuels in a temperature range of 0–80 °C (E10: 0–40 °C) measured using the VDC100 + MFA200 setup shown in Figure 6. E10 is a fuel mixture of 10% anhydrous ethanol and 90% gasoline and B0 diesel is of fossil origin only. Viscosities are higher at lower temperature.

**Figure 8.**

**Left**: viscosities for varying biodiesel content in fossil diesel. The lines follow a Grunberg–Nissan model in Equation (6).

**Right**: Densities for varying biodiesel content in fossil diesel. The lines are given by the binary mixture model in Equation (7). Dash-dotted lines represent the respective model with fitting parameters $\alpha $ and $\beta $ set to 0.

**Figure 9.**Sample series of viscosity (

**a**) and density (

**b**) measurements for varying concentrations at a temperature of T = 15 °C recorded at a rate of 1 sample/s. Each of the 300 samples is individually determined.

**Figure 10.**

**Left**: diesel and soot entry influence viscosity and density differently and can therefore be calculated using a fluid model. Various operating conditions at the engine test stand can therefore be evaluated online.

**Right**: Schematic of the laboratory test setup for concept evaluation.

**Figure 11.**Viscosity (

**a**) and density (

**(b**) of engine oil for two different dilution scenarios A and B. Soot increases viscosity and density, but diesel reduces viscosity, as shown in Figure 10. Both scenarios introduce diesel and soot, but at different ratios.

**Figure 12.**Resulting diesel concentrations (

**a**) and soot equivalents (

**b**) using a simple linearized mixing model. The dashed lines indicate theoretical values.

**Figure 13.**Particles are repeatedly stirred and their sedimentation is monitored using the QTF setup. Temperature is stabilized by means of an externally connected bath circulator.

**Figure 14.**

**Left**: The resonance frequencies are measured for a cyclically activated magnetic stirrer. (1) Shows a dispersion of PMMA particles of 20 µm nominal diameter with a concentration of 4.68%. Traces (2) show measurements with the sensor immersed 2.125 mm deeper, which results in a delayed particle front. For trace (3), the concentration is halved at lower immersion. For (4), particles of 40 µm diameter of the same concentration are used. They pass with accordingly higher velocities. (5) shows the measurement using clear DI-water for reference. The noise while stirring is higher due to mechanical vibration.

**Right**: Calculated distributions from the resonance frequency characteristics (traces 1–4) in the left figure. The dashed lines shown Gaussian distributions centered at 20 µm and 40 µm with the standard deviation given in the datasheet of the beads.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Voglhuber-Brunnmaier, T.; Niedermayer, A.O.; Feichtinger, F.; Jakoby, B.
Fluid Sensing Using Quartz Tuning Forks—Measurement Technology and Applications. *Sensors* **2019**, *19*, 2336.
https://doi.org/10.3390/s19102336

**AMA Style**

Voglhuber-Brunnmaier T, Niedermayer AO, Feichtinger F, Jakoby B.
Fluid Sensing Using Quartz Tuning Forks—Measurement Technology and Applications. *Sensors*. 2019; 19(10):2336.
https://doi.org/10.3390/s19102336

**Chicago/Turabian Style**

Voglhuber-Brunnmaier, Thomas, Alexander O. Niedermayer, Friedrich Feichtinger, and Bernhard Jakoby.
2019. "Fluid Sensing Using Quartz Tuning Forks—Measurement Technology and Applications" *Sensors* 19, no. 10: 2336.
https://doi.org/10.3390/s19102336