Temperature dependent performance of piezoelectric

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Temperature dependent performance of piezoelectric MEMS resonators for viscosity and density determination of liquids To cite this article: G Pfusterschmied et al 2015 J. Micromech. Microeng. 25 105014

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- Modelling and characterization of the roof tile-shaped modes of AlN-based cantilever resonators in liquid media V Ruiz-Díez, J Hernando-García, J Toledo et al. - Piezoelectric resonators and oscillator circuit based on higher-order out-of-plane modes for density-viscosity measurements of liquids J Toledo, T Manzaneque, V Ruiz-Díez et al. - Q-factor enhancement for self-actuated self-sensing piezoelectric MEMS resonators applying a lock-in driven feedback loop M Kucera, T Manzaneque, J L SánchezRojas et al.

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Journal of Micromechanics and Microengineering J. Micromech. Microeng. 25 (2015) 105014 (8pp)

doi:10.1088/0960-1317/25/10/105014

Temperature dependent performance of piezoelectric MEMS resonators for viscosity and density determination of liquids G Pfusterschmied1, M Kucera1,2, E Wistrela1, T Manzaneque3, V Ruiz-Díez3, J L Sánchez-Rojas3, A Bittner1 and U Schmid1 1

Institute of Sensor and Actuator Systems, Vienna University of Technology, Floragasse 7, A-1040 Vienna, Austria 2 AC2T Research GmbH, Viktor-Kaplan Str. 2, A-2700 Wiener Neustadt, Austria 3 Microsystems, Actuators and Sensor Group, ETSI Industriales, Universidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain E-mail: [email protected] Received 9 April 2015, revised 3 August 2015 Accepted for publication 5 August 2015 Published 15 September 2015 Abstract

It is the objective of this paper to report on the performance of piezoelectric MEMS resonators for viscosity and density measurements at elevated temperatures. A custom-built temperature controlled measurement setup is designed for fluid temperatures up to 100 °C. Piezoelectric single-side clamped resonators are fabricated, excited in 2nd order of the roof tile-shaped mode (13-mode) and exposed to several liquids (i.e. D5, N10, N35, PAO8, olive oil, ester oil and N100). At the next step, these results are analysed applying a straightforward evaluation model, thus demonstrating that with piezoelectric MEMS resonators the density (i.e. from ρmin = 785 kg m−3 to ρmax = 916 kg m−3) and viscosity (i.e. from µmin = 1.20 mPa s to µmax = 286.36 mPa s) values of liquids can be precisely determined in a wide range. Compared to standard measurement techniques, the results show for the first parameter a mean deviation of about 1.04% at 100 °C for all the liquids investigated. For the second parameter, the standard evaluation model implies a systematic deviation in viscosity with respect to the calibration being N35 in this study. This inherent lack of strength has a significant influence on the accuracy, especially at 100 °C due to fluids having a viscosity reduced by a factor of 30 for N100 compared to room temperature. This leads to relative deviations of about 23% at 100 °C and indicates the limits of the evaluation model. Keywords: piezoelectric, liquid sensing, MEMS resonators, elevated temperature (Some figures may appear in colour only in the online journal)

shear instead of compressive forces are transferred to the fluid [1, 12, 13]. Riesch et al used an in-plane plate viscosity sensor which is able to measure the viscosity of ethanol precisely (Q-factor = 2.75) [14]. For piezoelectric MEMS resonators, the potential of in-plane modes for liquid monitoring is limited, as both the surface fraction and the corresponding mechanical strain values are low, leading to poor input characteristics for the sensor electronics. Furthermore, measuring pure shear forces by in-plane modes do not allow an independent determination of the density and viscosity [15]. When targeting the

1. Introduction Over the past two decades the study of micromachined resonators has been a continuous field of research. In particular, micro-electro-mechanical-systems (MEMS) devices are used in a widespread field for the precise determination of both physical [1–3] and chemical quantities [4–9]. For liquid sensing application especially, the surrounding media causes high viscous damping [10, 11]. One established approach is to use in-plane modes, as predominantly 0960-1317/15/105014+8$33.00

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G Pfusterschmied et al

J. Micromech. Microeng. 25 (2015) 105014

determination of viscous losses with mass-sensitive resonators, high initial Q-factors are of utmost importance, resulting in a higher mass resolution [16]. Therefore, the question arises as to whether a vibration mode exists, which combines the beneficial properties of standard in-plane and out-of-plane modes. Most recently, a special class of excitation mode exceeding the overall performance of commonly-used out-of-plane vibration modes was introduced showing the highest Q-factor of MEMS resonators in liquid media up to now [15]. This most beneficial result can be used for viscosity and density monitoring purposes within a large variety of technical systems, such as oil degradation monitoring in combustion engines. In this everyday application scenario fluid temperatures reach 100 °C or even more. To the best of the authors’ knowledge, a study on the performance of resonantly operating cantilevers at these elevated temperatures has not been published until now. It is the objective of this paper to report on the performance of piezoelectric MEMS resonators for viscosity and density measurements at elevated temperatures. Therefore, a custombuilt temperature controlled measurement setup is realized. Piezoelectric self-sensing and self-actuating MEMS resonators are fabricated and evaluated in several liquids such as D5, N10, N35, PAO8, olive oil, ester oil and N100. Finally, the viscosity and density values are determined in a temperature range from 20 to 100 °C, whereas the measurement results of a commercial viscometer serve as a reference.

The resonant behaviour of the unperturbed resonator is described by a series resonance circuit, as given by Z m(ωres ) = Rm + jωres L m +

⎛ ω 2L C − 1 ⎞ 1 = Rm + j ⎜ res m m ⎟. ⎝ ⎠ jωresCm ωresCm

Viscous damping is modelled by a RL combination as

(2)

Z v(ωres ) = Rv + jωresL v = d2 ωresµ f ρf (1 + j ). (3)

and the added mass effect is considered as an additional inductance as Z t (ωres ) = jωresL t = jd1ωresρf . (4)

Sell et al used this approach for measuring viscosity and density in a gaseous environment where the gas pressure influences the cantilever damping additionally [19], considered by an additional parameter as Z p = jd3p. (5)

Finally, the motional branch, as depicted in figure 1, is given as ⎛ ⎞ 1 Z m(ωres ) = Rm + Rv + j⎜(L m + L v + L t )ωres − + d3 p⎟. ⎝ ⎠ ωresCm

(6) Equation (5) can be separated into real and imaginary parts according to Re{Z m(ωres )} = Rm + d2 µ f ρf ωres , (7)

2. Theory

Im{Z m(ωres )} = ωres L m −

1 + ωresd1ρf + d2 μf ρf ωres + d3 p. ωresCm

(8) The unknown parameters d1, d2 and d3 can be determined in a calibration process, allowing at the next step the determination of the liquid viscosity and density. For performing measurements in liquids equations (6) and (7) can be simplified by setting the parameter d3 = 0, which takes the gas pressure into account. First, the resonator has to be characterized under vacuum conditions. This pre-characterization can also be performed in air when targeting viscosity and density measurements in liquid media. These data are used to extract the unperturbed resonator parameters Rm, Lm and Cm. Next, a measurement is performed in a liquid environment with known viscosity and density to determine the parameters d1 and d2 in such a way that

2.1. Viscous modelling using a complex impedance

In 1988, Muramatsu et al showed that the frequency shift and motional resistance of an AT-cut quartz crystal resonator (QCR), operating in a thickness-shear-mode (TSM), depends linearly on the square root of the viscosity–density product [17]. Matsiev et al applied this relationship to a flexural resonator as, e.g. tuning forks [18]. He introduced a complex impedance Z (ωres ) at angular resonance frequency ωres as Z (ωres ) = d1 jωresρf + d2 ωresμf ρf (1 + j ), (1)

modelling the viscous damping in two terms: one is proportional to the liquid density d1 jωρf and the second represents a square root viscosity density product by the expression d2 ωresµ f ρf (1 + j ). Thereby, d1 and d2 are unknown parameters, ω is the angular frequency, µf describes the dynamic viscosity and ρf the density of the fluid. Transferred to an equivalent electrical circuit diagram, the liquid density proportional term d1 jωresρf can be considered as an additional inductance, whereas the term d2 ωresµ f ρf (1 + j ) being proportional to the square root of the viscosity–density product can be considered as an RvLv combination. This model is applied in several studies for the determination of the density and viscosity of both liquids and gases with tuning forks [4–6, 19]. In particular, the viscous damping is represented by a complex impedance based on the equivalent circuit, as shown in figure 1.

Re(Z m ) − Rm d2 = (9) µ f ρf ωres

and 1

Im(Z m ) − ωresL m + ω C − d2 μf ρf ωres − d3 p res m d(10) . 1= ωresρf

A different calibration routine can be performed by using a least squares fitting process to determine the parameters d1 and d2 from measurements performed with several liquids with known parameters. Finally, the determination of the unknown liquid density ρf is obtained by using the equation 2



Figure 1. Butterworth–van Dyke equivalent electrical circuit diagram. 1

Im(Z m ) − ωresL m + ω C − Re(Z m ) + Rm − d3 p res m ρ(11) f = ωres d1

and the viscosity µf is extracted by using

( ). (12) μ = Re(Z m ) − Rm 2 d2

f

ωres ρf

3. Experimental details 3.1. Sensor aspects

The piezoelectric self-sensing and self-actuating cantilevers used in this work are based on the fabrication process published recently [15, 20]. The optical micrograph, as shown in figure 2, depicts a typical die layout (9 mm × 9 mm) packaged in 24-pin DIP (dual inline package), including three single side-clamped cantilever structures with different geometrical dimensions and their non-released counterparts. For actuating and sensing, an aluminium nitride (AlN) thin-film with a thickness of 620 nm is sputter deposited onto the cantilever sandwiched between two 500 nm thin gold electrodes. The cantilever sensor used in this paper has a length of L = 1511 µm, a width of W = 1268 µm and a thickness of T = 45 µm, and uses an electrode design optimized for the excitation of a roof tile-shaped vibration mode, as published recently [22]. Thereby, two electrode pairs, covering half of the sensor surface are connected, allowing apart from standard in-plane [1] and out-of-plane [16] modes the excitation of either odd (e.g. 1st) or even (e.g. 2nd) roof tile-shaped modes [20] due to an in-parallel and anti-parallel electrical stimulation. This advanced class of vibration modes can be described as a transversal out-of-plane vibration mode with a free–free boundary condition along the length of a single-sided clamped beam. Finite element method (FEM) eigenmode analyses for the investigated roof tiled-shaped mode are presented in figures 3(a) and (b). Considering Leissa’s nomenclature [23] by counting the number of nodal lines in the x- and y-directions, this advanced roof tile-shaped mode is labelled in the following as 13-mode.

Figure 2. Optical micrograph of a typical die layout (9 mm × 9 mm), packaged and wire bonded in a 24-pin DIP (dual inline package), containing differently sized cantilevers and their non-released counterparts for an optional compensation of parasitic effects [15, 21].

Figure 3. Visualization of the 2nd order of the roof tile-shaped mode (13-mode) (a) and its top view (b). The coloured areas on the cantilever surface represent the local volume strain distribution with positive volume strain (tensile, red) and negative volume strain (compressive, blue), respectively.

illustrated in figure 4(a). The whole aluminium body is heated from the top side by a Peltier element and cooled by a 3.15 inch fan mounted on top of the Peltier element. For temperature sensing, a waterproof 4-wire PT100 class 1/3 DIN sensor in the form of a M8x10 screw is located as close as possible to the resonator and is connected to an Agilent 34410A multimeter for data acquisition. ¼ inch silicon tubes connected to the front and the back of the aluminium chamber cavity enable the easy feeding and removal of the liquid under investigation, as illustrated in figure 4(b). After every single measurement, the sensor cavity is cleaned by purging with toluene, followed by isopropanol. Finally, the aluminium chamber is dried

3.2. Setup for elevated temperature measurements

To perform measurements at elevated temperatures, the packaged resonator is mounted on the bottom side of an aluminium block having a cavity implemented at the sensor position, as 3



Figure 4. Schematic side view of the temperature measurement setup for elevated temperatures (a) and an optical photograph of the bottom of the open cavity including a wire bonded sensor-chip packaged in 24-pin DIP (b).

at +60 °C for 5 min to ensure the evaporation of all purging solvents. Due to the strong temperature dependency it is of utmost importance to precisely control the temperature of the liquid to minimize the uncertainty in viscosity and density determination. Therefore, temperature controller software, consisting of a proportional–integral (PI) controller and first order low-pass (PT1) pre-filter, is realized in a discrete algorithm written in LabView. The transfer function of the temperature-controlled system HS, modelled as a second order element (PT2-element), is characterized by a step response. The controller is designed using the symmetrical optimum to provide a good disturbance reaction, while the pre-filter is implemented to reduce high controller overshooting. A TTi CPX400DP power supply drives the Peltier element current via relays for switching the current direction at zero crossing, controlled by a NI Digital IO DAQMX interface. The sensor measurements were performed in a temperature range from +20 to +100 °C.

a function of the inverse viscosity–density product 1/ ρf µ f are given in figure 6. For the high viscous standard N100, the data points are perfectly described by a linear dependency. For the less viscous D5 the behaviour is linear with a reduced slope, which is in perfect agreement with the behaviour reported in [20]. 4.2. Viscosity and density determination

This evaluation takes advantage of the viscous modelling using a complex impedance, as introduced in section 2. The unperturbed resonator is measured in air at +20 °C using an Agilent 4294A impedance analyser. The corresponding Q-factors are determined using the Butterworth–van Dyke equivalent circuit in combination with a Levenberg–Marquardt algorithm [16], finally yielding the corresponding values for Rm, Lm and Cm, as given in table 1. The driving voltage of the impedance analyser was varied from 100 mV up to 500 mV to investigate the influence of the oscillation velocity of the cantilever on the damping in different liquids and, in further consequence, on the shear rate of the sensor signal. The output characteristics were not affected by the signal amplitude in this range, fitting to the shear-rate independent viscosity of the investigated Newtonian fluids. Due to these results, all further measurements are performed with a constant amplitude of the driving voltage of 500 mV. In the case of non-Newtonian fluids, it should be noted that the Butterworth–van Dyke equivalent circuit is not valid anymore, as the parameters Rv and Lv may depend on the shear rate and are functions of the driving voltage. As a next step, the resonator is calibrated at representative key temperatures (+20, +40 and +100 °C) in the viscosity standard N35. This reference standard is selected as both its viscosity and density represent a good reference with respect to most of the other liquids investigated in this study. For calibration purposes, the sensor-specific parameters d1 and d2 (see table 2) are finally calculated using equations (8) and (9) by applying the cantilever parameters Rm, Lm and Cm in air (see table 1) as well as the cantilever parameters Rm, Lm and Cm in the reference liquid N35 (see table 2). Several liquids

4. Experimental results 4.1. Influence of the parasitic feed-line resistance Rs

The modified Butterworth–van Dyke model, depicted in figure 1, neglects the parasitic feed line resistance Rs. This is a good approximation valid for cantilevers with small active surfaces, which results in relatively small parallel capacitance Cp, as there is almost no slope in the conductance characteristics. For cantilevers with larger active surfaces the higher parallel capacitance Cp causes in combination with a series resistance a positive slope in the conductance characteristics. This effect introduces the frequency dependence of the conductance characteristics, as shown in figure 5, in the range of the resonance frequency of the 2nd order (13)-mode, while the resonator is operated in D5 and N100 at different temperatures. Furthermore, due to a significant temperature dependency of Rs the base line shifts to higher values at elevated temperatures. This latter finding agrees well with the origin of the offset, described in a work published recently [15]. The Q-factors at different temperatures (20 to 100 °C) as 4



Figure 6. Q-factor as a function of the inverse viscosity–density product. Measurements are performed in the viscosity standards D5 (red) and N100 (black) in a temperature range from +20 to +100 °C. Table 1. Characterization of the resonator in air. Rm, Lm, Cm represent the unperturbed resonator in air.

f res (kHz)

Q

Rm (kΩ)

Lm (mH)

Cm (fF)

683.63

265.66

10.32

640.98

84.56

which was reported recently [22, 27]. Higher order features increased the Q-factors and therefore reduced the damping caused by the surrounding fluid [20]. In this content, Toledo et al [27] reported on the evaluation of viscosity with different out-of-plane modes (12-/14-mode). Furthermore, resolutions in density and viscosity were evaluated showing different values for different modes. Due to the higher resonance frequency and the higher Q-factor, the 14-mode shows superior resolution, reaching values of 3.92 × 10−5 g ml−1 for the density and 0.127 mPa s for the viscosity. These results support those made in this paper and demonstrate that higher order modes will enhance the sensor accuracy. Furthermore, the optimized electrode design increases the strain-related conductance peaks ΔG and, in further consequence, the ratio ΔG/Q [16], leading to high conductance peaks with narrow bandwidths [22]. When using the motional branch for evaluation, small changes caused by the damping of the liquids can be obtained with better accuracy if the conductance peak ΔG is high compared to commonly used out-of-plane or in-plane modes with lower ΔG/Q values. A comparison with respect to the conductance peak height ΔG between the 1x-modes and commonly used out-of-plane or in-plane modes can be found in [15, 20, 28]. Basically, in-plane-modes show better accuracy for viscosity evaluation [14], whereas out-of-plane modes are better suited for density evaluation of the surrounding liquid [27, 29]. Therefore, a combination of both modes is assumed to be a good approach for simultaneous density and viscosity sensing with high accuracy. A similar approach was performed by Riesch et al, where the dynamic behaviour of the vibration cantilevers was changed, resulting in a superior evaluation of the physical properties of liquids [30].

Figure 5. Impact of the fluid temperature on the electrical

characteristics in D5 (a) and N100 (b) for 20 °C, 50 °C and 100 °C, respectively. The corresponding Q-factors are indicated in the legend.

(i.e. D5, N10, N35, N100, olive oil, DITA4, PAO85, ester oil) are measured with the temperature-controlled measurement setup up to +100 °C. The viscosity and density values and the deviation with respect to reference values, measured with a Stabinger SVM3000, are calculated at +20 °C, +40 °C and +100 °C, and are presented in tables 3–5, as well as in figure 7. In general, the deviation between both density values is very low, e.g. the averaged deviation at +20 °C is 0.76%, at +40 °C it is 0.55% and for +100 °C it is 1.04%. In contrast, the agreement in viscosity is moderate with an averaged deviation of 6.35% for +20 °C, 6.87% for +40 °C and 23.44% for +100 °C. This high deviation at elevated temperatures implies that the temperature dependency of the resonance frequency and Q-factor strongly affects the measurement accuracy [24, 25]. Figure 8 shows the increase in absolute deviation with N35 as the calibration liquid. The absolute value is also determined at 20 and 40 °C, leading to averaged systematic deviations of 2.95 mPa s at 20 °C, 1.10 mPa s at 40 °C and 1.47 mPa s at 100 °C. Due to the decrease in the viscosity with the temperature above average, the impact of this systematic deviation up to 100 °C strongly increases and reduces the accuracy of the sensor at elevated temperatures. In [26], a more complex model for evaluation purposes is presented, where an additional damping term takes the oscillatory fluid-structure interaction into account. This approach may decrease the systematic deviation, but as an additionally unknown term is introduced, this approach was not considered in the scope of this study focusing on the basic temperature dependant performance of MEMS resonators in liquids. A model-independent approach to increase the accuracy of the viscosity measurement can be achieved by using higher order modes combined with an optimized electrode design,

5. Conclusions and outlook In summary, piezoelectric MEMS-resonators for liquid monitoring purposes were fabricated and excited in the 2nd order 5



Table 2. Calibration parameters d1, d2 and d3 obtained by calibration with the viscosity standard N35 at +20,+40 and +100 °C. The values

for the density and viscosity are gained from a standard laboratory viscometer Stabinger SVM3000. Rm, Lm, Cm represent the resonator motional branch parameters in N35.

a

ϑ (°C)

µfa (mPa s)

ρfa (kg m−3) Rm (kΩ)

Lm (mH)

Cm (fF)

d1

d2

d3

+20 +40 +100

73.834 27.388 4.527

858 846 809

1551.37 1608.57 1585.41

94.57 89.14 87.57

1.1922 1.1992 1.2215

14.3619 13.6254 11.4282

0 0 0

195.05 116.89 46.14

Indicates the values obtained with the Stabinger viscometer.

Table 3. Overview of the results gained from a standard laboratory viscometer Stabinger SVM3000 and a MEMS resonator. Measurements

are performed at +20 °C and the MEMS resonator was also calibrated with viscosity standard N35 at +20 °C. The deviations ερ and εµ are given as an absolute value.

a

Liquid

µfa (mPa s)

ρfa (kg m−3) Q

f res (kHz)

µf (mPa s)

ρf (kg m−3)

εµ (%)

ερ (%)

D5 N10 N35 N100 Olive oil DITA PAO8 Ester oil

5.718 18.004 73.834 286.36 81.355 58.632 93.561 98.884

839 851 858 866 913 912 829 916

424.210 420.754 415.519 408.437 407.705 408.735 417.643 406.245

4.803 17.305 73.834 288.290 87.875 61.193 100.694 102.695

844 853 858 851 907 910 835 912

16.01 3.88 0 0.67 8.01 4.37 7.62 3.85

0.59 0.27 0 1.72 0.64 0.14 0.73 0.39

76.73 43.87 22.36 11.98 20.79 23.94 20.33 19.16




a

Liquid

µfa (mPa s)

ρfa (kg m−3) Q

f res (kHz)

µf (mPa s)

ρf (kg m−3)

εµ (%)

ερ (%)


3.345 8.518 27.388 86.800 35.467 41.539 23.505 37.146

825 838 846 854 899 902 898 816

425.990 423.714 420.305 415.711 412.253 411.278 413.107 422.425

2.767 7.497 27.388 87.892 36.680 44.574 24.559 36.282

832 839 846 850 895 898 896 827

17.28 11.99 0 1.26 3.42 7.31 4.49 2.33

0.75 0.18 0 0.41 0.477 0.52 0.17 1.32

101.90 67.14 37.22 19.91 34.42 29.31 37.33 31.47




a

Liquid

µfa (mPa s)

ρfa (kg m−3) Q

f res (kHz)

µf (mPa s)

ρf (kg m−3)

εµ (%)

ερ (%)


1.198 2.143 4.527 9.712 7.301 7.907 4.527 6.204

785 799 809 818 860 863 857 780

430.27 428.47 427.14 425.47 419.33 421.41 419.52 432.64

1.012 2.082 4.527 12.433 9.355 10.241 5.548 8.528

795 804 809 812 854 839 856 771

15.52 2.87 0 28.02 28.13 29.52 22.55 37.47

1.30 0.61 0 0.69 0.69 2.79 0.06 1.15

161.25 126.31 96.62 62.06 68.11 71.82 88.89 76.69


causing very high Q-factors up to 161 in D5 at 100 °C. In further consequence, resonator specific parameters are implemented in a simple evaluation model to extract viscosity and density values in a wide range. The low averaged deviation in the density values predestines the 13-mode for density

of the roof tile-shaped mode (13-mode). Several liquids (i.e. D5, N10, N35, N100, olive oil, DITA4, PAO85, ester oil6) are characterized in a temperature range from 20 up to 100 °C. Therefore, a temperature-controlled test setup is realized, which allows precise control of the liquid media temperature, 6



takes an additional term for viscous damping into account, and considering measurements in the first in-plane mode may result in viscosity values with higher accuracy. This approach, combining two different modes to improve the overall device sensitivity, needs to be studied in more detail in the near future. Acknowledgments This work has been supported by the Austrian Research Promotion Agency within the COMET-K2 Project XTribology (Project-No 824187) and Spanish MINECO project ref. DPI2012-31203. Tomás Manzaneque and Víctor Ruiz-Díez acknowledge financial support from the Spanish Ministry of Economy and Competitiveness (grant FPI - BES-2010– 030770) and the Ministry of Education, Culture and Sport (grant FPU - AP2010-6059), respectively. References [1] Beardslee L A et al 2010 Thermal excitation and piezoresistive detection of cantilever in-plane resonance modes for sensing applications J. Microelectromech. Syst. 19 1015–7 [2] Manzaneque T et al 2014 Piezoelectric MEMS resonatorbased oscillator for density and viscosity sensing Sensors Actuators A 220 305–15 [3] Ruiz-Díez V et al 2015 Viscous and acoustic losses in lengthextensional microplate resonators in liquid media Appl. Phys. Lett. 106 083510 [4] Waszczuk K et al 2011 Application of piezoelectric tuning forks in liquid viscosity and density measurements Sensors Actuators B 160 517–23 [5] Sell J K et al 2010 Real-time monitoring of a high pressure reactor using a gas density sensor Sensors Actuators A 162 215–9 [6] Liu Y et al 2011 Measurement of density and viscosity of dodecane and decane with a piezoelectric tuning fork over 298–448 K and 0.1–137.9 MPa Sensors Actuators A 167 347–53 [7] Jakoby B et al 2010 Miniaturized sensors for the viscosity and density of liquids—performance and issues IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57 111–20 [8] Jakoby B and Vellekoop M J 2011 Physical sensors for liquid properties IEEE Sensors J. 11 3076–85 [9] Dufour I, Heinrich S M and Josse F 2007 Theoretical analysis of strong-axis bending mode vibrations for resonant microcantilever (bio)chemical sensors in gas or liquid phase J. Microelectromech. Syst. 16 44–9 [10] Yoshihiko H et al 1998 Resonance characteristics of micro cantilever in liquid Japan. J. Appl. Phys. 37 7064 [11] Kwon T Y et al 2007 In situ real-time monitoring of biomolecular interactions based on resonating microcantilevers immersed in a viscous fluid Appl. Phys. Lett. 90 223903 [12] Manzaneque T et al 2012 Characterization and simulation of the first extensional mode of rectangular micro-plates in liquid media Appl. Phys. Lett. 101 151904 [13] Jae Hyeong S and Brand O 2008 High Q-factor in-planemode resonant microsensor platform for gaseous/liquid environment J. Microelectromech. Syst. 17 483–93 [14] Riesch C et al 2009 A suspended plate viscosity sensor featuring in-plane vibration and piezoresistive readout J. Micromech. Microeng. 19 075010 [15] Kucera M et al 2014 Design-dependent performance of selfactuated and self-sensing piezoelectric-AlN cantilevers

Figure 7. Comparison between the standard laboratory viscometer Stabinger SVM3000 and the MEMS resonator results with respect to the density ρf and viscosity µf values at (a) +20 °C, (b) +40 °C and (c) +100 °C.

Figure 8. Systematic deviation of the Butterworth–van Dyke model at 100 °C for several liquids (D5, N10, PAO8, ester oil, olive oil, DITA and N100) with N35 as the calibration reference.

determination. The higher average deviation in the viscosity of 23.4% at 100 °C is caused by the systematic deviation of the used model. Applying a more specific model, which 7



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