Sensing the characteristic acoustic impedance of a fluid utilizing acoustic pressure waves

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Sensors and Actuators A 186 (2012) 94–99 Contents lists available at SciVerse ScienceDirect Sensors and Actuators A: Physical j ourna l h o me pa ge: www.elsevier.com/locate/sna Sensing the characteristic acoustic impedance of a fluid utilizing acoustic pressure waves Hannes Antlinger a,, Stefan Clara a , Roman Beigelbeck b , Samir Cerimovic c , Franz Keplinger c , Bernhard Jakoby a a Institute for Microelectronics and Microsensors, Johannes Kepler University Linz, Altenberger Str. 69, A-4040 Linz, Austria b Institute for Integrated Sensor Systems, Austrian Academy of Sciences, Viktor Kaplan Strasse 2, 2700 Wiener Neustadt, Austria c Institute of Sensor and Actuator Systems, Vienna University of Technology, Gusshausstrasse 27-29, 1040 Vienna, Austria a r t i c l e i n f o Article history: Received 20 October 2011 Received in revised form 28 February 2012 Accepted 28 February 2012 Available online 7 March 2012 Keywords: Pressure waves Fluid properties Characteristic acoustic impedance Liquid condition monitoring Viscosity sensors Ultrasonic sensors a b s t r a c t Ultrasonic sensors can be used to determine physical fluid parameters like viscosity, density, and speed of sound. In this contribution, we present the concept for an integrated sensor utilizing pressure waves to sense the characteristic acoustic impedance of a fluid. We note that the basic setup generally allows to determine the longitudinal viscosity and the speed of sound if it is operated in a resonant mode as will be discussed elsewhere. In this contribution, we particularly focus on a modified setup where interfer- ences are suppressed by introducing a wedge reflector. This enables sensing of the liquid’s characteristic acoustic impedance, which can serve as parameter in condition monitoring applications. We present a device model, experimental results and their evaluation. © 2012 Elsevier B.V. All rights reserved. 1. Introduction Liquid property sensors gain more and more importance in the monitoring of many technical processes (e.g. drain intervals of lubrication oil can be optimized by online-measurement of selected physical parameters). A lot of recent work has focused on viscos- ity sensing often combined with the determination of other fluid parameters like mass density or speed of sound in the liquid to be monitored. Standard laboratory equipment used for viscosity measurements mostly involves motors and/or rotating objects and is consequently bulky and maintenance-intensive. Moreover, they require manual sample withdrawal and they are therefore often less suited for online monitoring. Previously investigated minia- turized sensors utilizing shear vibrations suffer from the drawback that due to the strong attenuation of shear waves in the liquid only a thin fluid layer is being sensed [1]. We recently devised a novel sensor concept primarily based on the viscous attenuation of pressure waves, which enables sensing the bulk of the liquid sample. From the theory of the propagation of acoustic waves in gases the attenuation of pressure waves in fluids is well known [2]. In [3], we presented a setup utilizing this principle where the longitudinal viscosity coefficient rather than the shear viscos- Corresponding author. Tel.: +43 732 2468 6271. E-mail address: [email protected] (H. Antlinger). ity coefficient is sensed. Recently also acoustic spectroscopy was utilized to determine the longitudinal viscosity [4,5]. Compared to these approaches, we focused on an integrated sensor system rather than using laboratory equipment. The sensor setup basically utilizes interferences appearing in a resonant chamber containing the liquid sample and can also be used for the measurement of sound velocity [6]. In the present contribution, we briefly discuss the devised model and associated numerical simulation results for the res- onating setup. Then we focus on another sensing application using this setup, i.e. the determination of the characteristic acoustic impedance of the sample liquid, which can be achieved by a slight modification. We present an associated theoretical model, experi- mental results and their evaluation. 2. Theory and modeling The sensing concept is based on a previously proposed sensor setup [6] utilizing the attenuation of pressure waves in a liquid sam- ple. The basic sensor setup is sketched in Fig. 1. The arrangement consists of two rigid boundaries separated by a distance h, forming the chamber for the liquid sample. In one of the boundaries, a PZT transducer with a diameter d and a thickness l is flush-mounted. This transducer generates (resonating) pressure waves in the liquid. Owing to the mounting the backing of the transducer is air, resulting in a defined acoustic 0924-4247/$ see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2012.02.050

Transcript of Sensing the characteristic acoustic impedance of a fluid utilizing acoustic pressure waves

Page 1: Sensing the characteristic acoustic impedance of a fluid utilizing acoustic pressure waves

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Sensors and Actuators A 186 (2012) 94– 99

Contents lists available at SciVerse ScienceDirect

Sensors and Actuators A: Physical

j ourna l h o me pa ge: www.elsev ier .com/ locate /sna

ensing the characteristic acoustic impedance of a fluid utilizing acousticressure waves

annes Antlingera,∗, Stefan Claraa, Roman Beigelbeckb, Samir Cerimovicc, Franz Keplingerc,ernhard Jakobya

Institute for Microelectronics and Microsensors, Johannes Kepler University Linz, Altenberger Str. 69, A-4040 Linz, AustriaInstitute for Integrated Sensor Systems, Austrian Academy of Sciences, Viktor Kaplan Strasse 2, 2700 Wiener Neustadt, AustriaInstitute of Sensor and Actuator Systems, Vienna University of Technology, Gusshausstrasse 27-29, 1040 Vienna, Austria

r t i c l e i n f o

rticle history:eceived 20 October 2011eceived in revised form 28 February 2012ccepted 28 February 2012vailable online 7 March 2012

a b s t r a c t

Ultrasonic sensors can be used to determine physical fluid parameters like viscosity, density, and speedof sound. In this contribution, we present the concept for an integrated sensor utilizing pressure wavesto sense the characteristic acoustic impedance of a fluid. We note that the basic setup generally allowsto determine the longitudinal viscosity and the speed of sound if it is operated in a resonant mode as willbe discussed elsewhere. In this contribution, we particularly focus on a modified setup where interfer-ences are suppressed by introducing a wedge reflector. This enables sensing of the liquid’s characteristic

eywords:ressure wavesluid propertiesharacteristic acoustic impedanceiquid condition monitoring

acoustic impedance, which can serve as parameter in condition monitoring applications. We present adevice model, experimental results and their evaluation.

© 2012 Elsevier B.V. All rights reserved.

iscosity sensorsltrasonic sensors

. Introduction

Liquid property sensors gain more and more importance in theonitoring of many technical processes (e.g. drain intervals of

ubrication oil can be optimized by online-measurement of selectedhysical parameters). A lot of recent work has focused on viscos-

ty sensing often combined with the determination of other fluidarameters like mass density or speed of sound in the liquid toe monitored. Standard laboratory equipment used for viscosityeasurements mostly involves motors and/or rotating objects and

s consequently bulky and maintenance-intensive. Moreover, theyequire manual sample withdrawal and they are therefore ofteness suited for online monitoring. Previously investigated minia-urized sensors utilizing shear vibrations suffer from the drawbackhat due to the strong attenuation of shear waves in the liquidnly a thin fluid layer is being sensed [1]. We recently devised aovel sensor concept primarily based on the viscous attenuationf pressure waves, which enables sensing the bulk of the liquidample. From the theory of the propagation of acoustic waves in

ases the attenuation of pressure waves in fluids is well known2]. In [3], we presented a setup utilizing this principle wherehe longitudinal viscosity coefficient rather than the shear viscos-

∗ Corresponding author. Tel.: +43 732 2468 6271.E-mail address: [email protected] (H. Antlinger).

924-4247/$ – see front matter © 2012 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2012.02.050

ity coefficient is sensed. Recently also acoustic spectroscopy wasutilized to determine the longitudinal viscosity [4,5]. Comparedto these approaches, we focused on an integrated sensor systemrather than using laboratory equipment. The sensor setup basicallyutilizes interferences appearing in a resonant chamber containingthe liquid sample and can also be used for the measurement ofsound velocity [6].

In the present contribution, we briefly discuss the devisedmodel and associated numerical simulation results for the res-onating setup. Then we focus on another sensing application usingthis setup, i.e. the determination of the characteristic acousticimpedance of the sample liquid, which can be achieved by a slightmodification. We present an associated theoretical model, experi-mental results and their evaluation.

2. Theory and modeling

The sensing concept is based on a previously proposed sensorsetup [6] utilizing the attenuation of pressure waves in a liquid sam-ple. The basic sensor setup is sketched in Fig. 1. The arrangementconsists of two rigid boundaries separated by a distance h, formingthe chamber for the liquid sample.

In one of the boundaries, a PZT transducer with a diameterd and a thickness l is flush-mounted. This transducer generates(resonating) pressure waves in the liquid. Owing to the mountingthe backing of the transducer is air, resulting in a defined acoustic

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H. Antlinger et al. / Sensors and Ac

iiiui

uriibcmwaa

lcd

Z

w

Z

Z

Fm

Fig. 1. Basic sensor setup.

mpedance at the transducer’s back side. Even though an air back-ng reduces the wave amplitude that can be generated in the liquid,t yields the advantage that no complicated models with possiblynknown material parameters of a backing structure have to be

ncluded in the model presented below.Due to the mismatch of the acoustic impedances of the liq-

id and the rigid boundary, the pressure waves in the liquid areeflected at the opposite chamber wall, leading to a comb-likenterference pattern in the spectrum of the transducer’s electricalmpedance. The spacing of the comb-like resonances is governedy the speed of sound in the liquid under test [6]. The whole setupan be modeled by combining a standard 3-port PZT transducerodel with an acoustic transmission line representing the pressureave propagation in the liquid and two acoustic load impedances

ccounting for the PZT backing (Zac1) and the second boundary (ZL)s shown in Fig. 2.

According to [7], the electric impedance Z3 of a PZT transduceroaded with acoustic impedances Zac1 and Zac2 at the acoustic portsan be calculated by (assuming complex notation and a time depen-ence exp(jωt)), where j is the imaginary unit

3 = V3

I3= 1

jωC0

[1

+k2T

j(Zac1 + Zac2)ZC sin( ¯ al) − 2Z2C [1 − cos( ¯ al)]

[(Z2C + Zac1Zac2) sin( ¯ al) − j(Zac1 + Zac2)ZC cos( ¯ al)] ¯ al

],

(1)

here Zac1 and Zac2 represent acoustic load impedances defined by

F1 AT(−l/2)

ac1 = −

v1=

v(−l/2), (2)

ac2 = −F2

v2= −AT(l/2)

v(l/2). (3)

ig. 2. One-dimensional model of the sensor system with the transducer as 3-portodel combined with an acoustic transmission line representing the fluid.

tuators A 186 (2012) 94– 99 95

Here C0 denotes the capacitance of the mechanically clamped trans-ducer, ZC represents the acoustic impedance of the transducer withthe area A, ω is the angular frequency, and ¯ a is the effectivewavenumber of longitudinal waves within the PZT transducer. F1,2terms the normal forces at the transducer faces, T the associatednormal stresses, v1,2 the velocities (the indices 1 and 2 refer to theacoustic ports, 1 = transducer backside, 2 = side facing the samplechamber), and kT is the electromechanical coupling factor of thepiezoelectric material (PZT). For a more detailed general discussionabout the transducer modeling see [6,7]. Due to the air backing ofthe transducer, Zac1 can be approximately set to zero representingan acoustic shortcut because of the low acoustic impedance of aircompared to the typical acoustic impedances of PZT and of liquids.

Using a one-dimensional approximation, the pressure waves inthe liquid can be modeled by the following equations (we assumethat the wave propagates in y-direction)

Tyy = ∂uy

∂y

[1�s

+ jω(2� + �)]

,

∂Tyy

∂y= −�flω

2uy,

1�s

= �flc2fl .

(4)

Here Tyy, uy, �s, �fl, and cfl are the normal stress, the displacementamplitude in the liquid, the adiabatic compressibility, the massdensity, and the sound velocity of the fluid, respectively. Using theanalogy V (electric voltage) ↔ T and I (electric current) ↔ v, thecharacteristic acoustic impedance Zfl and the propagation constant�fl of the fluid can be found as (analogous to electric transmissionline theory) [8]

Zfl =√

�fl

[1�s

+ jω(2� + �)]

≈ �flcfl,

�fl = jω

√�fl

1/�s + jω(2� + �)≈ j

ω

cfl.

(5)

Owing to the viscous losses, Zfl and �fl are complex-valued. Fur-thermore, for realistic material data (e.g. water or glycerol) andneglecting the viscous losses, Zfl and �fl can be approximated asgiven in Eq. (5). The attenuation of the pressure waves is deter-mined by the longitudinal viscosity, which is given by � + 2�, where� and � are the first and second coefficients of viscosity, respec-tively, and thus affects the Q-factor of the resonances. The definitionfor the viscosity coefficients is unfortunately not unique [2,5]. Inthis paper, we adopt the notation of White [9] where the two vis-cosity coefficients are labeled as � and � (not to be confused withthe Lame constants in the theory of linear elasticity, which are oftenlabeled using the same symbols). Using this notation, the linearizedNavier–Stokes equation appears in the form

�flu = 1�s

∇(∇ · u) + (� + �)∇(∇ · u) + �∇2u. (6)

Here, u denotes the displacement vector and the dot above thesymbol its derivative with respect to time. � is the coefficient rep-resenting the shear viscosity (often only termed viscosity) while� describes the dilatational viscosity (associated with compres-sional stress components). Using another common notation (see,e.g., Landau–Lifshitz [2]), the terms (� + �)∇(∇ · u) + �∇2u in Eq.(6) are replaced by [(1/3) + B]∇(∇ · u) + ∇2u. Obviously, thetwo definitions (White and Landau–Lifshitz notation) can be con-verted into each other using the formulas = �, B = (2/3)� + �. The

longitudinal viscosity is then given by (2� + �) = [(4/3) + B].

As mentioned before, the liquid in the sample chamber ismodeled by a terminated acoustic transmission line. Accordingto common transmission line theory (see, e.g., [10]), the input

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9 nd Actuators A 186 (2012) 94– 99

ii

Z

Acduiliivcimptwmllb

Z

Z

Etfli

3

fcmdltb

••

A

Fig. 3. Simulated electric impedance of the PZT transducer for air, distilled water

6 H. Antlinger et al. / Sensors a

mpedance of the acoustic transmission line terminated with anmpedance ZL can be calculated as

ac2 = A · ZflZL + Zfl tanh(�flh)Zfl + ZL tanh(�flh)

. (7)

n ideal rigid boundary can be represented by an acoustic openircuit which means that the acoustic impedance ZL is infinite. Asescribed above, the interference pattern in the impedance can besed to determine the liquid’s properties, in particular the veloc-

ty of compressional waves and the longitudinal viscosity of theiquid. Alternatively, if interferences are suppressed, the character-stic acoustic impedance of the liquid can be determined, whichs essentially given by the density and the compressional waveelocity of the liquid while the influence of the longitudinal vis-osity can be most often neglected (see Eq. (5)). To suppress thenterferences, an infinitely long acoustic transmission line or a

atched load impedance ZL would have to be used. Therefore, welaced a wedge reflector in the transmission path which deviateshe propagating wave such that virtually no interference occurs,hich corresponds to an infinitely long transmission line in theodel. In that way, the characteristic acoustic impedance of the

iquid affects the transducer’s electrical impedance and the comb-ike resonances disappear, i.e., the acoustic impedance Zac2 is giveny Zfl rather than Eq. (7)

ac2 = A · Zfl ≈ A�flcfl. (8)

Eq. (1) can be rewritten (assuming Zac1 = 0 for the air backing) as

3 = V3

I3=↑

Zac1=0

1jωC0

[1 + k2

T

jAZfl sin( ¯ al) − 2ZC [1 − cos( ¯ al)]

[ZC sin( ¯ al) − jAZfl cos( ¯ al)] ¯ al

].

(9)

q. (9) states that the electrical impedance of the air backedransducer, apart from the frequency, primarily depends on theuid’s characteristic acoustic impedance Zfl, all other parameters

n Eq. (9) are determined by the PZT transducer.

. Simulation results

The 1D-model described above was implemented in MATLABor simulation purposes. For all simulations the value of the secondoefficient of viscosity � was arbitrarily set to zero as values forost materials are not securely established yet and since the values

o not affect the results significantly. This means that the assumedongitudinal viscosity used in the simulation is given by 2 �. Forhe simulations of the full 1D-model the following parameters haveeen used:

PZT disk: diameter d = 10 mm, thickness l = 0.5 mm, material PI-ceramic PIC-255, simulation data see [11].Geometry: h = 29 mmFluids (reference data taken from [12,13], for a temperature of20 ◦C), as the value of � is not known for most liquids yet, it wasarbitrarily set to zero such that the longitudinal viscosity is givenby 2 �). The following table gives the used values for the mixtures:

�fl [kg m−3] cfl [m s−1] � [Ns m−2] � [Ns m−2]

Distilled water 998.0 1499.3 1.0049 × 10−3 070% Glycerol 1184.1 1847.2 23.0936 × 10−3 0

For air, the following data according to [14] have been used:

�fl [kg m−3] cfl [m s−1] � [Ns m−2] � [Ns m−2]ir 991.161 1343 18.600 × 10−6 0

and a 70% glycerol–water mixture without using the metallic wedge reflector sothat the comb-like resonances can be seen.

Fig. 3 shows the simulation results for the electrical impedanceof the PZT disk when the sample chamber is filled with air, dis-tilled water, and a 70% glycerol–water mixture without using thereflecting wedge. In this case, interferences are not suppressed andconsequently characteristic comb-like resonances can be observed.The interference patterns are superposed to the transducer’s owncharacteristic impedance spectrum featuring a series resonance fol-lowed by a parallel resonance. As mentioned before, the spacing ofthe superposed resonances is determined by the sound velocityof the fluid in the test chamber. Furthermore the lower Q-factorand higher damping of the resonating pressure waves in the 70%glycerol–water mixture due to the higher viscosity of glycerol com-pared to distilled water can be observed.

The simulation results for different water–glycerol mixtures

using the metallic wedge to supress the interference effects areshown in Fig. 4. The comb-like resonances [3] disappear and thedependence on the fluid’s characteristic acoustic impedance Zfl canbe seen. With increasing Zfl, the electrical impedance of the PZT
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H. Antlinger et al. / Sensors and Actuators A 186 (2012) 94– 99 97

Fg

to

4

benfF

endotwi

Fig. 5. Prototype device with the PZT transducer (diameter 10 mm) connected tothe SMA connector embedded in the left wall. The metallic wedge can be seen in the

ig. 4. Simulated electric impedance of the PZT transducer for air and differentlycerol–water mixtures using the metallic wedge reflector.

ransducer decreases/increases at the intrinsic parallel/series res-nance of the transducer.

. Experimental results

A prototype setup shown in Fig. 5 was built. The sample cham-er is made of 1.5 mm FR4 PCB material. One of the wall features anmbedded PIC255 PZT disk (PI Ceramic, diameter d = 10 mm, thick-ess l = 0.5 mm) which is connected to an SMA connector. The disk

aces free space (air) on one side and the fluid sample on the other.or this device the distance h according to Fig. 1 is 50 mm.

An Agilent 4294 impedance analyzer was used to measure thelectric impedance of the PZT transducer. The metallic wedge iseeded for sensing the liquid’s characteristic acoustic impedance asescribed above. The reflection face of the wedge encloses an angle

f 60 with its base. The wedge is furthermore rotated (see Fig. 5)o avoid that the reflected wave is in the same plane as the incidentave. The exact wedge position was adjusted such that virtually no

nterference phenomena could be observed in the impedance of the

fluid chamber.

PZT disk. This justifies the model using an infinitely long acoustictransmission line.

Fig. 6 shows the measured magnitude and phase of thetransducer’s electrical impedance when the sample chamber isfilled with different media and using the metallic wedge tosuppress the interference effects. The qualitative behavior pre-dicted by our model can be observed. The electrical impedancedecreases/increases with increasing Zfl at parallel/series resonanceof the PZT transducer, respectively. However, it can be seen thatthe simulation values differ from the experimental values. Reasonsfor the differences are, e.g., losses in the PZT disk itself, acousticradiation into air, and additional damping due to the mounting ofthe transducer. Furthermore, particularly for the measurement inair, additional resonances can be seen at 4.12 MHz and 4.25 MHz.These resonances are supposed to be higher order modes of thePZT disk’s radial mode. The simple 1D-model used in our modelingapproach does not account for these modes. Further improvementsin the model and the prototype device are currently investigated(e.g., including transducer losses, PZT parameter fitting, alterna-tive modeling which account for the radial modes). As shown in[15,16], the PZT material data provided by the manufacturer hasvery high tolerances. This is one of the reasons for the shift in theresonance frequencies between the simulation and the measureddata. To get a feeling for the behavior of our setup, we performed aparameter fit for the PZT data (kT, εS

33, cD33 = c33RE + jc33IM, where

the imaginary part of cD33 accounts for damping effects) assuming a

reference value for the acoustic impedance Zfl which was obtainedfrom [12,13]. For the sake of comparison, this fitting procedure forthe PZT parameters was performed three times for three mixingratios, 0%, 50% and 100% weight of glycerol (yielding three slightlydifferent sets of PZT parameters). We then took each set of the soobtained PZT parameters and calculated the impedance spectra fora series of mixing ratios, which were fitted to the respective mea-surement data by fitting only Zfl. The so-obtained fitted Zfl-valueis then considered as the measured value. A hill climbing fit algo-rithm with a variable step size [17] implemented in MATLAB was

used to perform the fit procedure. The flowchart of the whole fittingis shown in Fig. 7.
Page 5: Sensing the characteristic acoustic impedance of a fluid utilizing acoustic pressure waves

98 H. Antlinger et al. / Sensors and Actuators A 186 (2012) 94– 99

Table 1Reference values, fit values for Zfl ≈ �flcfl , and the resulting relative errors.

Glycerol ratio �flcfl (ref. values) �flcfl (fit 0%) �flcfl (fit 50%) �flcfl (fit 100%) Rel. error 0% Rel. error 50% Rel. error 100%[%] [kg/(m2 s)] [kg/(m2 s)] [kg/(m2 s)] [kg/(m2 s)] [%] [%] [%]

0 1.4946E+06 1.4964E+06 1.6267E+06 1.5615E+06 – 8.8 4.520 1.6928E+06 1.6201E+06 1.7493E+06 1.6812E+06 −4.3 3.3 −0.740 1.9035E+06 1.7748E+06 1.9063E+06 1.8403E+06 −6.8 0.1 −3.350 2.0042E+06 1.8741E+06 2.0081E+06 1.9452E+06 −6.5 – −2.9

2.0303E+06 −6.5 −0.1 −3.22.2224E+06 −4.4 1.5 −1.52.3782E+06 −2.6 3.1 –

apsv

Fg

60 2.0979E+06 1.9621E+06 2.0953E+06

80 2.2565E+06 2.1578E+06 2.2905E+06100 2.3721E+06 2.3108E+06 2.4451E+06

The results and the resulting errors (which are, of course,pproximately zero for the particular mixture where the PZTarameters were fitted) are shown in Table 1 and Fig. 8. It can be

een that the maximum relative error compared to the referencealues [12,13] stays below 10% within the whole measurement

ig. 6. Measured electric impedance of the PZT transducer for air and differentlycerol–water mixtures using the metallic wedge reflector.

Fig. 7. Flowchart for the fit procedure. For the sake of comparison, the entire fitoperation has been performed three times by using different glycerol ratios (0%,50% and 100%) for the PZT-parameter fit (step 2).

Fig. 8. Reference values and fitted values for Zfl ≈ �flcfl .

Page 6: Sensing the characteristic acoustic impedance of a fluid utilizing acoustic pressure waves

nd Ac

rc

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pPsedttisbisoeysadmm

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[[[

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H. Antlinger et al. / Sensors a

ange so this parameter fit procedure can be seen as a kind ofalibration procedure.

. Conclusion and outlook

An approach for using acoustic pressure waves to sense fluidarameters was presented. Based on a standard 3-port model for aZT disc and the transmission theory for acoustic pressure waves aimple 1D-model for the sensor setup was devised. This 1D-modelnables qualitative predictions of the sensor behavior. A prototypeevice to obtain first experimental data to validate the simula-ion results was introduced. The experimental data obtained withhe prototype device show a clear dependence of the electricalmpedance on fluid parameters (e.g., sound of speed – frequencypacing, viscosity – damping) and validates the predicted sensorehavior from the simulation data. In the present contribution, the

nfluence of the liquid’s characteristic acoustic impedance was con-idered in particular. It was found that in the investigated rangef acoustic impedances a simple calibration procedure (providingstimates for the material parameters of the involved materials)ields measurement errors below 10%. Still, the experimental datahow also that the modeling needs some further refinements, e.g.,ccounting for acoustic losses in the setup, additional dampingue to the PZT mounting, and consideration of higher order radialodes of the PZT disk. Further research will cover a more detailedodel for the sensor setup and improvements of the prototypes.

cknowledgments

We gratefully acknowledge financial support by the Austriancience Fund (FWF): L657-N16 and by the COMET K project “Pro-ess Analytical Chemistry”.

eferences

[1] B. Jakoby, et al., IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 57 (1) (2010)111–120.

[2] L.D. Landau, E.M. Lifshitz, Fluid Mechanics, 2nd ed., Butterworth-Heinemann,1987.

[3] H. Antlinger, et al., A sensor for mechanical liquid properties utilizing pressurewaves, in: Sensor+Test Conference 2011, Nürnberg, June, 2011.

[4] M.J. Holmes, et al., J. Phys.: Conference Series (2011) arXiv:1002.3029v1(physics.flu-dyn).

[5] A.S. Dukhin, P.J. Goetz, J. Chem. Phys. 130 (2009) 124519.[6] H. Antlinger, R. Beigelbeck, S. Clara, S. Cerimovic, F. Keplinger, B. Jakoby,

A liquid properties sensor utilizing pressure waves, Proc. SPIE 8066 (2011),doi:10.1117/12.886357, 80661Z.

[7] Kino, S. Gordon, Acoustic Waves: Devices, Imaging, and Analog Signal Process-

ing, Prentice-Hall, Inc., 1987.

[8] A. Lenk, G. Pfeifer, R. Werthschützky, Elektromechanische Systeme, SpringerVerlag, 2001.

[9] Frank M. White, Viscous Fluid Flow, 3rd ed., McGraw-Hill International Edition,2006.

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10] D.M. Pozar, Microwave Engineering, Addison-Wesley, 1993.11] PI-Ceramic, PIC255 material coefficents data, http://www.piceramic.com.12] Ch. Prugne, J. van Esty, B. Cros, G. Lévêque, J. Attal, Measurement of the viscosity

of liquids by nearfield acoustics, Meas. Sci. Technol. 9 (1998) 1894–1898.13] N.S. Cheng, Formula for viscosity of glycerol–water mixture, Ind. Eng. Chem.

Res. 47 (2008) 3285–3288.14] R. Lide David, CRC Handbook of chemistry and physics, 86th ed., CRC Press

Taylor & Francis Group, 2005–2006.15] S.J. Rupitsch, R. Lerch, Inverse method to estimate material parameters for

piezoceramic disc actuators, Appl. Phys. A 97 (2009) 735–7740.16] B. Henning, J. Rautenberg, C. Unverzagt, A. Schröder, S. Olfert, Computer-

assisted design of transducers for ultrasonic sensor systems, Meas. Sci. Technol.20 (2009) 11pp, 124012.

17] S.J. Russell, N. Peter, Artificial Intelligence: A Modern Approach, 2nd ed.,Prentice Hall, Upper Saddle River, New Jersey, 2003, pp. 111–114, ISBN 0-13-790395-2.

Biographies

Hannes Antlinger graduated at the Johannes Kepler University Linz, Austria in2001 and received his Dipl.-Ing. (M.Sc.) degree in Mechatronics. After military ser-vice he worked as hardware design engineer for embedded systems at KEBA AG,Linz, Austria for several years, before he joined the Institute for Microelectronicsand Microsensors at the Johannes Kepler University in 2010, where he is currentlyworking as a researcher in the field of viscosity sensors.

Stefan Clara was born in Bruneck, Italy, in 1985. He received the Dipl.-Ing. (M.Sc.)degree in Mechatronics from the Johannes Kepler University, Linz, Austria, in 2010.Since 2011, he is working as a research assistant at the Institute for Microelectronicsand Microsensors at the Johannes Kepler University, Linz, Austria. His focus is onfluid properties sensors especially at high viscosities.

Samir Cerimovic received his master degree at the Vienna University of Technology.From 2006 to 2010 he was employed first at the Institute of Electrical Measure-ments and Circuit Design (Vienna University of Technology) and afterwards at theInstitute for Integrated Sensor Systems (Austrian Academy of Sciences), working onvarious research projects. In 2010 he joined Institute of Sensor and Actuator Sys-tems (Vienna University of Technology) as a researcher in the field of miniaturizedviscosity sensors. His research interests include modelling, development and fabri-cation of micromachined flow and viscosity sensors as well as the sensor electronicsin general.

Bernhard Jakoby obtained his Dipl.-Ing. (M.Sc.) in Communication Engineering andhis doctoral (PhD) degree in electrical engineering from the Vienna University ofTechnology (VUT), Austria, in 1991 and 1994, respectively. In 2001 he obtained avenia legendi from the VUT. From 1991 to 1994 he worked as a Research Assis-tant at the Institute of General Electrical Engineering and Electronics of the VUT.Subsequently he stayed as an Erwin Schrödinger Fellow at the University of Ghent,Belgium, performing research on the electrodynamics of complex media. From 1996to 1999 he held the position of a Research Associate and later Assistant Profes-sor at the Delft University of Technology, The Netherlands, working in the field ofmicroacoustic sensors. From 1999 to 2001 he was with the Automotive ElectronicsDivision of the Robert Bosch GmbH, Germany, where he was conducting develop-ment projects in the field of automotive liquid sensors. In 2001 he joined the newlyformed Industrial Sensor Systems group of the VUT as an Associate Professor. In2005 he was appointed Full Professor of Microelectronics at the Johannes KeplerUniversity Linz, Austria. He is currently working in the field of liquid sensors andmonitoring systems. Bernhard Jakoby is a Senior Member of the IEEE. He served

as Technical Co-Chair and Local Chair for the IEEE Sensors Conference, as GeneralChair for the Eurosensors 2010 conference, and he currently is an Associate Edi-tor of the IEEE Sensors Journal and the Journal of Sensors. Recently he was electedEurosensors Fellow (2009) and received the Outstanding Paper Award 2010 of theIEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.