A

HBa

b

c

a

ARRAA

KPPSLVU

1

tfsicioo)mpsolaspt

s

0h

Sensors and Actuators A 202 (2013) 23– 29

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

jo ur nal homepage: www.elsev ier .com/ locate /sna

n acoustic transmission sensor for the longitudinal viscosity of fluids

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 22 October 2012eceived in revised form 12 March 2013ccepted 13 March 2013vailable online 19 March 2013

a b s t r a c t

Physical fluid parameters like viscosity, mass density and sound velocity can be determined utilizingultrasonic sensors. We introduce the concept of a recently devised transmission based sensor utilizingpressure waves to determine the longitudinal viscosity, bulk viscosity, and second coefficient of viscosityof a sample fluid in a test chamber. A model is presented which allows determining these parametersfrom measurement values by means of a fit. The setup is particularly suited for liquids featuring higherviscosities for which measurement data are scarcely available to date. The setup can also be used to

eywords:ressure waveshysical fluid propertiesecond coefficient of viscosityiquid condition monitoringiscosity sensors

estimate the sound velocity in a simple manner from the phase of the transfer function.© 2013 Elsevier B.V. Open access under CC BY-NC-ND license.

ltrasonic sensors

. Introduction

As the knowledge of (physical) liquid properties plays an impor-ant role in modern process control, there is an increasing demandor robust and reasonably priced sensors, especially for sensorsensing physical liquid properties, e.g., mass density, sound veloc-ty and viscosity. In particular, sensors with online measurementapabilities are preferred to standard laboratory equipment, whichs often bulky, service intensive and mostly less or not suited fornline measurements. As discussed, e.g., in [1] and [2], recently a lotf effort has been spent on the investigation of sensors for (shear-

viscosity usually in combination with other parameters like theass density or speed of sound. Acoustic viscosity sensor princi-

les utilizing shear waves suffer from the drawback that due to themall penetration depth (in the range of a few microns dependingn the excitation frequency) of the excited shear waves into theiquid only a thin fluid layer is being sensed [1,2]. Therefore thesepproaches are prone to surface contamination and less suited forensing complex liquids such as emulsions or suspensions featuringarticle sizes in the range or greater than the penetration depth of

he utilized acoustic shear wave [3].

In this contribution, we report on a recently introduced [4]ensor setup using a piezoelectric PZT (lead zirconate titanate)

∗ Corresponding author. Tel.: +43 732 2468 6271.E-mail address: hannes.antlinger@jku.at (H. Antlinger).

924-4247 © 2013 Elsevier B.V. ttp://dx.doi.org/10.1016/j.sna.2013.03.011

Open access under CC BY-NC-ND license.

transmitter and receiver for exciting and detecting pressure waves(rather than shear waves) in a small test chamber containing the liq-uid to be investigated. Utilizing pressure waves senses the so calledlongitudinal viscosity coefficient rather than the shear viscositycoefficient, which can also be used for condition monitoring appli-cations. Furthermore the bulk of the probe is being sensed whichtherefore overcomes the drawbacks associated with the small pen-etration depths which is characteristic for shear wave approaches.

2. Theory and modeling

The basic concept of our sensor setup is based on the well-known theory of the viscous attenuation of pressure waves [5].Fig. 1 depicts the elementary setup.

The setup consists of two planar, rigid boundaries separatedby a distance h. These two boundaries form the sample chambercontaining the liquid to be investigated. In one boundary, a PZTtransmitting transducer (diameter dT, thickness lT) is flush mountedwhile in the opposite boundary another flush-mounted PZT trans-ducer (diameter dR, thickness lR) serves as receiving device. Thetransducers are standard PZT disks, which are further specifiedbelow. When operated in the thickness-extensional mode (alsocalled the “33-mode”), the transmitter excites pressure waves into

the liquid, which are detected by the receiver upon impingement,thus a transfer function can be obtained.

Fig. 2 sketches the model of the whole sensor setup. The trans-ducers represent a connection between the electric and acoustic

24 H. Antlinger et al. / Sensors and Ac

dsatmpawowdcttotavccadbtii

mseiatc

D

w

model (see also Fig. 2) is connected to constant impedances Zac1T

Fig. 1. Elementary sensor setup.

omain. In the equivalent circuit, the normal forces (i.e. the pres-ure times the active transducer area and the velocities at thecoustic ports are represented by voltages and currents, respec-ively. The setup can be operated in a transient and a continuous

ode; in this contribution, we consider the latter (for an exam-le of a burst-based approach, see, e.g. [6]). In contrast to [6] ourpproach operates using a fixed distance between the transducers,hich simplifies the setup. Furthermore our setup intentionally

perates in the transducer’s near field and utilizes a continuousave excitation of the transmitting transducer. The transmitter isriven by an AC source (internal impedance ZS) providing an openircuit voltage Vs exciting pressure waves which are detected byhe receiver generating an electric output signal VOUT at the elec-ric load impedance ZL. Particularly for the case of low attenuationf the waves in the fluid in the sample chamber, i.e. low viscosities,he reflections occurring at the transducers occur lead to char-cteristic interference patterns in the frequency response of theoltage transfer function VOUT/VIN. Fig. 2 shows an equivalent cir-uit of the setup where the PZT transducers are represented byommonly used three-port systems featuring one electrical portnd two acoustic ports representing the two faces of the transducerisks [7,8]. The acoustic backing of the PZT elements is representedy the acoustic impedances Zac1T for the transmitter and Zac1R forhe receiver. In our case this backing is given by the surround-ng air which, due to its comparatively low characteristic acousticmpedance, can be approximated as an acoustic short circuit.

The acoustic transmission between the transducers can beodeled by an acoustic transmission line connecting the corre-

ponding acoustic ports of the transducers. As discussed in [9–11],specially for low viscous fluids diffraction effects have to be takennto account. Diffraction effects lead to an additional attenuationnd phase shift of the pressure waves [10,11]. According to [10]he diffraction loss factor D (assuming dT = dR) for emission from aircular source can be calculated as,

(s) = 1 − e(−j(2�/s))[

J0

(2�

s

)+ jJ1

(2�

s

)](1)

ith s defined as s = 4�fl

d2T

h.

Fig. 2. Model of the whole sensor system with AC signal source (left), transm

tuators A 202 (2013) 23– 29

The relation given in (1) holds if one of the following conditionsis fulfilled [10]:

dT

2> 7�fl or h >

72

dT (2)

these conditions have to be fulfilled in order for the approximationgiven in (1) to be valid. For our setup (dT = dR = 10 mm, �fl in theorder of 0.35 mm @ 4 MHz) the first of these conditions is fulfilled.

In (1) and (2) J0 and J1 are Bessel functions of the first kind, �flis the wavelength of the pressure waves in the fluid (not to be con-fused with the second coefficient of viscosity � introduced below),and j is the imaginary unit. The complex-valued factor D providesinformation about the additional damping and phase shift due todiffraction. We now can define additional attenuation constant andphase constant �˛ and �ˇ, respectively, accounting for the effectsof diffraction by setting

D(s) = e(−�˛−j�ˇ)h. (3)

Note that this assignment holds only for a particular distance h,i.e. the so defined �˛ and �ˇ depend on h. The 1D-transmissionline model does not account for diffraction effects but can beextended to include the additional attenuation and phase shift dueto diffraction as discussed below.

The electric transfer function between the electric ports can beobtained by using the ABCD-matrix (chain matrix) approach knownfrom the theory of electrical networks relating the input voltage VIN

and current IIN to the output voltage VOUT (=VIN,i+1) and current IOUT(=−IIN,i+1) [7]. Fig. 3 (top) shows an elementary two-port element.The ABCD-matrix is defined as

Ai =[

VIN,i

IIN,i

]=

[Ai Bi

Ci Di

] [VIN,i+1

−IIN,i+1

]. (4)

For a chain of two-ports as shown in Fig. 3, the overall ABCD-matrix A is determined by multiplying the ABCD-matrices Ai of theindividual two-ports, i.e.

A- =[

A B

C D

]=

∏n

i=1Ai. (5)

From the components of A the voltage transfer function G of theentire system can be calculated as [7];

G = VOUT

VIN= ZL

AZL + B. (6)

The ABCD-matrix for the PZT elements relating the electric portand the acoustic port connected to the fluid can be obtained fromKLM-equivalent circuit [7,8]. The other acoustic port in the KLM-

and Zac1R representing the air backing.The ABCD-matrix of the transmission line representing the fluid

is derived in analogy to an electric transmission line with a length

itter, acoustic transmission line, receiver, and load impedance (right).

H. Antlinger et al. / Sensors and Actuators A 202 (2013) 23– 29 25

p) an

h(

l

[1 +

� + �

�

tpn�acappba

caGah

tt

Fig. 3. Elementary two-port (to

, a characteristic impedance Zfl and a propagation constant �flassociated with a plane pressure wave) as [12]

Zfl =√

�fl

[�flc

2fl

+ jω(2� + �)]

= �flcfl

√1 + j

ω

�flc2fl

(2� + �) ≈ �flcf

�fl = ˛0 + jˇ0 = jω

cfl

√1

1 + j(ω/�flc2fl)(2� + �)

≈ jω

cfl

[1 − j

ω

2�flc2fl

(2

Here the approximation holds for the common case that ω(2� +)/(�flc

2fl) � 1. As it can be seen in Eq. (7), in this 1D-model the

ransfer function of the system is affected by the following fluidarameters: sound velocity cfl, mass density �fl, and the longitudi-al viscosity term (2� + �), where � denotes the shear viscosity and

denotes the second coefficient of viscosity. We note that therere different conventions as to how to define the second coeffi-ient of viscosity, we adopt that also used by White [12,13], seelso below. ˛0 and ˇ0 represent the attenuation constant and thehase constant. In the equivalent 1D-transmission line model, theropagation constant is related to the transmission line parametersy (the distributed resistance of the transmission line R′ is assumeds R′ = 0 [14]),

Zfl =√

jωL′

(G′ + jωC ′)=

√L′

C ′

√1

1 − j(G′/ωC ′)

≈√

L′

C ′

(1 + j

G′

2ωC ′

)�fl = ˛0 + jˇ0 =

√jωL′(G′ + jωC ′)

= jω√

L′C ′√

1 − jG′

ωC ′ ≈ jω√

L′C ′(

1 − jG′

2ωC ′

).

(8)

In (8) the equivalent distributed inductance, conductance andapacitance are represented by L′, G′ and C′ respectively. Thepproximation in (8) holds for the case of small losses, i.e.′/(ωC′) � 1. For the sake of completeness, we mention that in thepproximations given in (7) and (8) the following relationshipsave been utilized (first order taylor series approximation),

√1 + x ≈ 1 + x

2;

√1

1 + x≈ 1 − x

2;

√1

1 − x≈ 1 + x

2;

√1 − x ≈ 1 − x

2.

These approximations are justified for x � 1 which correspondso the assumptions given above which are particularly fulfilled forhe liquids investigated. By equating the approximations derived

d chain of two-ports (bottom).

jω

2�flc2fl

(2� + �)

]

)

].

(7)

in (7) and (8) the approximate equivalent transmission line param-eters can be identified as

L′ ⇔ �fl

G′ ⇔ ω2

�2flc4

fl

(2� + �)

C ′ ⇔ 1

�flc2fl

.

(9)

The diffraction effects can now be formally included in themodel by modifying the propagation constant to obtain a new con-stant �D and accordingly, modify the values for the distributedconductance and capacitance, modeling the additional attenuationconstant �˛ and phase constant �ˇ. The modified parameters forthe fluidic transmission line (subscript “D”) considering diffractioncan be obtained as (parameters with subscript “0” refer to the caseneglecting diffraction)

G′D = 2(˛0 + �˛)(ˇ0 + �ˇ)

ωL′

C ′D = − (˛0 + �˛)2 − (ˇ0 + �ˇ)2

ω2L′

ZD =√

jωL′

(G′D + jωC ′

D)

�D =√

jωL′(G′D + jωC ′

D) = (˛0 + �˛) + j(ˇ0 + �ˇ).

(10)

So the ABCD matrix for the fluid-line in the diffraction free caseis given as

A-0 =

⎡⎢⎢⎢⎢⎣

cosh (�flh)

(d2

T

4�

)Zflsinh (�flh)

1(d2

T �

)Z

sinh (�flh) cosh (�flh)

⎤⎥⎥⎥⎥⎦ . (11)

4 fl

For the case of including diffraction, AD is obtained by replacingZfl and �fl by ZD and �D in (11).

26 H. Antlinger et al. / Sensors and Actuators A 202 (2013) 23– 29

FS

3

FcPnfltctts

iVlc

y2tbampit

tfl([tirWmbtrwt

� of the oil was used in the simulation runs. Furthermore, the massdensity and the sound velocity of the S200 standard were measuredusing an Anton-Paar DSA5000 density and sound velocity meter.Table 1 shows the S200 fluid parameters used for the simulation

Table 1Material parameters for test fluid (S200 viscosity standard oil) at different temper-atures (the second coefficient of viscosity is not provided in the literature).

Temperature [◦C] � [kgm−3] c [ms−1] � [Ns m−2]

ig. 4. Prototype device with the PZT transducers embedded in the chamber walls.MA connectors provide the electrical connection.

. Simulation and experimental results

To obtain experimental data, the prototype device shown inig. 4 has been built. The sample chamber consists of 1.5 mm FR4opper coated PCB material. In each chamber wall, a PI-ceramicIC255 PZT disk (dT = dR = 10 mm, lT = lR = 0.5 mm, fres ≈ 4 MHz), con-ected to an SMA connector providing the electric connection isush mounted. Since due to the mounting one side of each PZTransducer is facing air, it is approximated by an acoustic short cir-uit in the modeling as described above. The distance h accordingo Fig. 1 is 34 mm for the setup investigated in this work. This dis-ance is below the Rayleigh distance N, given by N = d2

T /(4�fl) [15]uch that we are operating in the near field of the transducer.

As AC-source, an Agilent 81150A function generator with annternal impedance of 50 has been used. The measurement ofIN and VOUT was performed with a LeCroy Waverunner 44Xi oscil-

oscope resulting in a load impedance ZL of 1 M in parallel with aapacitance of 16 pF.

In principle, the model can be fitted to measurement resultsielding the unknown parameter (i.e. the longitudinal viscosity� + �). However, in order to so, the other model parameters haveo be firmly established. Especially the PZT material data providedy the manufacturer are prone to large tolerances [16,17]. To obtain

correction for the PZT parameters tolerances a reference measure-ent for the electric impedance of the PZT elements in air has been

erformed. By fitting the measured values of the PZT’s electricalmpedance in air to the theoretical values obtained from a standardhree-port PZT model [7], corrected parameters can be determined.

Fig. 5 shows the measured values for the magnitude and phase ofhe electric impedance of the PZT transmitter and receiver in air (nouid in the sample chamber) together with the simulation valuesKLM model [7,8]) using the PZT data provided by the manufacturer18] as well as with the fitted PZT parameters. The influence of theolerances of the PZT parameters can clearly be seen. Furthermoren the measurement results, spurious influences of higher orderadial modes which are not covered by the 1D-model can be seen.

e note that these higher order radial modes are not due to theounting of PZT transducers in the walls of the sample chamber,

ut due to the geometry of the disk transducer. A higher diameter

o thickness ratio would decrease the influence of these spuriousadial modes. In order to obtain a setup being as small as possible,e nonetheless chose a disk featuring a relatively small diameter. In

he literature [19–21], 2D-models covering this coupling between

Fig. 5. Magnitude and phase of the PZT transducers electric impedance in air (sim-ulated and measured values). The impedance characteristics for the receiving andtransmitting transducer were virtually identical.

the thickness and the planar modes are discussed, however, due totheir complexity and the number of additional parameters, thesemodels are hardly suited for a parameter fit based on an impedancemeasurement as used in our approach. For all simulations givenbelow, the so fitted PZT parameters have been used. We performedmeasurements using an S200 viscosity standard oil at three tem-peratures (20 ◦C, 25 ◦C and 40 ◦C) where the nominal shear viscosity

fl fl

20 886.8 1497.96 602.2 × 10−3

25 883.8 1478.97 418.1 × 10−3

40 874.6 1425.09 160.5 × 10−3

H. Antlinger et al. / Sensors and Actuators A 202 (2013) 23– 29 27

Ff�

rgb

a�afdActistN

Fv

ig. 6. Measurement and simulation results (with and without diffraction included)or G for different temperatures (20 ◦C, 25 ◦C and 40 ◦C). Note that for the simulation

was set to zero.

uns (as the value of � is not known yet it was set to zero, so the lon-itudinal viscosity 2� + � for the simulation runs is de facto giveny 2�):

Fig. 6 shows the transfer function G obtained from measurementnd simulation. A mismatch is expected due to the assumption

= 0 in the simulation. This parameter can now be varied to obtain fit between these characteristics (Fig. 7). The resulting valuesor (2� + �) and the often used parameter B (bulk viscosity) areepicted in Fig. 8 (using the model with and without diffraction).s discussed in [12], B is another common parameter used toharacterize the second coefficient of viscosity and is related tohe parameters � and � by B = (2/3� + �). B describes the viscos-ty associated with volume changes due to isotropic (compressive)

tresses [22]. The determined B virtually does not change withemperature while (2� + �) decreases with increasing temperature.ote that the sample shows a bulk viscosity that is considerably

ig. 7. Measured and fitted (with a fit of 2� + � and diffraction effects included)alues for G for different temperatures (20 ◦C, 25 ◦C and 40 ◦C).

Fig. 8. Nominal datasheet values for the shear viscosity � and the 2� + � and B

values obtained from the fit with and without diffraction effects included.

higher than that of other fluids which have thus far been investi-gated in literature using acoustic spectroscopy setups, e.g., [23]. Thepresent more compact setup featuring smaller propagation pathsand thus smaller attenuation is specifically targeting at the determi-nation of the longitudinal viscosity of highly viscous liquids (takingspurious losses associated with near field distortion into account,see also below). In turn, the measurement of low viscous liquidswith our setup will lead to increased errors as spurious attenua-tion and interference effects (which are not accurately covered bythe model) will be more pronounced in comparison to the targetedviscous attenuation effect.

In contrast to the shear viscosity, which is much better investi-gated for most standard fluids, data for the longitudinal viscosityare rare, which is confirmed by recent papers on this subject (see,e.g., [6] where the longitudinal viscosity is termed acoustic viscos-ity). This makes it difficult to verify our results by comparing toreference data for liquids. In [24] the ratio B/� for some liquidsis given. This ratio is related to the ratio (2� + �)/� by (2� + �)/�= 4/3 + B/�. As an indicator, it is stated that B/� is rarely greaterthan 20 or less than 0.1 with a common value around about one [24].It is further stated that the bulk viscosity shows a similar temper-ature dependence as the shear viscosity, where in particular, theratio B/� and thus also (2� + �)/� (which is equal to 4/3 + B/�)only shows a slight temperature dependence. For our data, it canbe observed that (i) the ratio (2� + �)/� lies in the proper order ofmagnitude and (ii) the temperature dependence of (2� + �) is sim-ilar to that of the shear viscosity �. However, the ratio (2� + �)/�shows a significant temperature dependence, which is also docu-mented by the fact that the values for B do not show a similartemperature dependence as the shear viscosity � (see Fig. 8).

This behavior could be explained by considering that, apart fromthe diffraction, there are other loss mechanisms not covered byour model. Examples for such mechanism are additional viscoelas-tic damping in the transducer which is not covered by our fit ofthe transducer’s impedance in air and signal losses due the non-uniform shape of the wavefront in the near field, which leads tospurious signal reduction when the wave amplitudes are averagedover the planar area of the receiving transducer. As these signallosses are not included in our model, they would lead to an over-

estimate in the longitudinal viscosity (2� + �), which, according toour model, is directly proportional to the damping coefficient ofthe acoustic wave in the liquid given by ̨ ≈ ω2

2�flc3fl

(2� + �), see also

28 H. Antlinger et al. / Sensors and Ac

Fig. 9. Sound velocity, measured with an Anton-Paar DSA5000 and estimated fromsimulated transfer function with and without diffraction effects, and estimatedfrP

(ftctdrdsitiaim[m

dmmdn

eNofF

ϕ

v

v

[

[

rom the measured transfer function. Note that the simulation and measurementesults have not been corrected for the additional phase shifts introduced by theZT transducers which explains the deviations.

7). Thus, the correct longitudinal viscosity would be that obtainedrom the fit using our model (see Fig. 8) reduced by a correctionerm which is related to the spurious additional damping yielding aorrected longitudinal viscosity (2� + �)corr. Assuming for instancehat the subtractive term does not show a significant temperatureependence, one can find that the temperature dependence of theatio (2� + �)corr/� can be minimized conforming to the behaviorescribed in [24]. For our experimental data, the correspondingubtractive term would be in the order of 190 mPas. Due to thenvolved assumptions (e.g., temperature-independent subtractiveerm), this simple consideration should not be over-interpreted andn the present form particularly certainly cannot serve as a basis for

numerical correction of the measurement data. But it provides anndication that we are still missing relevant loss mechanisms in our

odel as discussed above. Other works using similar approaches6] also introduced correction terms accounting for various loss

echanisms, which were then determined in a calibration step.Regardless of the errors introduced by the spurious additional

amping, the longitudinal viscosity derived from the measure-ents shows the qualitatively correct behavior and correct order ofagnitude such that it can serve as monitoring parameter in con-

ition monitoring applications where changes in the observed fluideed to be sensed.

We finally note that the presented setup can also be used tostimate the sound velocity of the liquid in the sample chamber.eglecting the phase shifts of the transducers, the wavenumber kf the pressure waves is related to the phase shift ϕ of the transferunction by (for a given distance of the transducers h as depicted inig. 1),

= kh (12)

The group velocity vG of the waves is defined as,

G =(

∂k

∂ω

)−1

(13)

Thus we have,

G = h

(∂ϕ

∂ω

)−1

(14)[

tuators A 202 (2013) 23– 29

which, for negligible dispersion, corresponds to the sound veloc-ity in the liquid. Fig. 9 depicts the values for the sound velocityobtained by a measurement with an Anton-Paar DS5000 densityand sound velocity meter, compared to the values obtained fromthe simulation and measurement results. The values show the sametendency although there is a mismatch in the absolute values. Thedifference can be related to additional phase shifts from the PZTtransducers not considered in the above formula. As can be seenin Figs. 8 and 9 both parameters, the longitudinal viscosity term(2� + �) and the sound velocity decrease with increasing tempera-ture. This behavior is well known for a lot of liquids. For the soundvelocity we confirmed this behavior by the measurements withthe commercial Anton-Paar DSA5000 laboratory instrument. Forthe longitudinal viscosity this behavior is also well-known (see thediscussion above).

4. Conclusions

We presented an approach for a transmission sensor setuputilizing pressure waves. Based on the KLM-model for a PZT trans-ducer, the acoustic wave transmission theory and the ABCD-matrixapproach, a simple 1D-model for the sensor was introduced. By fit-ting the simulated transfer functions to measurement results, anestimate for the longitudinal viscosity, and in turn, the bulk viscos-ity of the sample liquid can be determined. The setup is particularlysuited for liquids featuring bulk viscosities above ∼150 mPas forwhich measurement results have been scarcely reported so far. Asan example we determined the of a S200 viscosity standard oil.Beside the suitability of evaluating the second coefficient of viscos-ity the setup can be used to estimate the sound velocity from themeasured phase shift in a straightforward manner.

Acknowledgments

This work was supported by the Austrian Science Fund (FWF),grant L657-N16 and by the Austrian COMET program (AustrianCenter of Competence of Mechatronics and K-Project PAC).

References

[1] B. Jakoby, et al., Transactions on Ultrasonics Ferroelectrics, and Frequency Con-trol 1 (57) (2010) 111–120.

[2] B. Jakoby, M.J. Vellekoop, Physical sensors for liquid properties, IEEE SensorsJournal 11 (December (12)) (2011) 3076–3085.

[3] B. Jakoby, A. Ecker, M.J. Vellekoop, Monitoring macro-and microemulsionsusing physical chemosensors, Sensors and Actuators A: Physical 115 (2) (2004)209–214.

[4] H. Antlinger, et al., An acoustic transmission sensor for the characterizationof fluids in terms of their longitudinal viscosity, Eurosensors 2012, Krakau,September 2012.

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

[6] H.S. Ju, E. Gottlieb, D. Augenstein, G. Brown, B.R. Tittmann, An empirical methodto estimate the viscosity of mineral oil by means of ultrasonic attenuation,Transactions on Ultrasonics Ferroelectrics, and Frequency Control 57 (7) (2010)1612–1620.

[7] Arnau Vives, Antonio (Eds.), Piezoelectric Transducers and Applications, 2nded., Springer-Verlag, Berlin Heidelberg, 2008.

[8] Kino, S. Gordon, Acoustic Waves: Devices, Imaging, and Analog SignalProcessing, Prentice-Hall, Inc., 1987.

[9] H. Seki, A. Granato, R. Truell, Diffraction effects in the ultrasonic field of a pis-ton source and their importance in the accurate measurement of attenuation,Journal of the Acoustical Society of America 28 (1956) 230–238.

10] G. Leveque, E. Rosenkrantz, D. Laux, Correction of diffraction effects in soundvelocity and absorption measurements, Measurement Science &Technology 18(11) (2007) 3458–3462.

11] J. Johansson, P.-E. Martinsson, Incorporation of diffraction effects in simulations

of ultrasonic systems using PSpice models, Proceedings of the IEEE UltrasonicsSymposium (2001) 405–410.

12] H. Antlinger et al., Sensing the characteristic acoustic impedance of a fluidutilizing acoustic pressure waves, Sensors and Actuators A: Physical, ISSN 0924-4247, http://dx.doi.org/10.1016/j.sna.2012.02.050

nd Ac

[

[

[

[

[

[[

[

[

[

[[

B

HahAMw

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-

H. Antlinger et al. / Sensors a

13] F.M. White, Viscous Fluid Flow, 3rd ed., McGraw-Hill International Edition,2006, ISBN 007-124493-x.

14] J. Johansson, P.-E. Martinsson, J. Delsing, Simulation of absolute amplitudes ofultrasound signals using equivalent circuits, IEEE Transactions on Ultrasonics,Ferroelectrics, and Frequency Control 54 (2007) 1977–1982.

15] R. Lerch, G. Sessler, D. Wolf, Technische Akustik, Grundlagen und Anwendun-gen, Springer-Verlag, Berlin Heidelberg, 2009.

16] S.J. Rupitsch, R. Lerch, Inverse method to estimate material parameters forpiezoceramic disc actuators, Applied Physics A 97 (2009) 735–740.

17] B. Henning, J. Rautenberg, C. Unverzagt, A. Schröder, S. Olfert, Computer-assisted design of transducers for ultrasonic sensor systems, MeasurementScience and Technology 20 (2009) 124012 (11pp.).

18] PI-Ceramic, PIC255 material coefficients data, http://www.piceramic.com19] A. Iula, N. Lamberti, M. Pappalardo, An approximated 3D model of cylinder-

shaped piezoceramic element for transducer design, IEEE Transactionson Ultrasonics, Ferroelectrics and Frequency Control 45 (4) (July, 1998)1056–1064.

20] J.-M. Galliere, P. Papet, L. Latorre, A 2-D VHDL-AMS Model for Disk-Shape Piezoelectric Transducers, in: IEEE International Behavioral Modelingand Simulation Workshop, 2008. BMAS 2008, 25–26 September, 2008,pp. 148–152.

21] J.-M. Galliere, L. Latorre, P. Papet, A 2D KLM model for disk-shape piezoelec-tric transducers, in: CENICS ‘09 Second International Conference on Advancesin Circuits, Electronics and Micro-electronics, 2009, 11–16 October, 2009, pp.40–43.

22] Kolumban Hutter, Fluid-und Thermodynamik, eine Einführung, Springer Ver-lag, 2nd ed., ISBN 3-540-43734-7.

23] A.S. Dukhin, P.J. Goetz, Journal of the Chemical Physics 130 (2009) 124519.24] T.A. Litovitz, C.M. Davis, Structural and shear relaxation in liquids, in: W.P.

Mason (Ed.), Physical Acoustics, vol. II, Part A, Academic Press, New York, 1965,pp. 281–349.

iographies

annes Antlinger graduated at the Johannes Kepler University Linz, Austria in 2001

nd received his Dipl.-Ing. (M.Sc.) degree in Mechatronics. After military servicee worked as hardware design engineer for embedded systems at KEBA AG, Linz,ustria for several years, before he joined the Institute for Microelectronics andicrosensors at the Johannes Kepler University in 2010, where he is currentlyorking as a researcher in the field of viscosity sensors.

tuators A 202 (2013) 23– 29 29

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.

Roman Beigelbeck to be provided.

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 modeling, development and fabri-cation of micromachined flow and viscosity sensors as well as the sensor electronicsin general.

Franz Keplinger to be provided.

Bernhard Jakoby obtained his Dipl.-Ing. (M.Sc.) in Communication Engineering andhis doctoral (Ph.D.) 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

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.