Reprinted from

Ultrasonics 34 ( 1996) 8 17-824

Effect of viscosity on ultrasound wave reflection from asolid/liquid interface

Vimal Shah, Krishnan Balasubramaniam *Department of Aerospace Engineering and Mechanics , Mississippi State University, Mississippi State , MS 39762, USA

Received 4 April 1996; revised 7 October 1996

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EDITORSProf. M. Rosen (Editor-in-Chief), Mater. Sci. & Engng. Dept. and Center for NDE, Johns Hopkins University,

Balt imore, MD 21218, USADr. B. Hosten, Laboratoire de Mecanique Physique, URA CNRS 867, Universite de Bordeaux, 33405 Talence, France

Prof. W.G. Mayer, Department of Physics, Georgetown University, Washington, DC 20057, USAProf. W.N. McDicken, Department of Medical Physics and Engineering, University of Edinburgh, EH3 9YW, UK

Prof. S. Ueha, Tokyo Institute of Technology, 4259 Natsuda, Midori-ku, Yokohama 227, Japan

International Advisory Board

Belg ium J a p a n0. Leroy E. MoriKU. Leuven, Kortri jk Takushoku University, Tokyo

UKR.J. DewhurstUMIST, Manchester

C a n a d aJ.F. BussiereIndustrial Materials Institute, Quebec

ChinaYing Chong-FuInstitute of Acoustics, Beijing

FranceD. RoyerISCPI , Par is

A. ZarembowitchUniversity of Paris VI

0. NomotoKobayashi Institute of Physical Research,Tokyo

PolandA . S . S l i w i n s k iUniversity of Gdansk

Russian Federat ionV.A. AkulichevInst i tute of Marine Technology Problems,Vladivostok

D.A. HutchinsUniversity of Warwick

USAL.J. BondUniversity of Denver

D.E. ChimentiIowa State University, Ames

L.A. CrumUniversity of Washington, Seattle

GermanyK.J. LangenbergUniversity of Kassel

R. ReiboldPhysikalisch- Technische Bundesanstalt,Braunschweig

I t a l yA. AlippiUniversitci di Roma

L.A. OstrovskiiRussian Academy of Sciences, NizhniNovgorod

A.P. SarvazyanRussian Academy of Sciences, Pushchino

Spa inJ.A. Gallego-JuarezInstituto de Acustica, Madrid

F. DunnUniversity of Illinois, Urbana

W.L. NyborgUniversity of Vermont

W. SachseCornell University, Ithaca

B.R. TittmannPenn State University

Ultrasonics is the world’s leading journal dedicated to the wholescience and technology of ultrasound. Contributed material is wel-comed in the following fields: elasticity, anelasticity and magneto-elasticity; ultrasonic sensors for process monitoring; nondestructivematerials characterization; generation and detection of ultrasound;ultrasonic NDE and NDT; SAW devices; signal processing; acousto-optics; physics of ultrasound; ultrasonic wave propagation; ultrasonicvisualization; ultrasonic microscopy; physics and technology of ultra-sound in medicine and biology; high-power ultrasonics; actuators andmotors; industrial ultrasonics; underwater ultrasonics.

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ELSEVIER Ultrasonics 34 (1996) 817-824

Effect of viscosity on ultrasound wave reflection from asolid/liquid interface

Vimal Shah, Krishnan Balasubramaniam *Department of Aerospace Engineering and Mechanics, Mississippi State University, Mississippi State, MS 39762, USA

Received 4 April 1996; revised 7 October 1996

Abstract

A study of the simulated reflection of a wideband ultrasound shear wave from the solid/viscous fluid interface is presented.Various parameters affecting reflection factors including the material properties of the solid, fluid properties like density andviscosity, and the operating frequency are discussed. Simulated ultrasonic response waveforms are compared with the experimentallyobtained data for NIST traceable calibration standards of viscosity. A good agreement was observed between the simulated andexperimental waveforms at various viscosities and for different solid substrates.

Keywords: Viscosity; Ultrasound reflection; Simulation

1. Introduction

Measurement of material properties using ultrasoundis a well-researched area of study. Ultrasound has beenused to measure the viscosity of fluids as early as 1949[ 11. It has since been explored as a device for non-invasive, on-line property and process monitoring [ 2-51.Early research has concentrated on the conventionalmeans of producing and detecting ultrasound [ 61. Thismethod of employing piezoelectric transducers to gener-ate and receive ultrasound is, by far, the simplestapproach. Piezoelectric transducers have many distinctadvantages [7], which have so far outweighed theirdisadvantages. Recently, a hybrid system using laser-based generation and piezoelectric transducer-baseddetection has been used to measure viscosity [ 81.

The traditional ultrasound-based approach to obtain-ing viscosity has been to correlate it with ultrasoundproperties like attenuation and reflection factors. Aviscosity sensor based on shear horizontal acoustic sur-face wave mode has been developed [9] where thepropagation loss and the phase shift between the refer-ence and the loaded waveforms were used to predict theviscosity. Approaches based on continuity of stressesand displacements [lo] at the solid/liquid interface havealso been used to derive the reflection/transmissioncoefficients. Based on these derivations, a method of

* Corresponding author. Department of Aerospace Engineering andMechanics, Mail Stop 9549, Mississippi State University, MS 39762,USA; fax: + l-601-325-7730; e-mail: KBI@ra.msstate.edu.

predicting viscosity using only the magnitude of areflected shear ultrasound RF pulse has been demon-strated by Sheen et al. [ 51. Since the ultrasound responseto viscous loading depends on frequency, most measure-ments were made assuming that the operating frequencywas the resonant central frequency of a wideband ultra-sonic transducer. The aim of this paper is to understandthe effect of broadbanded nature of the transducer onthe solid-viscous fluid interface.

2. Theoretical background

The basis of shear reflectance method was obtainedby Moore and McSkimin [6] using stress equality atthe surface of contact between the viscous fluid and thesolid base (Fig. 1). This relation is further modified [ 111to obtain a relation between the viscous impedance ofthe fluid and complex ultrasound reflection factor for agiven set of substrate material properties. Since thecomplex reflection factor can be represented in an expo-nential form, the amplitude is referred to as the absolutereflection factor and phase as the phase difference inthis paper.

The complex acoustic impedance (2) of the fluid interms of its viscosity and density is given as 2 = (ipqm)1/2[ 121, where p is the density and q is the shear viscosityof the fluid, and co is the circular frequency of thepropagating wave. If we assume the complex impedanceof the fluid as 2 = R + ix, a relation between the phase

0041-624X/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reservedPII SOO41-624X(96)00082-0

8 1 8 Vimal Shah, Krishnan Balasubramaniam / Ultrasonics 34 (1996) 817-824

Inter1

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US MIby Elsl(valid I

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Viscous Liquid

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Fig. 1. Schematic of plane polarized shear horizontal wavepropagation at a solid-fluid interface.

difference (@) and the absolute reflection factor (r) isobtained by equating the real parts:

1 - 2r2( 1 + 2 sin”(@)) + r4 = 0. (1)

The imaginary part gives the relation between viscosity,phase difference and the absolute reflection factor as,

2p; C: c0s2(ef) r sin(@)( 1 - r2)Y -= nPf c02(e,) (1 + r2 + 2r COS(Q~’

(2)

where ps and c, are the density and shear wave speed inthe substrate respectively, f is the frequency of propagat-ing wave and, 0, and of are the angles of incidence andtransmission of the ultrasound wave at the interfacedefined by Snell’s law and the shear wave velocities c,and cf as,

ef = sin-l [sin(B,)cf/c,l.

In these relations, we assume the fluid media to beperfectly viscous (Newtonian fluid), and therefore neglectthe elastic component of the shear modulus of the fluid.The reflection factor relationship with viscosity has beendecoupled to a relation between viscosity and either theabsolute reflection factor or the phase difference.

2.1. Parameters aficting reflection factors

The effect of viscosity on the absolute reflection factorand the phase difference are shown in Fig. 2. With anincrease in the viscosity of the fluid media, the absolutereflection factor decreases exponentially (Fig. 2a). Thephase on the other hand increases (Fig. 2b). This beha-vior holds until the phase reaches a discontinuity(r z 0.41). In the physical problem, other effects such asrelaxation [9] become important and this state is notachieved for Fig. 2. As the angle of incidence of theultrasound wave increases, effect of viscous loading onthe shear wave becomes more prominent, leading to anincrease in sensitivity of the reflection factors to changein viscosity.

The fluid properties p and q both have a similarrelationship with the reflection factors [Eq. (Z)]. Thefluid properties of NIST traceable calibration standards

(obtained from Cannon Instruments Inc.) were used tostudy their relative effects on the reflection factors. Atypical variation in fluid density is 891 to 872 kg/m3 dueto a temperature change from 25 to 60°C and thecorresponding variation in viscosity is from 416 to26 poise. Density change due to temperature variationis an order of magnitude less than corresponding viscos-ity change. Hence, the effect of density on the reflectionfactors is also an order of magnitude less than the effectof viscosity change (Fig. 3).

The operating frequency governs the sensitivity ofreflection factors to viscosity (Fig. 4). As the operatingfrequency (f) increases, the slope of the viscosity versusreflection factors curve increases, leading to greatersensitivity to small viscosity changes. This is true forboth phase difference and absolute reflection factor. Thesolid substrate material properties come into effect bythe virtue of an impedance mismatch. As the impedancemismatch decreases (Fig. 5), the total energy transferredto the fluid increases and consequently the reflectedenergy and phase are more sensitive to a change inviscosity of the fluid.

2.2. Simulation of reflected ultrasonic wave response

For the simulation of the ultrasonic shear waveresponse from a solid-fluid interface, normal incidencesituation (e, = of = 0) were considered. Material proper-ties of three solid substrates (Plexiglas, graphite andaluminum) and various calibration fluids were usedin the simulation. To simulate the fluid loading, theactual reference signals had to be obtained for eachtransducer/substrate combination. The reference signalswere obtained at zero load (stress free state), from theback-wall reflection of a solid substrate (Fig. 6).Wideband ultrasound waves were generated andreceived by Y-cut broadband piezoelectric transducers(Panametrics V153 and V154, with center frequencies1 and 2.25 MHz respectively), pulsed using a pulser/receiver (Panametrics PR5052). The received ultrasonicsignals were averaged at 256 samples per signal to reducerandom noise. These signals were digitized using an 8 bitdigital oscilloscope (Tektronix TDS 320). The digitizedsignals (x(t)) were gated and windowed using a rectangu-lar window to avoid pseudo phase changes associatedwith other windows. The amplitude (AR(CL))) and phase(&(co)) information was obtained using standard Fouriertransforms [ 13,141 represented as follows:

(4)

A -6 dB bandwidth of the ultrasound signal wasassumed to avoid portions of the spectrum with a lowsignal/noise ratio (SNR). The reflection factors (r&, q))for the substrate-fluid interface were theoretically com-

Vimal Shah, Krishnan Balasubramaniam / Ultrasonics 34 (1996) 817-824 8 1 9

,S E\Lb

we1LL

jrresk

Lanir

Fig. 2. Typical plots (theoretical) showing the va.riation of (a) the absolute reflectionof incidence of plane polarized shear wave at the solid (Plexiglas)/fluid (oil) interface.

: T*>-.,\.: ’ k: $J,, ,

zi 2500

.-

E 2000

c.-

* 1500*-v)

zv) 1000

5

500

00

puted using Eqs. (1) and (2) as: expected response spectrum using standard algorithms:

A lookup table was used, since the relationshipbetween viscosity and reflection factors is indirect. Theabsolute reflection factors and phase differences corre-sponding to each frequency were factored from thefrequency spectrum using the relations:

4s(w, rl) = h&4 - @th Y)* (7)An inverse Fourier transform was performed on the

factor and (b) the phase difference, with viscosity and angle

The real part of this inverse transform gives the simulatedRF response. This simulated RF response was archivedfor comparison with experiments.

The experimental RF response was also obtainedusing the experimental setup illustrated in Fig. 6. Afterthe reference signal required for the simulation wasobtained, the substrate was loaded with the calibrationfluid. The fluid was maintained at a constant temper-ature, and the experimental RF response (AE(t)), due to

820 Vimal Shah, Krishnan Balasubramaniam / U l t r a s o n i c s 3 4 ( 1 9 9 6 ) 8 1 7 - 8 2 4

-

BcK

CJ .II

CY11

-13,

Density of Fluid

- - - n e - - - 860 kg/m3

---a---- 900 kg/m3

I I I I I I I I I I .I

6 0 0 8 0 0 1000

Viscosi ty in Poise

Fig. 3. Variation of phase difference with change in fluid density and viscosity.

a-.‘-

/w==ee’..=-

_- 0”8 C-

..e- *.a----

Operating

._.* *.--l--a ---

-.--A---

frequency

1 MHz

4 MHz

8 MHz

50 100

Viscosi ty in Poise

150

Fig. 4. Effect of operating frequency on the relation between the phase difference and viscosity.

the viscous loading assumed in the simulation, wasobtained.

3. Results and discussion

Plexiglas, graphite and aluminum substrates wereused to obtain the experimental data. Fig. 7 shows theexperimental and simulated waveforms obtained forPlexiglas/fluid N15000 (q = 416.4 poise and p =

891.3 kg/m3 at 25°C) interface. Fig. 7(a) shows the refer-ence signal (x(t)) for a Plexiglas/air interface. The ampli-tude spectra (A&)) of this reference signal and responsedue to the assumed viscous loading (I Q(CC), q)l), withinthe bandwidth of the RF signal are shown in Fig. 7(b).Corresponding phase spectra (#&I)) and response dueto the assumed viscous loading (@&I, q)) for the sameRF signal are illustrated in Fig. 7(c). the simulated RFresponse (A,(t)) is plotted along with the reference (AR(t))and the experiment (&(t)) in Fig. 7(d). The experimental

Vimal Shah, Krishnan Balasubramaniam / Ultrasonics 34 (1996) 817-824 8 2 1

-a -’

A’-A’

A’ --+--- GraphiteA’ Y

,yAA -+b---- Aluminum

- -4 - - Steel- - 4 -

- - + - - +

+ / 4 - - - - + - A - - *--4

&‘4-

0 5 0 0 0 10000 15000 2 0 0 0 0 2 5 0 0 0 3 0 0 0 0

Viscosi ty in Poise

Fig. 5. Effect of substrate material properties on the relation between the phase difference and viscosity.

Shear-

vi8couaPhrid Pu~cccivc8 (PRSOSZ)

D&Pmcwor -

Fig. 6. Block diagram showing experimental setup.

and the simulated responses are similar and as expected,have a reduced amplitude and a phase delay whencompared with the reference. Figs. 8, 9 and 10 show thecorrelation of experimental and simulated data fordifferent substrates. Data, obtained using Plexiglas asthe substrate, show the most sensitivity to change inviscosity (Fig. 8). The response of aluminum/viscousfluid interface to change in viscosity, shows the leastsensitivity (Fig. 10).

In general, we observed that the comparison betweenthe experimental data and the simulation showed a goodagreement at the onset of the waveform until the firstpeak. After the first rise (or the second rise when the1 MHz transducer is used), the correlation began todegrade. It was observed that the degradation becamesevere with an increase in viscosity of the fluid. This wastrue for all three types of substrates. Some factors that

may be contributing to the disagreement in comparisonare discussed next.

In the derivation of Eq. (2), it is assumed that themedia is semi-infinite and the incident wave is a planewave. In the experiment, however the substrate andsource were both finite. The plane wave assumption isnot strictly valid and the generated waves were sphericalin nature. Also, the transducer does not generate aperfect shear wave and due to the Poisson’s effect shearwave generation is always associated with simultaneousgeneration of compressional waves. Compressionalwaves normally travel almost twice as fast as shearwaves in solids and are affected by the fluid bulkmodulus and viscosity. Depending on the substratecharacteristics, these waves could be received at thesame time as shear waves and so may interfere. It isdifficult to eliminate the effects of these compressionalwaves entirely.

A maximum error of + 2.5% is expected in all the-measurements. Temporal averaging was used to reducethe instrument noise. Trigger jittering delay may havebeen averaged and could have led to experimental errorsin the measurement of the phase.

Accounting for phase difference in the reflected waveis not in complete agreement with the experimentalphase difference. In the simulations, the phase differencerelation is assumed to be valid only within the bandwidthof the received ultrasound signal. Physically, the relationis valid for the low and high frequency regions beyondthe bandwidth. So, the fluid responds to the entirefrequency range, whereas the simulation response is onlywith respect to the bandwidth. Hence, a small differencein the simulated signal compared with the experimentaldata can be expected.

822 Vimal Shah, Krishnan Balasubramaniam / U l t r a s o n i c s 3 4 ( 1 9 9 6 ) 8 1 7 - 8 2 4

-0.1520 40 60 80

Frequency in 12.2 * KHz0 100 200

Time in 20 * nanosec.

-620 40 60 80

Frequency in 12.2 * KHz Time in 20 * nanosec.

Fig. 7. Simulation of reflection from Plexiglas/fluid N15000 (416.4 poise at 25°C) interface for 1 MHz transducer. (a) Reference signal (@),(b) amplitude spectrum (-) and viscous loading response ( x) to amplitide, (c) phase spectrum (-) and viscous loading response ( x) to phase, and(d) comparison between reference (@), experimental (0) and simulated (-) waveforms.

+! 0.10.L*43 -0.05f”4

-0.200 5 0 100 0 50 100

Time in 5 * nanosec. Time in 5 * nanosec.

-0.100 50 100

Time in 5* nanosec.0 50 100 150

Time in 5 * nanosec.

Fig. 8. Comparison of simulated (-) and experimental (0) reflections from a Plexiglas/viscous fluid interface. Simulations for fluids (a) NlOOO(19.94 poise) (b) N2000 (52.49 poise), (c) N4000 (104.5 poise), and (d) all three simulations shown together (+ NlOOO, + N2000, x N4000), for2.25 MHz transducer at 25°C.

4. Conclusions

Simulations based on the impedance model of reflec-tion of plane polarized ultrasound shear waves from asolid/fluid substrate were presented and validated by

experiments. Simulations compare well with the experi-mental measurements. The comparison is dependent onthe acoustic impedance mismatch between the substrateand the viscous fluid, as well as the viscosity of the fluid.The sensitivity of the shear wave reflection response to

;. ’

Vimal Shah, Krishnan Balasubramaniam / Ultrasonics 34 (1996) 817-824 8 2 3

150 300 0 150 300Time in 10 * nanosec. Time in 10 * nanosec.

~ 0.3Ec 0.1.LII

5 -0.1a$ -0.3

Time in 10 * nanosec. Time in 10 * nanosec.

Fig. 9. Comparison of simulated (-) and experimental (0) reflections from a graphite/viscous fluid interface. Simulations for fluids (a) NlOOO(19.94 poise), (b) N2000 (52.49 poise), (c) N4000 (104.5 poise) and (d) all three simulations shown together (+ NlOOO, + N2000, x N4000), for1 MHz transducer at 25°C.

0 150Time in 10 * nanosec.

0C

:I I I I I I I I I

- 0 . 8

0 150Time in 10 * nanosecs .

4-0 .8

0 150Time in 10 * nanosecs .

0 150Time in 10 * nanosecs

Fig. 10. Comparison of simulated (-) and experimental (0) reflections from an aluminum/viscous fluid interface. Simulations for fluids (a) NlOOO(19.94 poise), (b) N2000 (52.49 poise), (c) N4000 (104.5 poise) and (d) all three simulations shown together (+ NlOOO, + N2000, x N4000) for1 MHz transducer at 25°C.

changes in viscosity was obtained for the substrate withbest impedance match. Some reasons for discrepanciesbetween the impedance model-based simulations andthe experiments were discussed in the context of experi-mental and signal processing procedures.

Acknowledgements

This work is supported by the United StatesDepartment of Energy, through grant numberDE-FG02-93CH-10575 t o t h e D i a g n o s t i c Instru-

824 Vimal Shah, Krishnan Balasubramaniam / Ultrasonics 34 (1996) 817-824

mentation and Analysis Laboratory at the MississippiState University.

References

I31PI

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I31

WI

W.P. Mason et al., Phys. Rev. 75(6) (1949) 936.W.P. Mason and H.J. McSkimin, Bell Systems Tech. J. 3( 1)(1952) 122.W. Roth and S.R. Rich, J. Appl. Phys. 24(7) (1953) 940.L.C. Lynnworth, IEEE Trans. Sonics and Ultrasonics 22(2)(1974) 71.S.H. Sheen et al., Rev. Prog. QNDE, eds. D.O. Thompson andD.E. Chimenti, 14(A) (1995) 1151.R.S. Moore and H.J. McSkimin, 1970 Physical Acoustics, Vol. 6,ed. W.P. Mason (Academic Press, New York, 1970) pp. 167-243.

[7] J. Krautkramer and H. Krautkramer, Ultrasonic Testing ofMaterials (Springer, Berlin, 1990).

[8] R.D. Costley Jr. et al., Rev. Prog. QNDE eds. D.O. Thompsonand D.E. Chimenti, 15 (1996).

[9] T. Sato et al., Jpn. J. Appl. Phys. 32 (5B 1) (1993) 2392.[ lo] H.T. Chien (1995) Private communication.[ 1 l] V.V. Shah et al., Rev. Prog. QNDE, eds. D.O. Thompson and

D.E. Chimenti, 15 (1996) 2067.[ 121 K.F. Herzfeld and T.A. Litovitz, Absorption and Dispersion of

Ultrasonic Waves (Academic Press, New York, 1959).[ 131 E. Oran Brigham, The Fast Fourier Transform and its

Applications (Prentice-Hall, New Jersey, 1988).[ 141 A. Papoulis, Signal Analysis (McGraw-Hill, Singapore, 1984).[ 153 T.A. Litovitz and C.M. Davis, Physical Acoustics, Vol. 2, ed.

W.P. Mason (Academic Press New York, 1964) pp. 218-349.[ 161 M.C. Davis, J. Acoust. Sot. Amer. 64(2) (1978) 406.[ 17) S.H. Sheen et al., IEEE Symp. Ultrasonics (1988) 537.

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824 Vimal Shah, Krishnan Balasubramaniam / U l t r a s o n i c s 3 4 ( 1 9 9 6 ) 8 1 7 - 8 2 4

mentation and Analysis Laboratory at the MississippiState University.

[7] J. Krautkramer and H. Krautkramer, Ultrasonic Testing ofMaterials (Springer, Berlin, 1990).

[8] R.D. Costley Jr. et al., Rev. Prog. QNDE eds. D.O. Thompsonand D.E. Chimenti, 15 (1996).

References[9] T. Sato et al., Jpn. J. Appl. Phys. 32 (5B 1) (1993) 2392.

[lo] H.T. Chien (1995) Private communication.

Cl1L-21

I31I31

I31

PI

W.P. Mason et al., Phys. Rev. 75(6) (1949) 936.W.P. Mason and H.J. McSkimin, Bell Systems Tech. J. 3(l)(1952) 122.W. Roth and S.R. Rich, J. Appl. Phys. 24(7) (1953) 940.L.C. Lynnworth, IEEE Trans. Sonics and Ultrasonics 22(2)(1974) 71.S.H. Sheen et al., Rev. Prog. QNDE, eds. D.O. Thompson andD.E. Chimenti, 14(A) (1995) 1151.R.S. Moore and H.J. McSkimin, 1970 Physical Acoustics, Vol. 6,ed. W.P. Mason (Academic Press, New York, 1970) pp. 167-243.

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