Adamowski, Julio C.

Buiochi, Flávio

Franco, Ediguer

Higuti, Ricardo T.

Silva, Emílio Carlos Nelli

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  50. Internationales  Wissenschaftliches Kolloquium   September, 19-23, 2005   Maschinenbau  von Makro bis Nano / Mechanical Engineering  from Macro to Nano   Proceedings    Fakultät für Maschinenbau / Faculty of Mechanical Engineering     Startseite / Index:  http://www.db-thueringen.de/servlets/DocumentServlet?id=15745 Impressum  Herausgeber: Der Rektor der Technischen Universität llmenau  Univ.-Prof. Dr. rer. nat. habil. Peter Scharff  Redaktion: Referat Marketing und Studentische Angelegenheiten  Andrea Schneider   Fakultät für Maschinenbau  Univ.-Prof. Dr.-Ing. habil. Peter Kurtz, Univ.-Prof. Dipl.-Ing. Dr. med. (habil.) Hartmut Witte, Univ.-Prof. Dr.-Ing. habil. Gerhard Linß,  Dr.-Ing. Beate Schlütter, Dipl.-Biol. Danja Voges,  Dipl.-Ing. Jörg Mämpel, Dipl.-Ing. Susanne Töpfer,  Dipl.-Ing. Silke Stauche  Redaktionsschluss: 31. August 2005 (CD-Rom-Ausgabe)  Technische Realisierung:  Institut für Medientechnik an der TU Ilmenau (CD-Rom-Ausgabe) Dipl.-Ing. Christian Weigel Dipl.-Ing. Helge Drumm Dipl.-Ing. Marco Albrecht  Technische Realisierung: Universitätsbibliothek Ilmenau (Online-Ausgabe)   Postfach 10 05 65  98684 Ilmenau  Verlag:   Verlag ISLE, Betriebsstätte des ISLE e.V.  Werner-von-Siemens-Str. 16  98693 llmenau   © Technische Universität llmenau (Thür.) 2005   Diese Publikationen und alle in ihr enthaltenen Beiträge und Abbildungen sind urheberrechtlich geschützt.   ISBN (Druckausgabe): 3-932633-98-9  (978-3-932633-98-0) ISBN (CD-Rom-Ausgabe): 3-932633-99-7 (978-3-932633-99-7)  Startseite / Index: http://www.db-thueringen.de/servlets/DocumentServlet?id=15745 50. Internationales Wissenschaftliches Kolloquium Technische Universität Ilmenau 19.-23. September 2005  F. Buiochi / E. E. Franco / R. T. Higuti / E. C. N. Silva / J. C. Adamowski   Liquid dynamic viscosity measurement by ultrasonic wave mode conversion   ABSTRACT  This work presents a cell to measure the liquid dynamic viscosity using an ultrasonic wave mode conversion from longitudinal to shear wave and vice-versa. A prototype-measuring cell was constructed to test the proposed method.  Measurements of the viscosity of automotive oils (SAE 90 and SAE140) were obtained in the frequency range from 1 to 10 MHz. These results are also compared with the Maxwell model with two relaxation times, showing the dependency of dynamic viscosity with the frequency of the shear wave. The experimental data are in good agreement with those provided by the Maxwell model.   INTRODUCTION  Viscosity is the main parameter that characterizes the flow of liquids in an industrial process, and its measurement provides information on the resistance to flow in tubes or in autoclaves during the molding operations. Besides, viscosity measurements are used to develop and to control the quality of the finished products, and to optimize product properties. So the knowledge of viscosity is crucial to many industrial processes in the chemical, food industry and so on.  Typical methods to measure the viscosity at low frequencies depend on the drag on an oscillating surface immersed in the liquid. Such methods are not appropriate for real-time process control. A more suitable method for real-time control employs ultrasonic waves to obtain the viscosity of liquids. The ultrasonic reflectance method was developed to measure the viscosity of liquids as early as 1949 by Mason et al. [1]. This method is based on the measurement of the complex reflection coefficient of a plane shear wave reflected in a solid-liquid interface at an oblique or normal incidence.  The cell discussed in this paper uses a piezoelectric transducer that generates longitudinal waves and a PVDF membrane that responds only to the longitudinal mode. The shear wave is generated by a mode conversion. Since the acoustic impedance of the shear waves for the solid part of the cell is known, the dynamic viscosity of the liquid can be obtained from the density of the liquid and the complex reflection coefficient at the solid-liquid interface.   THEORY  In Fig. 1, the propagation of a harmonic shear wave along the z-axis in a viscoelastic isotropic medium (medium 2) can be described by:  22*2222tuGzu xx∂∂ρ∂∂ = ,               (1)  where ux is the transverse displacement in the x direction,  the complex shear modulus of medium 2, and *2G2ρ  the density of the medium 2. The complex shear modulus is defined as the ratio of shear stress to shear strain, , where G  is the storage modulus and  the loss modulus, which is related to the dynamic viscosity "'*2 jGGG += ' G"2η  by the following equation:  ωη"2G= ,                (2)  where ω is the angular frequency. The complex characteristic acoustic impedance  for shear waves of the medium 2 is given by *2Z 2*2*2 ρGZ = .                (3)  Now considering the propagation of shear waves from the medium 1 (second buffer rod) to the medium 2 (sample), the complex reflection coefficient at the interface is given by  1*21*2*12 ZZZZR +−= ,                (4)  where 111 cZ ρ=  is the characteristic acoustic impedance of medium 1, a solid material with a known density 1ρ  and a propagation velocity to be determined . In general, the solid introduces very little attenuation, and its impedance can be considered real. The medium 2 is the viscoelastic 1cmedium whose viscosity is being measured and it has a complex impedance. Hence the complex reflection coefficient can be represented in an exponential form, , where Rθθπ jj eReRR 12)(12*12 −== +12 is the magnitude and )( θπ +  the phase angle. If the medium 2 is an air sample (reference),  and 112 =R 0=θ . Consequently, the reflected wave is 180o out of phase with the incident wave. If medium 2 is a liquid sample, R12 is smaller than 1 and θ is the phase shift (a negative quantity). These quantities, R12 and θ , caused by the liquid, can be measured by comparing the reflected wave at the solid-liquid interface with that of the reference wave at the solid-air interface. The value of the dynamic viscosity is obtained by the following expression:  The value of the dynamic viscosity is obtained by the following expression:  2211212212122122)()cos21(sen)1(4ωρρθθη cRRRR++−−= ,              (5)  where R12 and θ are the magnitude and phase of the complex reflection coefficient, ω is the angular frequency, ρ1 and c1 are the density and phase velocity of the medium 1, and ρ2 is the density of the medium 2 [2].    MEASUREMENT CELL  The cell discussed in this paper, as shown in Fig. 1, consists of a piezoelectric ceramic transmitter, a PVDF (Poly-Vinylidene Fluoride) membrane receiver, PMMA (polymethyl-methacrylate) buffer rod, and an aluminum solid prism. The liquid sample is loaded on a face of the prism, which is opposite to an oblique face immersed in water. The transmitter emits a short longitudinal wave that travels through the PMMA buffer rod, the PVDF membrane and the water buffer, and reaches the prism oblique face. At this oblique water-solid interface, there is a wave mode conversion from longitudinal wave to shear wave. The shear wave propagates through the prism and reaches the solid-sample interface at normal incidence. At this interface, the shear wave reflects and returns to the receiver after back propagating through the prism and water. The reflected waves are measured in the longitudinal mode by the aperture PVDF membrane, which is sufficiently large to intercept the entire propagating pulse avoiding errors due to the acoustic diffraction effect and the lack of stability, in time, of the emitter and the associated electronic. The strategy used to obtain the viscosity is based on the measurement of the complex reflection coefficient of shear waves at the solid-liquid sample interface, using the relative reflection method. The complex reflection coefficient (magnitude and phase) is obtained by normalizing, in the frequency domain, the solid-sample echo with respect to the solid-air echo recorded in a previous experiment [1], [2], [3].   PMMA buffer rodWater  bufferCeramic transducer ( transmitter ) PVDF membrane( receiver ) Liquid sample 1 Solid prism2Shear waveLongitudinalwave T1aaxz Figure 1. Schematic draw of the measurement cell.  The method employed in the measurement of the magnitude of the reflection coefficient and the phase is in reality a set of two measurements at the same temperature. First, an air sample is taken as a reference, obtaining the signals aT(air) and a1(air). The Fourier transforms at a selected frequency are calculated, resulting in the values AT(air) and A1(air). Then the measurement is repeated for the liquid sample, obtaining A1(liq) and AT(liq). The magnitude and the phase of the reflection coefficient can be calculated as the ratio of the second to the first measurements. To eliminate the problems with equipment drift [4] the relative reflection method employs a normalization with respect to AT(liq) and AT(air). The complex reflection coefficient is given by:  )()(1)()(1*12 //airTairliqTliqAAAAR −= ,              (5)  EXPERIMENTAL RESULTS  Figure 2 shows the viscosity versus frequency for the aluminum prism, these results are compared with the theoretical ones obtained by the Maxwell model (dashed line) and the Newtonian liquid model (solid line). Taking the values obtained by the measurement cells and comparing them with the measured values by the rotational viscometer (Newtonian liquid), the relative errors are in the range from 4% to 40% for SAE90 and from 20% to 50% for SAE140. The large error is due to the elastic effect (non-Newtonian liquid) is not neglected to higher frequencies and to higher viscosity liquids.  1 2 3 4 5 6 7 8 9 10 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Viscosity (Pa.s) Frequency(MHz)SAE 140 SAE 90  Figure 2. Viscosity versus frequency for the aluminum prism   CONCLUSION  A cell to measure the dynamic viscosity of liquids using wave mode conversion was presented. The experimental results are in good agreement when compared with the Maxwell model with two relaxation times, showing how the dynamic viscosity varies with frequency.  ACKNOWLEDGEMENT  The authors would like to thank CAPES, FAPESP, CNPq - Brazil for funding this research program.  References: [1] W. P. Mason, W. O. Baker, H. J. McSkimin and J. H. Heiss, 1949, Measurement of shear elasticity and viscosity of liquids at ultrasonic frequencies. Phys. Rev., vol. 75, pp. 936-946. [2] F. Buiochi, J. C. Adamowski and C. M. Furukawa, 1998, Measurement of viscosity using wave mode conversion, IEEE International Ultrasonics Symposium, October 5-8, Sendai, Japan, pp. 1193- 1196. [3] F. Cohen-Tenoudji, W. J. Pardee, B. R. Tittmann, L. A. Ahlberg and R. K. Elsley, 1987, A shear wave rheology sensor, IEEE Trans. Ultrason. Ferroelec., Freq. Contr., vol. 34, n. 2, pp. 263-269. [4] J. C. Adamowski, F. Buiochi, C. Simon, E. C. N. Silva and R.A. Sigelmann, 1995, Ultrasonic measurement of density of liquids, J. Acoust. Soc. Am., vol. 97, pp. 354-361.  Authors: Assistant Professor Flávio Buiochi Eng. Ediguer Franco Assistant Professor Ricardo T. Higuti Associate Professor Emílio C. N. Silva Associate Professor Julio C. Adamowski Department of Mechatronics Engineering, Escola Politécnica da Universidade de São Paulo Av. Prof. Mello Moraes, 2231, 05508-900 São Paulo, SP, Brazil E-mail: fbuiochi@usp.br 

Liquid dynamic viscosity measurement by ultrasonic wave mode conversion

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Liquid dynamic viscosity measurement by ultrasonic wave mode conversion

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