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Study of Ultrasound Transmission through an Immersed Glass Plate in view of Sonochemical Reactor Design Optimisation

Study of Ultrasound Transmission through an Immersed Glass Plate in view of Sonochemical Reactor... Hindawi Publishing Corporation Advances in Acoustics and Vibration Volume 2009, Article ID 512839, 9 pages doi:10.1155/2009/512839 Research Article Study of Ultrasound Transmission through an Immersed Glass Plate in view of Sonochemical Reactor Design Optimisation 1 1 1, 2 2 R. Viennet, J.-Y. Hihn, M. Jeannot, and R. Berriet Institut UTINAM-SRS, Universit´ e de Franche-Comt´ e, UMR CNRS 6213, 30 avenue de l’Observatoire, 25009 Besanc ¸on Cedex, France IMASONIC SAS, Z.A. rue des Savourots, 70190 Voray sur l’Ognon, France Correspondence should be addressed to R. Viennet, remy.viennet@univ-fcomte.fr Received 17 February 2009; Accepted 6 April 2009 Recommended by KM Liew The purpose of this paper is to improve the design of an ultrasonic reactor for industrial applications in liquids, which consists of a double-structured tank. This paper presents an experimental approach for studying ultrasonic transmission through an immersed glass plate. Several inclination angles, between 0 and 40 , and several thicknesses have been investigated. Acoustic efficiency was determined using hydrophone measurements in different places in the reactor. A first reactor prototype was built and the optimised configuration defined was experimentally partially characterized and validated. Copyright © 2009 R. Viennet et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction frequency transducer was developed by the Laboratory of Molecular and Environmental Chemistry (University of Several works have been carried out with ultrasound applied Savoie, Chamber ´ y, France). This material exhibits good to various chemical and electrochemical processes, with great insulating and noncorrosive properties. However, Pyrex glass effects of ultrasound irradiation [1, 2]. In the particular case is not resistant to shock or thermal expansion and has low of electrochemistry, modifications alter many heterogeneous thermal conductivity that is a major drawback for transducer system mechanisms, for example, accelerated corrosion tests cooling. Moreover, poor cooling results in a decrease of which have been developed using power ultrasound at transmitted ultrasonic powers and irradiation times. 20 and 40 kHz [3, 4]. High frequency power ultrasounds Thefinalgoalofthisworkistoproduce areactor for which this protective glass sheet would not be stuck on the are used to improve recovery of silver from photographic processing solutions [5], electroless deposition of copper [6], ceramic, but hang a little distance away, in the form of a or electrosynthesis [2]. As these various power ultrasound double-structured tank. The inner compartment contains the reactional medium, and the transducer is attached to applications are often carried out in aggressive environments, they are limited to a small scale and require the use of the bottom of the outer cell. In the space between these a protective material stuck on a piezoelectric ceramic [7]. two cells, a noncorrosive cooling fluid can be used, making This protective plate, made of stainless steel or glass, allows use of protective material unnecessary for the transducer. wave transmission to the medium. To make this transmission Two previous works have shown that use of an optimised possible, protective plate thickness has to be a fractional part slanted bottom could improve transmission characteristics of of wavelength and depend on sound velocity in the protective double-structured ultrasonic high frequency reactors [8, 9]. material. Handling of this protective plate is often tricky, Moreover, it is a well-known fact that sound transmittivity through an immersed plate is a function of incidence angle which leads to major problems in wave transmission to the medium. The protective plate material is also an important and plate thickness [10–12]. choice criterion. Use of steel for protective material requires The first step in designing a reliable reactor consisted an electric contact with the piezoelectric element that makes in extending the previous study to more numerous config- electromechanical reaction impossible. Consequently, use urations, investigating ultrasound transmission throughout of Pyrex glass offers many advantages. This type of high a glass plate for an extensive number of inclination angles 2 Advances in Acoustics and Vibration Absorption and plate thicknesses. To conduct this study, our first aim was to simulate the ultrasound fields generated in the reactor 110 mm by a 500 kHz transducer in order to define an optimal Reactional configuration. A calculation code using finite elements was medium used to conduct a temporal analysis of our problem. The configuration shown in Figure 1 was simulated and three Thickness angles (20, 30 and 40 ) of inclination were retained with different glass thicknesses of the slanted bottom. These values were close to the optimal ones found in the two previous mm works. For these simulations, the transmission coefficient Absorption is defined by W /W where W is the integral of (α,e) 0 (α,e) the acoustic of the intensities in one plane reactor, for an inclination angle α and a thickness e,and W is the integral Cooling fluid of the acoustic intensities in one plane reactor corresponding to the available power leaving the transducer. Figure 2 shows the transmission coefficient as a function of the inclination Incident plan waves generated by the angles for 3 standard glass thicknesses. We can observe transducer that the global shape of the curve obtained with a 3.3 mm Reflexion thickness is fairly close to results of the previous experimental Figure 1: Simulated configuration. works [9]. A better glass plate inclination angle for wave transmission is obtained in this case at about 30 for a 0.5 3 mm plate thickness, where an optimal inclination angle 0.45 of 30 has been found for a 3 mm glass plate [9]. Whereas 0.4 the global behaviour of the curve obtained by simulation is 0.35 always correct for a 5 mm thickness, this is not completely the case for the 2 mm thickness. Allowance must also be 0.3 made for differences in calculation mode of the transmission 0.25 coefficient between the various works. The simulations take 0.2 into account the average of the ultrasound energy on a 0.15 wide surface, while the previous works were limited to the 0.1 central zone. This can account for some discrepancies in the 0.05 range of magnitude of the values, and justify the choice of 20 22 24 26 28 30 32 34 36 38 40 an experimental validation in new operating conditions to Inclination angle ( ) check the relevance of the code of calculation used for the simulations before pursuing the theoretical approach. 2mm 3.3mm 5mm 2. Experimental Study of Ultrasound Figure 2: Transmission coefficient for 3 different plate thicknesses: Transmission through a Glass Plate Welded in 2.2, 3.3 and 5 mm. an Oblong or a Cylindrical Reactor This series of experiments was carried out using appropriate plate at the same distance (corresponding to the available equipment with an ultrasonic source and a hydrophone on power leaving the transducer) has been calculated. both sides of a plate with known thickness and inclination. The operating conditions were chosen to allow validation of the simulations, that is, they were conducted in complete 2.1. Oblong Reactor. Results obtained for the three inclina- reactors to take into account wall reflections. Two different tion angles are shown in Figure 6 in termsofcurvesatiso- geometries of reactors (Figure 3) were used: oblong (close to intensity, graduated in dB. The greater the angle is, the more the simulated configuration) and cylindrical (as used in most the influence of reflections on edges can be observed. This sonoelectrochemical applications). induces a deformation of the focal spot, which becomes The acoustic field in the reactor was mapped using irregular when the angle increases. The same observations hydrophone measurements. The acoustic intensities and were made in different measurement planes. Table 1 includes their distribution in the reactor were obtained by recording the maximal values of Vpp and the transmission coefficient the peak to peak voltage in different planes inside the reactor. for three angles and two measurements planes: the first near The hydrophone motions are described in Figure 4 (mapping the plate and the second at 5 cm (corresponding to Figures zones) and Figure 5 (measurement planes). In order to 5(a) and 5(b)). The results presented here are more suitable determine the transmission coefficient, the integral of the to the range of magnitude of the simulated ones, due to acoustic intensities measured in a plane for a slant plate angle the fact that the transmission coefficients are calculated over α on the integral of the acoustic intensities measured without a larger zone (ratio of average acoustic intensity with or Transmission coefficient Advances in Acoustics and Vibration 3 Transducer 60 mm 1 Plane of measure 20°, 30°, 40° 300 mm 110 mm 200 mm Patch of aluminium (a) Hydrophone Transducer (a) 60 mm Plane of measure 200 mm (b) Figure 3: (a) Oblong reactor, (b) cylindrical reactor. Hydrophone 5 cm Hydrophone (b) Figure 5: (a) First plane of measurement near the slant plate, (b) 8.7 cm second plane 5 cm from the slant plate. Table 1: Main results obtained in oblong reactor. (a) Hydrophone Angles Hydrophone position Vpp max Transmission coefficient Near the plate 2.72 0.45 5 cm from the plate 2.62 0.40 Near the plate 2.06 0.37 5 cm from the plate 1.75 0.34 5 cm Near the plate 0.66 0.11 5 cm from the plate 0.66 0.10 included in the cylinder diameter, and for several distances (b) from the inclined glass plate (8, 12 and 16 cm). Results are shown for the various distances for each inclination angle. Figure 4: Hydrophone motions (a) in oblong reactor (b) in cylindrical reactor. The peak-to-peak voltages (Vpp) were measured and the iso- acoustic intensity curves were drawn. For a 20 inclination angle, we can observe one focal spot clearly drawn in the centre of the scanned zone. Ultrasound propagates through without plate). If we examine the focal spot, the transmission the plate without being affected by serious deformation coefficient restricted to this limited area reaches a value of in distribution of the acoustic intensity that it entails. 80% and was obtained for an inclination of 20 . This will be This distribution persists when we move away from the of particular interest for the electrochemical reaction which oblique plate (Figure 7). For an inclination angle of 30, takes place at an electrode, mainly centred in the reactor. the focal spot becomes irregular when we move away from the plate (Figure 8), and in the same way as the oblong 2.2. Cylindrical Reactor. For this geometry, the hydrophone reactor at maximum inclination angles, acoustic ultrasonic was moved in a square (with 5 cm diagonal—Figure 4(b)) intensity distribution is seriously disturbed by plate presence 4 Advances in Acoustics and Vibration Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −35 −40 −40 −45 −45 −50 −50 −50 −30 −10 10 30 50 −60 −40 −20 0 20 40 60 Axis 1-mm Axis 1-mm (a) (b) Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −35 −40 −40 −45 −45 −50 −50 −60 −40 −20 0 20 40 60 −60 −40 −20 0 20 40 60 Axis 1-mm Axis 1-mm (c) (d) ◦ ◦ ◦ Figure 6: Maps of peak-to-peak voltages observed in the system without oblique plate (a), with a plate tilted at 20 (b), at 30 (c ) and at 40 (d) for an excitation burst signal of four periods with 10 Vpp amplitude. Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour 5dB per contour 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 −5 −5 −5 −10 −10 −10 −15 −15 −15 −20 −20 −20 −20 −15 −10 −50 5 10 15 20 −20 −15 −10 −50 5 10 15 20 −20 −15 −10 −50 5 10 15 20 Axis 1-mm Axis 1-mm Axis 1-mm (a) (b) (c) Figure 7: Maps of peak-to-peak voltages observed in the system with a plate tilted at 20 : (a) at 8 cm, (b) at 12 cm, and (c) at 16 cm from the plate for an excitation burst signal of four periods with 10 Vpp amplitude. (Figure 9). Table 2 includes the maximal values of Vpp and Nevertheless, it is impossible to validate the simulation the transmission coefficient for three angles and the three correctly in this way. The software for our arrangement positions of the hydrophone. The values obtained are even uses a temporal analysis and it would have been preferable better than for the oblong reactor for a 20 inclination angle. to use a harmonics analysis. 3 inclination angle values On the other hand, for 40 , a marked decrease is observed are not sufficient for complete matching of the adjustable with extremely weak values of the transmission coefficients. parameters of the calculation code, and some discrepancies Axis 2-mm Axis 2-mm Axis 2-mm Axis 2-mm Axis 2-mm Axis 2-mm Axis 2-mm Advances in Acoustics and Vibration 5 Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour 5dB per contour 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 −5 −5 −5 −10 −10 −10 −15 −15 −15 −20 −20 −20 −15 −10 −5 0 5 1015 2025 −15 −10 −5 0 5 1015 2025 −15 −10 −5 0 5 1015 2025 Axis 1-mm Axis 1-mm Axis 1-mm (a) (b) (c) Figure 8: Maps of peak-to-peak voltages observed in the system with a plate tilted at 30 : (a) at 8 cm, (b) at 12 cm, and (c) at 16 cm from the plate for an excitation burst signal of four periods with 10 Vpp amplitude. Table 2: Main results obtained in cylindrical reactor. 5, 6 and 10 mm. Transmission coefficients correspond to the ratio of the maximal peak to peak voltage with and Angles Hydrophone position Vpp max Transmission coefficient without plate between hydrophone and the transducer. These 8 cm 2.7 0.50 peak-to-peak voltages were determined by calculating the 12 cm 2.4 0.50 integral of acoustic intensities in the measurement plane. If 16 cm 2.2 0.51 we examine the results grouped in Figure 11, we note that 8 cm 2.1 0.28 the behaviour of the curves corresponding to the 2.2, 3 and 30 4 mm thicknesses is very close to what we observed in the 12 cm 2.1 0.29 previous work [8, 9], namely,acoefficient of fairly weak 16 cm 1.6 0.30 transmission for the majority of inclination angles, and a 8 cm 0.6 0.02 ◦ very net optimum for a given angle. This also applies to the 12 cm 0.6 0.02 6 mm thick plate, with a surprisingly excellent coefficient of 16 cm 0.6 0.02 transmission for a horizontal position (angle of inclination of 0 ), while curves are less well defined for the 5 mm and 10 mm plates. persist. To obtain values as well as sufficient and reliable Therefore, we arrange several (thickness/inclination information to help develop a new reactor, we then decided angle) pairs which appear of interest for the design of to conduct a study with more systematic characteristics of prototypes of complete reactors, for example 35 of angle of plate thicknesses and angles of inclination. inclination for a glass thickness of 2.2 mm. At first, our choice concerned the solution which corresponds to the angle of inclination 0 for a thickness of roughly 6 mm. This solution 3. Systematic Study of Ultrasonic Intensity had the merit of finding a simple theoretical explanation Transmission throughout a Glass Plate for (application of Rayleigh’s law) and of being easier to build. Various Plate Thicknesses and Inclination Angles 4. Optimal Configuration Determination For these experiments, we used another experimental device which consists of a glass plate fixed to an axis, positioned The major drawback of the chosen configuration is the between a transducer used in emission and another in recep- possibility of reflections on the plate, which can lead to a tion. The entire system is immersed in water (Figure 10). damage to the transducer. Therefore, we decided to check The advantages of this system are that it allows easy and reflection and transmission for different plate thicknesses. continuous variation of the angle of inclination, and that the Two transducers located in front of one another were used studied thickness is modifiable quickly by changing the glass for evaluation purposes (Figure 12). The first one, used in plate. However, on the other hand, the reflections against emission/reception was supplied with a 10 Vpp sinusoidal walls are not taken into account and we are thus less close to long burst signal, whereas the second was used only in the real behaviour of a reactor. Peak to peak maximal voltages reception. A glass plate was placed between these two were measured for inclination angles varying between 0 and transducers. The emitted signal of the first transducer and 40 , and for the following glass plate thicknesses: 2.2, 3, 4, the reflected signal from the glass plate were recorded on an Axis 2-mm Axis 2-mm Axis 2-mm 6 Advances in Acoustics and Vibration Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour 5dB per contour 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 −5 −5 −5 −10 −10 −10 −15 −15 −15 −20 −20 −20 −20 −15 −10 −50 5 10 15 20 −20 −15 −10 −50 5 10 15 20 −20 −15 −10 −50 5 10 15 20 Axis 1-mm Axis 1-mm Axis 1-mm (a) (b) (c) Figure 9: Maps of peak-to-peak voltages observed in the system with a plate tilted at 40 : (a) at 8 cm, (b) at 12 cm, and (c) at 16 cm from the plate for an excitation burst signal of four periods with 10 Vpp amplitude. the transducer and surrounding media considered as an equivalent electrical circuit. With the KLM model, we defined the following configu- 60 mm ration for the system. 140 mm (1) Matching layer thickness: 0.5 mm. (2) Glass plate thickness: 11.03 mm. Inclined Transducer plate (3) Space between transducer and glass plate: about 160 mm 10 mm, this value does not need to be very precise. However, it must be sufficient to assure correct Figure 10: Experimental setup configuration. cooling of the transducer. (4) Liquid height in the reactor is not an important parameter. oscilloscope together with the signal received by the second transducer. A transmission coefficient, T,and areflection 5. Transducer Manufacturing and Initial coefficient, R, were calculated by Characterization Reflected voltage Transmitted voltage The first step consisted of adjusting the thickness of a R = , T = . Emitted voltage Emitted voltage 40 mm diameter ceramic P1 89 A4 micron and producing an (1) electroless copper deposit on both faces. The matching layer was created by a resin polymerisation moulded by means of a Results are shown in Figure 13.The reflectioncoefficient 54 mm diameter ring. The moulding process was optimized does not exceed 6% and the transmission coefficient is to reduce the constraints imposed by polymerisation on the maximal for a 6 mm thickness. The sound velocity in the ceramic. The acoustic adaptation of the system “transducer, plate was measured as 5514.2 m/s, thus the optimal working matching layer” was created with an adapter made up frequency was determined as 475 kHz for a glass thickness of of a transformer, six condensers (three of 330 pf, one of 6 mm. We notice here that the system is in very narrow busy 1000 pF, one of 2200 pF and one 4700 pF), a switch and two band with a glass thickness λ, and that variations, even small, resistances. around its nominal frequency will be impossible. A solution The transducer is inserted into a Teflon circular plate will then be a glass blade of thickness λ/2 for 500 kHz, and embedded in the reactor. The glass reactor (Figure 14) excitation of the system with frequencies of 250 and 750 kHz was produced by Dijon Verre Labo (Dijon France). The corresponding to wavelengths of λ and 3λ/2. 11.03 mm thickness glass plate is in Pyrex Corning. To determine optimal design (thickness of the ceramic, The radiation force balance method has been chosen for thickness of matching layer, etc.), the complete reactor was initial characterization of the prototype [14]asitwas easy simulated by means of a software (Piezo-Cad) based on to carry out. A target is placed in front of the transducer the KLM model [13], that is, one-dimensional model of to obtain only the axial constituent of the weight which is Axis 2-mm Axis 2-mm Axis 2-mm Advances in Acoustics and Vibration 7 Transmission coefficient (2.2mm) Transmission coefficient (3.3mm) 35 30 0 0 0 102030 40 50 0 10 203040 50 ◦ ◦ Angle ( ) Angle ( ) (a) (b) Transmission coefficient (4 mm) Transmission coefficient (5 mm) 60 60 50 50 40 40 30 30 20 20 10 10 0 0 0 102030 40 50 0 102030 40 50 ◦ ◦ Angle ( ) Angle ( ) (c) (d) Transmission coefficient (6 mm) Transmission coefficient (10 mm) 100 35 0 0 0 102030 40 50 010 20 30 40 50 ◦ ◦ Angle ( ) Angle ( ) (e) (f ) Figure 11: Transmission coefficient versus angle inclination for different glass plate thicknesses. recorded by means of a balance. Values with and without 6. Concluding Remarks inner reactor were compared with an emitter running at 750 kHz. A yield equal to 40% was obtained in the inner The results of ultrasound transmission through a plate, reactor, compared to 53% in its absence. This first result in the case of cylindrical and oblong reactors, always in is encouraging because it indicates a correct yield with this simplified configuration, constitute a first step for future configuration. reactor design works. These results confirm partially the 8 Advances in Acoustics and Vibration 60 mm 100 mm 11.03 mm 30 mm (a) 93 mm Transducer Figure 14: Glass reactor. a two-component one (shear and compression) after the liquid/solid interface. Moreover, the most valuable results are obtained over the critical angle of reflection, which complicates modelling and simulation whenever the basic relationship is clearly determined (Reissner theory [10]). The creation of a prototype using some of the results of the (b) systematic study shows through its success that change is Figure 12: Experimental set-up used for determination of reflec- possible, and the first results obtained for 750 kHz confirm tions. our belief that the double-structured tank is a good design solution. Some work has still to be carried out to characterize this reactor completely. Other possible frequencies, 500 kHz and 750 kHz, must be tested in the same conditions. The presence of the cavitation phenomenon in the inner reactor should also be confirmed by appropriate chemical or electrochemical techniques. Finally, practical problems persist. The tests carried out on the prototype revealed very low tolerance in variations of thickness or showed drift in exiting frequency applied to the transducer. This is annoying as it decreases the robustness of the reactor and makes it nearly as hard to produce as a classic 02 4 6 8 10 reactor with a stuck glass plate. This problem could be solved Thickness (mm) by use of a dissimilar transducer, which has a wider busy band, and boosts the interest of the slanted bottom which Reflection coefficient (%) has a wider tolerance. Transmission coefficient (%) Figure 13: Transmission and reflection coefficients versus glass References plate thickness. [1] T.J.Mason andJ.P.Lorimer, Sonochemistry: The Applications and Uses of Ultrasound in Chemistry, John Willey & Sons, New York, NY, USA, 1988. results of the previous works and provide possible solutions [2] D. J. Walton and S. S. Phull, “Sonoelectrochemistry,” in through exploitable pairs (angle of inclination, thickness of Advances in Sonochemistry. Vol. 4, pp. 205–284, JAI Press, glass plate). However, the need for calculation codes adapted London, UK, 1996. to these complex geometries persists, because the behaviour [3] M.-L. Doche, J.-Y. Hihn, F. Touyeras, J. P. Lorimer, T. J. Mason, of the tested systems is as yet far from being completely and M. Plattes, “Electrochemical behaviour of zinc in 20 kHz accounted for. The major problem is to take into account sonicated NaOH electrolytes,” Ultrasonics Sonochemistry, vol. the fact that the longitudinal wave in the liquid becomes 8, no. 3, pp. 291–298, 2001. Advances in Acoustics and Vibration 9 [4] V. Ligier, J. Y. Hihn, M. Wer ´ y, and M. Tachez, “Effects of 20 kHz and 500 kHz ultrasound on the corrosion of zinc 2− − precoated steels in [Cl ][SO ][HCO ][H O ]electrolytes,” 4 3 2 2 Journal of Applied Electrochemistry, vol. 31, no. 2, pp. 213–222, [5] B. Pollet, J. P. Lorimer, S. S. Phull, and J. Y. Hihn, “Sonoelec- trochemical recovery of silver from photographic processing solutions,” Ultrasonics Sonochemistry, vol. 7, no. 2, pp. 69–76, [6] F. Touyeras, J.-Y. Hihn, M.-L. Doche, and X. Roizard, “Elec- troless copper coating of epoxide plates in an ultrasonic field,” Ultrasonics Sonochemistry, vol. 8, no. 3, pp. 285–290. [7] A. Francony, Ph.D. thesis,Universited ´ eSavoie,Chamber ´ y, France, 1995. [8] H. Hatano and S. Kanai, “High-frequency ultrasonic cleaning tank utilizing oblique incidence,” IEEE Transactions on Ultra- sonics, Ferroelectrics, and Frequency Control,vol. 43, no.4,pp. 531–535, 1996. [9] J.-Y. Hihn, D. Ber ´ eziat, ´ M.-L. Doche, et al., “Double- structured ultrasonic high frequency reactor using an opti- mised slant bottom,” Ultrasonics Sonochemistry,vol. 7, no.4, pp. 201–205, 2000. [10] H. Reissner, “Der senkrechte und schrage ¨ Durchtritt einer in einem flussigen ¨ Medium erzeugten ebenen Dilatations- Welle durch eine in diesem Medium befindliche planparallele feste Platte,” Helvetica Physica Acta, vol. 11, pp. 140–155, 1938. [11] F. H. Sanders, “Transmission of sound through thin plates,” Canadian Journal of Research, vol. 17, no. 9, pp. 179–193, 1939. [12] R. D. Fay and O. V. Fortier, “Transmission of sound through steel plates immersed in water,” Journal of the Acoustical Society of America, vol. 23, no. 3, pp. 339–346, 1951. [13] R. Krimholtz, D. A. Leedom, and G. L. Matthaei, “New equivalent circuits for elementary piezoelectric transducers,” Electronics Letters, vol. 6, no. 12, pp. 398–399, 1970. [14] International standard IEC 1161 First edition 1992-07. 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Study of Ultrasound Transmission through an Immersed Glass Plate in view of Sonochemical Reactor Design Optimisation

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Copyright © 2009 R. Viennet et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Publishing Corporation Advances in Acoustics and Vibration Volume 2009, Article ID 512839, 9 pages doi:10.1155/2009/512839 Research Article Study of Ultrasound Transmission through an Immersed Glass Plate in view of Sonochemical Reactor Design Optimisation 1 1 1, 2 2 R. Viennet, J.-Y. Hihn, M. Jeannot, and R. Berriet Institut UTINAM-SRS, Universit´ e de Franche-Comt´ e, UMR CNRS 6213, 30 avenue de l’Observatoire, 25009 Besanc ¸on Cedex, France IMASONIC SAS, Z.A. rue des Savourots, 70190 Voray sur l’Ognon, France Correspondence should be addressed to R. Viennet, remy.viennet@univ-fcomte.fr Received 17 February 2009; Accepted 6 April 2009 Recommended by KM Liew The purpose of this paper is to improve the design of an ultrasonic reactor for industrial applications in liquids, which consists of a double-structured tank. This paper presents an experimental approach for studying ultrasonic transmission through an immersed glass plate. Several inclination angles, between 0 and 40 , and several thicknesses have been investigated. Acoustic efficiency was determined using hydrophone measurements in different places in the reactor. A first reactor prototype was built and the optimised configuration defined was experimentally partially characterized and validated. Copyright © 2009 R. Viennet et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction frequency transducer was developed by the Laboratory of Molecular and Environmental Chemistry (University of Several works have been carried out with ultrasound applied Savoie, Chamber ´ y, France). This material exhibits good to various chemical and electrochemical processes, with great insulating and noncorrosive properties. However, Pyrex glass effects of ultrasound irradiation [1, 2]. In the particular case is not resistant to shock or thermal expansion and has low of electrochemistry, modifications alter many heterogeneous thermal conductivity that is a major drawback for transducer system mechanisms, for example, accelerated corrosion tests cooling. Moreover, poor cooling results in a decrease of which have been developed using power ultrasound at transmitted ultrasonic powers and irradiation times. 20 and 40 kHz [3, 4]. High frequency power ultrasounds Thefinalgoalofthisworkistoproduce areactor for which this protective glass sheet would not be stuck on the are used to improve recovery of silver from photographic processing solutions [5], electroless deposition of copper [6], ceramic, but hang a little distance away, in the form of a or electrosynthesis [2]. As these various power ultrasound double-structured tank. The inner compartment contains the reactional medium, and the transducer is attached to applications are often carried out in aggressive environments, they are limited to a small scale and require the use of the bottom of the outer cell. In the space between these a protective material stuck on a piezoelectric ceramic [7]. two cells, a noncorrosive cooling fluid can be used, making This protective plate, made of stainless steel or glass, allows use of protective material unnecessary for the transducer. wave transmission to the medium. To make this transmission Two previous works have shown that use of an optimised possible, protective plate thickness has to be a fractional part slanted bottom could improve transmission characteristics of of wavelength and depend on sound velocity in the protective double-structured ultrasonic high frequency reactors [8, 9]. material. Handling of this protective plate is often tricky, Moreover, it is a well-known fact that sound transmittivity through an immersed plate is a function of incidence angle which leads to major problems in wave transmission to the medium. The protective plate material is also an important and plate thickness [10–12]. choice criterion. Use of steel for protective material requires The first step in designing a reliable reactor consisted an electric contact with the piezoelectric element that makes in extending the previous study to more numerous config- electromechanical reaction impossible. Consequently, use urations, investigating ultrasound transmission throughout of Pyrex glass offers many advantages. This type of high a glass plate for an extensive number of inclination angles 2 Advances in Acoustics and Vibration Absorption and plate thicknesses. To conduct this study, our first aim was to simulate the ultrasound fields generated in the reactor 110 mm by a 500 kHz transducer in order to define an optimal Reactional configuration. A calculation code using finite elements was medium used to conduct a temporal analysis of our problem. The configuration shown in Figure 1 was simulated and three Thickness angles (20, 30 and 40 ) of inclination were retained with different glass thicknesses of the slanted bottom. These values were close to the optimal ones found in the two previous mm works. For these simulations, the transmission coefficient Absorption is defined by W /W where W is the integral of (α,e) 0 (α,e) the acoustic of the intensities in one plane reactor, for an inclination angle α and a thickness e,and W is the integral Cooling fluid of the acoustic intensities in one plane reactor corresponding to the available power leaving the transducer. Figure 2 shows the transmission coefficient as a function of the inclination Incident plan waves generated by the angles for 3 standard glass thicknesses. We can observe transducer that the global shape of the curve obtained with a 3.3 mm Reflexion thickness is fairly close to results of the previous experimental Figure 1: Simulated configuration. works [9]. A better glass plate inclination angle for wave transmission is obtained in this case at about 30 for a 0.5 3 mm plate thickness, where an optimal inclination angle 0.45 of 30 has been found for a 3 mm glass plate [9]. Whereas 0.4 the global behaviour of the curve obtained by simulation is 0.35 always correct for a 5 mm thickness, this is not completely the case for the 2 mm thickness. Allowance must also be 0.3 made for differences in calculation mode of the transmission 0.25 coefficient between the various works. The simulations take 0.2 into account the average of the ultrasound energy on a 0.15 wide surface, while the previous works were limited to the 0.1 central zone. This can account for some discrepancies in the 0.05 range of magnitude of the values, and justify the choice of 20 22 24 26 28 30 32 34 36 38 40 an experimental validation in new operating conditions to Inclination angle ( ) check the relevance of the code of calculation used for the simulations before pursuing the theoretical approach. 2mm 3.3mm 5mm 2. Experimental Study of Ultrasound Figure 2: Transmission coefficient for 3 different plate thicknesses: Transmission through a Glass Plate Welded in 2.2, 3.3 and 5 mm. an Oblong or a Cylindrical Reactor This series of experiments was carried out using appropriate plate at the same distance (corresponding to the available equipment with an ultrasonic source and a hydrophone on power leaving the transducer) has been calculated. both sides of a plate with known thickness and inclination. The operating conditions were chosen to allow validation of the simulations, that is, they were conducted in complete 2.1. Oblong Reactor. Results obtained for the three inclina- reactors to take into account wall reflections. Two different tion angles are shown in Figure 6 in termsofcurvesatiso- geometries of reactors (Figure 3) were used: oblong (close to intensity, graduated in dB. The greater the angle is, the more the simulated configuration) and cylindrical (as used in most the influence of reflections on edges can be observed. This sonoelectrochemical applications). induces a deformation of the focal spot, which becomes The acoustic field in the reactor was mapped using irregular when the angle increases. The same observations hydrophone measurements. The acoustic intensities and were made in different measurement planes. Table 1 includes their distribution in the reactor were obtained by recording the maximal values of Vpp and the transmission coefficient the peak to peak voltage in different planes inside the reactor. for three angles and two measurements planes: the first near The hydrophone motions are described in Figure 4 (mapping the plate and the second at 5 cm (corresponding to Figures zones) and Figure 5 (measurement planes). In order to 5(a) and 5(b)). The results presented here are more suitable determine the transmission coefficient, the integral of the to the range of magnitude of the simulated ones, due to acoustic intensities measured in a plane for a slant plate angle the fact that the transmission coefficients are calculated over α on the integral of the acoustic intensities measured without a larger zone (ratio of average acoustic intensity with or Transmission coefficient Advances in Acoustics and Vibration 3 Transducer 60 mm 1 Plane of measure 20°, 30°, 40° 300 mm 110 mm 200 mm Patch of aluminium (a) Hydrophone Transducer (a) 60 mm Plane of measure 200 mm (b) Figure 3: (a) Oblong reactor, (b) cylindrical reactor. Hydrophone 5 cm Hydrophone (b) Figure 5: (a) First plane of measurement near the slant plate, (b) 8.7 cm second plane 5 cm from the slant plate. Table 1: Main results obtained in oblong reactor. (a) Hydrophone Angles Hydrophone position Vpp max Transmission coefficient Near the plate 2.72 0.45 5 cm from the plate 2.62 0.40 Near the plate 2.06 0.37 5 cm from the plate 1.75 0.34 5 cm Near the plate 0.66 0.11 5 cm from the plate 0.66 0.10 included in the cylinder diameter, and for several distances (b) from the inclined glass plate (8, 12 and 16 cm). Results are shown for the various distances for each inclination angle. Figure 4: Hydrophone motions (a) in oblong reactor (b) in cylindrical reactor. The peak-to-peak voltages (Vpp) were measured and the iso- acoustic intensity curves were drawn. For a 20 inclination angle, we can observe one focal spot clearly drawn in the centre of the scanned zone. Ultrasound propagates through without plate). If we examine the focal spot, the transmission the plate without being affected by serious deformation coefficient restricted to this limited area reaches a value of in distribution of the acoustic intensity that it entails. 80% and was obtained for an inclination of 20 . This will be This distribution persists when we move away from the of particular interest for the electrochemical reaction which oblique plate (Figure 7). For an inclination angle of 30, takes place at an electrode, mainly centred in the reactor. the focal spot becomes irregular when we move away from the plate (Figure 8), and in the same way as the oblong 2.2. Cylindrical Reactor. For this geometry, the hydrophone reactor at maximum inclination angles, acoustic ultrasonic was moved in a square (with 5 cm diagonal—Figure 4(b)) intensity distribution is seriously disturbed by plate presence 4 Advances in Acoustics and Vibration Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −35 −40 −40 −45 −45 −50 −50 −50 −30 −10 10 30 50 −60 −40 −20 0 20 40 60 Axis 1-mm Axis 1-mm (a) (b) Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour −5 −5 −10 −10 −15 −15 −20 −20 −25 −25 −30 −30 −35 −35 −40 −40 −45 −45 −50 −50 −60 −40 −20 0 20 40 60 −60 −40 −20 0 20 40 60 Axis 1-mm Axis 1-mm (c) (d) ◦ ◦ ◦ Figure 6: Maps of peak-to-peak voltages observed in the system without oblique plate (a), with a plate tilted at 20 (b), at 30 (c ) and at 40 (d) for an excitation burst signal of four periods with 10 Vpp amplitude. Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour 5dB per contour 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 −5 −5 −5 −10 −10 −10 −15 −15 −15 −20 −20 −20 −20 −15 −10 −50 5 10 15 20 −20 −15 −10 −50 5 10 15 20 −20 −15 −10 −50 5 10 15 20 Axis 1-mm Axis 1-mm Axis 1-mm (a) (b) (c) Figure 7: Maps of peak-to-peak voltages observed in the system with a plate tilted at 20 : (a) at 8 cm, (b) at 12 cm, and (c) at 16 cm from the plate for an excitation burst signal of four periods with 10 Vpp amplitude. (Figure 9). Table 2 includes the maximal values of Vpp and Nevertheless, it is impossible to validate the simulation the transmission coefficient for three angles and the three correctly in this way. The software for our arrangement positions of the hydrophone. The values obtained are even uses a temporal analysis and it would have been preferable better than for the oblong reactor for a 20 inclination angle. to use a harmonics analysis. 3 inclination angle values On the other hand, for 40 , a marked decrease is observed are not sufficient for complete matching of the adjustable with extremely weak values of the transmission coefficients. parameters of the calculation code, and some discrepancies Axis 2-mm Axis 2-mm Axis 2-mm Axis 2-mm Axis 2-mm Axis 2-mm Axis 2-mm Advances in Acoustics and Vibration 5 Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour 5dB per contour 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 −5 −5 −5 −10 −10 −10 −15 −15 −15 −20 −20 −20 −15 −10 −5 0 5 1015 2025 −15 −10 −5 0 5 1015 2025 −15 −10 −5 0 5 1015 2025 Axis 1-mm Axis 1-mm Axis 1-mm (a) (b) (c) Figure 8: Maps of peak-to-peak voltages observed in the system with a plate tilted at 30 : (a) at 8 cm, (b) at 12 cm, and (c) at 16 cm from the plate for an excitation burst signal of four periods with 10 Vpp amplitude. Table 2: Main results obtained in cylindrical reactor. 5, 6 and 10 mm. Transmission coefficients correspond to the ratio of the maximal peak to peak voltage with and Angles Hydrophone position Vpp max Transmission coefficient without plate between hydrophone and the transducer. These 8 cm 2.7 0.50 peak-to-peak voltages were determined by calculating the 12 cm 2.4 0.50 integral of acoustic intensities in the measurement plane. If 16 cm 2.2 0.51 we examine the results grouped in Figure 11, we note that 8 cm 2.1 0.28 the behaviour of the curves corresponding to the 2.2, 3 and 30 4 mm thicknesses is very close to what we observed in the 12 cm 2.1 0.29 previous work [8, 9], namely,acoefficient of fairly weak 16 cm 1.6 0.30 transmission for the majority of inclination angles, and a 8 cm 0.6 0.02 ◦ very net optimum for a given angle. This also applies to the 12 cm 0.6 0.02 6 mm thick plate, with a surprisingly excellent coefficient of 16 cm 0.6 0.02 transmission for a horizontal position (angle of inclination of 0 ), while curves are less well defined for the 5 mm and 10 mm plates. persist. To obtain values as well as sufficient and reliable Therefore, we arrange several (thickness/inclination information to help develop a new reactor, we then decided angle) pairs which appear of interest for the design of to conduct a study with more systematic characteristics of prototypes of complete reactors, for example 35 of angle of plate thicknesses and angles of inclination. inclination for a glass thickness of 2.2 mm. At first, our choice concerned the solution which corresponds to the angle of inclination 0 for a thickness of roughly 6 mm. This solution 3. Systematic Study of Ultrasonic Intensity had the merit of finding a simple theoretical explanation Transmission throughout a Glass Plate for (application of Rayleigh’s law) and of being easier to build. Various Plate Thicknesses and Inclination Angles 4. Optimal Configuration Determination For these experiments, we used another experimental device which consists of a glass plate fixed to an axis, positioned The major drawback of the chosen configuration is the between a transducer used in emission and another in recep- possibility of reflections on the plate, which can lead to a tion. The entire system is immersed in water (Figure 10). damage to the transducer. Therefore, we decided to check The advantages of this system are that it allows easy and reflection and transmission for different plate thicknesses. continuous variation of the angle of inclination, and that the Two transducers located in front of one another were used studied thickness is modifiable quickly by changing the glass for evaluation purposes (Figure 12). The first one, used in plate. However, on the other hand, the reflections against emission/reception was supplied with a 10 Vpp sinusoidal walls are not taken into account and we are thus less close to long burst signal, whereas the second was used only in the real behaviour of a reactor. Peak to peak maximal voltages reception. A glass plate was placed between these two were measured for inclination angles varying between 0 and transducers. The emitted signal of the first transducer and 40 , and for the following glass plate thicknesses: 2.2, 3, 4, the reflected signal from the glass plate were recorded on an Axis 2-mm Axis 2-mm Axis 2-mm 6 Advances in Acoustics and Vibration Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage Contour plot: peak-to-peak voltage 5dB per contour 5dB per contour 5dB per contour 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 −5 −5 −5 −10 −10 −10 −15 −15 −15 −20 −20 −20 −20 −15 −10 −50 5 10 15 20 −20 −15 −10 −50 5 10 15 20 −20 −15 −10 −50 5 10 15 20 Axis 1-mm Axis 1-mm Axis 1-mm (a) (b) (c) Figure 9: Maps of peak-to-peak voltages observed in the system with a plate tilted at 40 : (a) at 8 cm, (b) at 12 cm, and (c) at 16 cm from the plate for an excitation burst signal of four periods with 10 Vpp amplitude. the transducer and surrounding media considered as an equivalent electrical circuit. With the KLM model, we defined the following configu- 60 mm ration for the system. 140 mm (1) Matching layer thickness: 0.5 mm. (2) Glass plate thickness: 11.03 mm. Inclined Transducer plate (3) Space between transducer and glass plate: about 160 mm 10 mm, this value does not need to be very precise. However, it must be sufficient to assure correct Figure 10: Experimental setup configuration. cooling of the transducer. (4) Liquid height in the reactor is not an important parameter. oscilloscope together with the signal received by the second transducer. A transmission coefficient, T,and areflection 5. Transducer Manufacturing and Initial coefficient, R, were calculated by Characterization Reflected voltage Transmitted voltage The first step consisted of adjusting the thickness of a R = , T = . Emitted voltage Emitted voltage 40 mm diameter ceramic P1 89 A4 micron and producing an (1) electroless copper deposit on both faces. The matching layer was created by a resin polymerisation moulded by means of a Results are shown in Figure 13.The reflectioncoefficient 54 mm diameter ring. The moulding process was optimized does not exceed 6% and the transmission coefficient is to reduce the constraints imposed by polymerisation on the maximal for a 6 mm thickness. The sound velocity in the ceramic. The acoustic adaptation of the system “transducer, plate was measured as 5514.2 m/s, thus the optimal working matching layer” was created with an adapter made up frequency was determined as 475 kHz for a glass thickness of of a transformer, six condensers (three of 330 pf, one of 6 mm. We notice here that the system is in very narrow busy 1000 pF, one of 2200 pF and one 4700 pF), a switch and two band with a glass thickness λ, and that variations, even small, resistances. around its nominal frequency will be impossible. A solution The transducer is inserted into a Teflon circular plate will then be a glass blade of thickness λ/2 for 500 kHz, and embedded in the reactor. The glass reactor (Figure 14) excitation of the system with frequencies of 250 and 750 kHz was produced by Dijon Verre Labo (Dijon France). The corresponding to wavelengths of λ and 3λ/2. 11.03 mm thickness glass plate is in Pyrex Corning. To determine optimal design (thickness of the ceramic, The radiation force balance method has been chosen for thickness of matching layer, etc.), the complete reactor was initial characterization of the prototype [14]asitwas easy simulated by means of a software (Piezo-Cad) based on to carry out. A target is placed in front of the transducer the KLM model [13], that is, one-dimensional model of to obtain only the axial constituent of the weight which is Axis 2-mm Axis 2-mm Axis 2-mm Advances in Acoustics and Vibration 7 Transmission coefficient (2.2mm) Transmission coefficient (3.3mm) 35 30 0 0 0 102030 40 50 0 10 203040 50 ◦ ◦ Angle ( ) Angle ( ) (a) (b) Transmission coefficient (4 mm) Transmission coefficient (5 mm) 60 60 50 50 40 40 30 30 20 20 10 10 0 0 0 102030 40 50 0 102030 40 50 ◦ ◦ Angle ( ) Angle ( ) (c) (d) Transmission coefficient (6 mm) Transmission coefficient (10 mm) 100 35 0 0 0 102030 40 50 010 20 30 40 50 ◦ ◦ Angle ( ) Angle ( ) (e) (f ) Figure 11: Transmission coefficient versus angle inclination for different glass plate thicknesses. recorded by means of a balance. Values with and without 6. Concluding Remarks inner reactor were compared with an emitter running at 750 kHz. A yield equal to 40% was obtained in the inner The results of ultrasound transmission through a plate, reactor, compared to 53% in its absence. This first result in the case of cylindrical and oblong reactors, always in is encouraging because it indicates a correct yield with this simplified configuration, constitute a first step for future configuration. reactor design works. These results confirm partially the 8 Advances in Acoustics and Vibration 60 mm 100 mm 11.03 mm 30 mm (a) 93 mm Transducer Figure 14: Glass reactor. a two-component one (shear and compression) after the liquid/solid interface. Moreover, the most valuable results are obtained over the critical angle of reflection, which complicates modelling and simulation whenever the basic relationship is clearly determined (Reissner theory [10]). The creation of a prototype using some of the results of the (b) systematic study shows through its success that change is Figure 12: Experimental set-up used for determination of reflec- possible, and the first results obtained for 750 kHz confirm tions. our belief that the double-structured tank is a good design solution. Some work has still to be carried out to characterize this reactor completely. Other possible frequencies, 500 kHz and 750 kHz, must be tested in the same conditions. The presence of the cavitation phenomenon in the inner reactor should also be confirmed by appropriate chemical or electrochemical techniques. Finally, practical problems persist. The tests carried out on the prototype revealed very low tolerance in variations of thickness or showed drift in exiting frequency applied to the transducer. This is annoying as it decreases the robustness of the reactor and makes it nearly as hard to produce as a classic 02 4 6 8 10 reactor with a stuck glass plate. This problem could be solved Thickness (mm) by use of a dissimilar transducer, which has a wider busy band, and boosts the interest of the slanted bottom which Reflection coefficient (%) has a wider tolerance. Transmission coefficient (%) Figure 13: Transmission and reflection coefficients versus glass References plate thickness. [1] T.J.Mason andJ.P.Lorimer, Sonochemistry: The Applications and Uses of Ultrasound in Chemistry, John Willey & Sons, New York, NY, USA, 1988. results of the previous works and provide possible solutions [2] D. J. Walton and S. S. Phull, “Sonoelectrochemistry,” in through exploitable pairs (angle of inclination, thickness of Advances in Sonochemistry. Vol. 4, pp. 205–284, JAI Press, glass plate). However, the need for calculation codes adapted London, UK, 1996. to these complex geometries persists, because the behaviour [3] M.-L. Doche, J.-Y. Hihn, F. Touyeras, J. P. Lorimer, T. J. Mason, of the tested systems is as yet far from being completely and M. Plattes, “Electrochemical behaviour of zinc in 20 kHz accounted for. The major problem is to take into account sonicated NaOH electrolytes,” Ultrasonics Sonochemistry, vol. the fact that the longitudinal wave in the liquid becomes 8, no. 3, pp. 291–298, 2001. Advances in Acoustics and Vibration 9 [4] V. Ligier, J. Y. Hihn, M. Wer ´ y, and M. Tachez, “Effects of 20 kHz and 500 kHz ultrasound on the corrosion of zinc 2− − precoated steels in [Cl ][SO ][HCO ][H O ]electrolytes,” 4 3 2 2 Journal of Applied Electrochemistry, vol. 31, no. 2, pp. 213–222, [5] B. Pollet, J. P. Lorimer, S. S. Phull, and J. Y. Hihn, “Sonoelec- trochemical recovery of silver from photographic processing solutions,” Ultrasonics Sonochemistry, vol. 7, no. 2, pp. 69–76, [6] F. Touyeras, J.-Y. Hihn, M.-L. Doche, and X. Roizard, “Elec- troless copper coating of epoxide plates in an ultrasonic field,” Ultrasonics Sonochemistry, vol. 8, no. 3, pp. 285–290. [7] A. Francony, Ph.D. thesis,Universited ´ eSavoie,Chamber ´ y, France, 1995. [8] H. Hatano and S. Kanai, “High-frequency ultrasonic cleaning tank utilizing oblique incidence,” IEEE Transactions on Ultra- sonics, Ferroelectrics, and Frequency Control,vol. 43, no.4,pp. 531–535, 1996. [9] J.-Y. Hihn, D. Ber ´ eziat, ´ M.-L. Doche, et al., “Double- structured ultrasonic high frequency reactor using an opti- mised slant bottom,” Ultrasonics Sonochemistry,vol. 7, no.4, pp. 201–205, 2000. [10] H. Reissner, “Der senkrechte und schrage ¨ Durchtritt einer in einem flussigen ¨ Medium erzeugten ebenen Dilatations- Welle durch eine in diesem Medium befindliche planparallele feste Platte,” Helvetica Physica Acta, vol. 11, pp. 140–155, 1938. [11] F. H. Sanders, “Transmission of sound through thin plates,” Canadian Journal of Research, vol. 17, no. 9, pp. 179–193, 1939. [12] R. D. Fay and O. V. Fortier, “Transmission of sound through steel plates immersed in water,” Journal of the Acoustical Society of America, vol. 23, no. 3, pp. 339–346, 1951. [13] R. Krimholtz, D. A. Leedom, and G. L. Matthaei, “New equivalent circuits for elementary piezoelectric transducers,” Electronics Letters, vol. 6, no. 12, pp. 398–399, 1970. [14] International standard IEC 1161 First edition 1992-07. 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