Characterization of HIFU transducers designed for sonochemistry application: Acoustic streaming

Ultrasonics Sonochemistry 29 (2016) 420–427

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Characterization of HIFU transducers designed for sonochemistry application: Acoustic streaming L. Hallez a, F. Touyeras a, J.-Y. Hihn a,⇑, Y. Bailly b a b

Institut UTINAM/SRS, UMR 6213, CNRS, University of Bourgogne Franche-Comté, Besançon, France Institut FEMTO-ST/ENISYS, UMR 6174, CNRS, University of Bourgogne Franche-Comté, ENSMM, UTBM, Belfort, France

a r t i c l e

i n f o

Article history: Received 8 March 2014 Received in revised form 5 October 2015 Accepted 27 October 2015 Available online 27 October 2015 Keywords: HIFU Acoustic streaming Hydrodynamic behavior Cavitation Bubbles behavior

a b s t r a c t Cavitation distribution in a High Intensity Focused Ultrasound sonoreactors (HIFU) has been extensively described in the recent literature, including quantification by an optical method (Sonochemiluminescence SCL). The present paper provides complementary measurements through the study of acoustic streaming generated by the same kind of HIFU transducers. To this end, results of mass transfer measurements (electrodiffusional method) were compared to optical method ones (Particle Image Velocimetry). This last one was used in various configurations: with or without an electrode in the acoustic field in order to have the same perturbation of the wave propagation. Results show that the maximum velocity is not located at the focal but shifted near the transducer, and that this shift is greater for high powers. The two cavitation modes (stationary and moving bubbles) are greatly affect the hydrodynamic behavior of our sonoreactors: acoustic streaming and the fluid generated by bubble motion. The results obtained by electrochemical measurements show the same low hydrodynamic activity in the transducer vicinity, the same shift of the active focal toward the transducer, and the same absence of activity in the post-focal axial zone. The comparison with theoretical Eckart’s velocities (acoustic streaming in non-cavitating media) confirms a very high activity at the ‘‘sonochemical focal”, accounted for by wave distortion, which induced greater absorption coefficients. Moreover, the equivalent liquid velocities are one order of magnitude larger than the ones measured by PIV, confirming the enhancement of mass transfer by bubbles oscillation and collapse close to the surface, rather than from a pure streaming effect. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction In the first part of this study [1], we have described the cavitation distribution in a sonoreactor equipped with High Intensity Focused Ultrasound (HIFU) and quantified them with an optical method (SCL). The use of HIFU enables generation of very intense acoustic intensities at high frequencies, which is not possible with classical flat transducers. This large density of acoustic energy had already paved the way for very interesting medical applications, allowing specific innovations in therapeutics [2,3]. More recently, prospects have emerged in surface treatments such as selective ablation of polymers [4], study of cavitation and hydrodynamic effects on the selective stripping of acrylic coatings, selective polymerization known as ‘‘acoustic masking” [5,6], or modification of compactness and ions repartition of polypyrrole coatings electro-

⇑ Corresponding author. E-mail address: [email protected] (J.-Y. Hihn). http://dx.doi.org/10.1016/j.ultsonch.2015.10.019 1350-4177/Ó 2015 Elsevier B.V. All rights reserved.

synthesized under ultrasonic irradiation and selective oxidation of pyrrole on oxydable metals. Characterization of this kind of transducer is rather complex due to the presence of cavitation bubbles in the acoustic field. As predictive tools are not available for cavitation phenomenon, experimental studies had to be conducted to describe their specific behavior. In a previous paper [1], the dynamics of cavitation bubbles can be defined in two modes: ‘‘stationary bubbles” (bubbles trapped in the pressure antinodes of the standing wave) and ‘‘moving bubbles” (bubbles in motion in the acoustic field). The present work concerns the acoustic streaming generated by HIFU. The flows generated by ultrasound are nearly always present in all sonoreactors, along with cavitation and other induced effects. Such flows are well known to enhance mass transfer in processes limited by diffusion [7,8], to favor heat exchanges [9,10] or indeed to perform mixing or micromixing [11,12]. Wave propagation in a viscous fluid induces a transfer of energy between the acoustic wave and the propagation media, leading to a large scale flow commonly called ‘‘acoustic streaming” [13]. In a non-cavitating media,

L. Hallez et al. / Ultrasonics Sonochemistry 29 (2016) 420–427

two kinds of acoustic streaming can be seen: Eckart’s streaming (or quartz wind), generated in the bulk by the Reynolds tensions resulting from wave absorption in a viscous media, and Rayleigh streaming where the Reynolds tensions act on the hydrodynamic limiting layer in the vicinity of the reactor wall [14]. In cavitating media (heterogeneous media), a variety of factors are involved in global agitation. The present work is based on experimental measurements using optical method (Particle Image Velocimetry) and electrochemical method to describe the global agitation generated by HIFU. 2. Experimental details 2.1. Instrumentation

2.2. Operating procedures In the present work, streaming velocities were measured by two methods. Particle Image Velocimetry (PIV) is an optical visualization method dedicated to velocity measurements by determining particle displacement over time using a double-pulsed laser technique [16,17]. The liquid media was seeded by tracers, which have a density close to water (microparticles of Rilsan 30 lm). A light sheet, generated by a laser Continuum Nd-Yag (532 nm) and an optical system with cylindrical lenses, illuminates the acoustic axis plane. Particle locations are recorded in this plane using a CDD camera (Sensicam PCO 12 bits, 1280
1024 pixels). A fraction of a second later, a second image of the particle was taken and from these two images, analysis algorithms allowed to obtain the particle displacements for the entire flow region mapped. For each experiment, 50 pairs of images were recorded and post-treated using INSIGHT 3D software. The second method was the determination of mass transfer by cyclic voltammetry using the well-known quasi reversible redox 4 couple Fe(CN)3 6 /Fe(CN)6 . The work of Coury et al. [18–20] and Compton et al. [21] investigated mass-transfer phenomena under sonication. Sonication decreases the diffusion layer thickness d (m) and increases the limited current of diffusion j~ jD j (A m2) lim

attributed to the stirring effect in the reactor, its mean acoustic streaming and microjets generated by bubble collapses in cavitating media. Stirring in the neighborhood of the electrode can be expressed by the dimensionless Sherwood number [22–24]:

j~jD jlim Relec ; nDFC sol

Relec = 103 m

is 10

electrodes; the working electrode can be located at various distances from the transducer. This limiting current density can be linked to an equivalent circulation of electrolyte Ueq, able to produce the same electrochemical signal in silent conditions, using equations of mass transfer and mass balance. Pollet and Hihn proposed the following equation [23]:

U eq ¼

1 ð0:45nFC sol Þ2

D4=3 m1=3 Relec j~jD j2lim ;

where m is the kinematic viscosity. All experiments were conducted by a Tacussel PGZ 301 potensiostat. 3. Results and discussion

All experiments were conducted using two composite HIFUs designed by IMASONIC (Besançon, France). The first operates at 3 MHz (Tfc3000) with a 40 mm geometrical focal length, while the second operates at a frequency of 750 kHz (Tfc750) with a 100 mm geometrical focal length. Transducers were set on the vessel’s bottom. The geometrical focal corresponds to the center of spherical cap of the emitting surface characterized by its radius [15]. The reactor (750 mL) consists of a double walls cylindrical Pyrex vessel (92 mm diameter) equipped with a displacement system with four degrees of freedom [1]: three translations guided by micrometric screws and one rotation axis to avoid reflections toward the transducer.

Sh ¼

421

the 1

electrode

radius,

DFeðCNÞ4 ¼ 6

m s the diffusion coefficient of the species ð5:60  0:21Þ  10 determined with a rotating electrode, F the Faraday constant, and Csol the concentration of the species. Experiments were carried out with a concentration in ferri4 ferrocyanide [Fe(CN)3 6 ] = [Fe(CN)6 ] = 5 mM in a background salt NaOH = 0.2 M. We used a classical setup with 3 platinum 2

3.1. Velocity vector fields measured by PIV The PIV method was previously used in many configurations with an interesting sensitivity [25,26]. Indeed the behavior of cavitation bubble field is dependent on many parameters such as acoustic power, reflector nature, i.e. whether the surface facing the transducer is free (case of a liquid without obstacle) or not (electrode surface) [4] and even on wave generation mode (continuous or pulsed). Therefore, first tests consisted in irradiating a free surface, whereas in the second test, an electrode was located in the acoustic field (giving an opportunity to compare with electrochemical measurements). It was observed that the polyamide particles (Rilsan 30 lm diameter) used as tracers formed cavitation germs, thus leading to a decrease in cavitation threshold (reach here for the lowest available powers instead of a few Watts in previous works [1]. The values of the axial velocity (fluid velocity on the acoustic axis) measured by PIV were averaged with a MATLAB post-treatment software, over a 5
5 mm2 window, centered on the propagation axis, and sliding by steps from the vicinity of the transducer up to the free surface. 3.2. Irradiation of a free surface The velocity vector fields obtained by PIV measurements for both HIFU transducers (Tfc750 and Tfc3000) for 20 W (acoustic power measured by calorimetry) are shown in Fig. 1. A conical shape is visible in both cases, with the same global pattern as the distribution of the active bubbles observed in a previous study [1]. Velocities reach their maximum values in the acoustic axis, and a whirlpool recirculating flow is visible close to the walls in the upper part of the reactor. The average vectors are plotted as a function of transducer distance at various powers. Fig. 2a gives the results for the Tfc750 transducer. Velocities increase with distance and irrespective of power maximum values are reached of between 70 and 80 mm, slightly above the acoustic focal (90 mm), which corresponds to the maximum cavitation activity previously observed [1,27]. After the maximum, the presence of a large number of bubbles and the divergence of the acoustic field lead to fluid decelerations. Nevertheless, dependence of axial velocity on power is low, seemingly reaching a kind of saturation beyond 20 W and around 120 mm s1. On the contrary, an increase in axial velocity vs. power is noticeable in the zone close to the transducer. For example, if we look at its evolution at a given distance of 20 mm from the transducer, velocity evolves from a few mm s1 at 10 W to more than 60 mm s1 at 40 W. Results for the Tfc3000 transducer are shown in Fig. 2b. The same global trends are observed, i.e. the average value of the axial component of the velocity vectors increases as a function of distance to the horn up to a maximum of between 45 and 50 mm, but located just beyond the acoustic

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HIFU

HIFU

Fig. 1. Velocity vector fields of acoustic streaming generated by HIFU (Tfc750 and Tfc3000) at 20 W.

Fig. 2a. Evolution of the axial average velocity of acoustic streaming vs. distance from the transducer for various powers (Tfc750).

Fig. 2b. Evolution of the axial average velocity of acoustic streaming vs. distance from the transducer for various powers (Tfc3000).

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focal (40 mm). In this case, the decrease in recorded velocities is slow and velocities remain at a high value up to the reactor top. This last phenomenon is certainly due to fewer and less active cavitation bubbles at this frequency. On another hand, a singular behavior is observed for the highest power (20 W), resulting in a sudden increase in the fluid velocity just after the acoustic focal. To understand this better, the dependence of the maximum of axial velocities on acoustic powers is plotted on Fig. 3, where we can observe a break in the curve of fluid velocities, particularly clear for the 3 MHz Tfc 3000 transducer. In this case, axial velocity increases regularly as a function of acoustic power up to 20 W. This corresponds to the Eckart theory where streaming is proportional to acoustic intensity. Beyond this power, a steep increase is observed, related to the sudden bubble motion: these are bubbles that were trapped in the pressure antinodes of the standing wave at low powers. Nevertheless, the power threshold value is difficult to determine with accuracy due to its randomness. As a germination phenomenon, water purity (bear in mind tracer presence) or shocks on the vessels can trigger irreversibly the global fluid motion. Once this phenomenon is activated, this additional contribution to the convection flow (Eckart streaming) is rapidly saturated for the higher powers. In the case of Tfc 750, the same behavior is observed but at lower powers (2 W) and most of the time is hardly noticeable. This was expected because cavitation occurs sooner at low frequencies. Then, for higher powers (beyond 2 W), velocities are no longer dependent on power and the curve reaches a plateau, which illustrates saturation. These results go hand in hand with observation of bubble dynamics in an acoustic field: at low powers, bubbles are in levitation in the standing wave at pressure antinodes, whereas they start to move at higher powers [1,15]. It is clear that two factors of hydrodynamic agitation (motion of fluid itself relative to the vessel) exist. The first, in the stationary bubble mode or in cavitation less conditions, corresponds to the convective flow described by Eckart equations. We recall that this flow is directed following the wave propagation axis and results from energy transfer between the acoustic wave and the propagation media through presence of viscous forces. Even if bubbles can move relatively to the liquid in an oscillating mode, which can therefore be pushed back and forth by the bubbles [28], the liquid itself is only concerned by a very little average motion. The second is observed only

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in cavitating media, and concerns a huge bubble motion relative to the liquid. This bubble motion appears suddenly and is triggered by the loss of equilibrium between forces acting on bubbles. The power increase affected the radiation and Bjerknes forces as well as the Eckart’s streaming. We can assume than the high number of bubbles which move to the top of the reactor contributes to the global motion of the fluid itself, through viscous friction. To compare PIV results to equivalent velocities obtained by electrochemistry, it appears necessary to add measurements in presence of an obstacle (electrode). 3.3. Presence of an obstacle in the acoustic field (Pt-PTFE electrode) Fig. 4 shows velocity vector fields obtained by PIV measurements for both HIFU transducers (Tfc750 and Tfc3000) at 20 W when an electrode is located at the acoustic focal. Far from preventing liquid circulation, an intense activity is noticeable in the electrode vicinity, directly in the zone facing the transducer and all along the electrode body. In all cases, the presence of the electrode leads to a major perturbation. The agitation generated close to the electrode is the most important phenomenon, because it is directly linked to the mass transfer measurements, which will be undertaken later on. The average velocities (normal and tangential components of the vector fields) are calculated in a zone (5
5 mm2) in the vicinity of the electrode, and plotted as a function of the location of the electrode in the reactor (moving from the transducer to the free surface on the acoustic axis). Results are shown in Fig. 5a (Tfc750) and Fig. 5b (Tfc3000). As previously observed without an obstacle for the Tfc 750 transducer, the maximum values for tangential and normal velocity are reached when the electrode is located at the focal (around 90 mm from the transducer). For the Tfc 3000, the maximum values are also found at the focal (around 40 mm from the transducer), which was not the case in electrode absence. At 750 kHz, cavitation activity is intense and bubbles act as a reflector, ever for low powers, and the electrode will not introduce any changes. Although this is not systematically the case at higher frequencies, the electrode will reflect the waves, introducing a marked change in the cavitation field and inducing an increase in stirring. It seems that electrode presence tends to displace the maximum velocities in the direction of the transducer, a type of behavior already observed for bubble distribution by luminol measurements in HIFU [1]. The higher velocities observed at 750 kHz than at 3 MHz attract our attention. Indeed, Eckart’s theory predicts a velocity 16 times lower for a frequency 4 times lower, as the absorption coefficient is propositional to the square of frequency [13,29]. This discrepancy can be attributed to a huge modification of the absorption coefficient due to the presence of bubbles, which are numerous at lower frequencies. To conclude, the values of acoustic winds measured by PIV in the present work are within the range of magnitude as previously measured in the case of low frequency plane transducers [25], i.e. a few cm s1, but with a distribution specific to HIFU geometries. 3.4. Electrochemical measurement: mass transfer and expression of an equivalent velocity

Fig. 3. Evolution of the axial maximum velocity of acoustic streaming vs. distance from the transducer for various powers (Tfc750 and Tfc3000): detection of the cavitation mode.

3.4.1. Mass transfer measurement This measurement helps us to understand the influence of local agitation at the electrode surface, yielding quantitative information on bubble dynamics and flow circulation. Fig. 6 shows the evolution of the cathodic current vs potential decrease (linear sweep voltammetry) by positioning the working electrode in the propagation axis of the Tfc750. Ultrasound and voltammetry start simultaneously. Firstly, current increases with potential (0–0.05 V/Pt)

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HIFU

HIFU

Fig. 4. Velocity vector fields of acoustic streaming in presence of an electrode located at the acoustic focal (Tfc750: 10 W; Tfc3000: 20 W).

Fig. 5a. Average normal and tangential velocity components in the reactor axis determined by PIV in presence of an electrode at various distances from the emitting surface (Tf750:10 W).

corresponding to the limitation by electron transfer kinetics, before a slowdown attributed to the limitation by mass transfer as already observed in many cases for this kind of technique [23,24]. Usually for reversible electrochemical systems, the current reaches a plateau proportional to agitation. It is interesting to note that, after about 30 s where stationary cavitation bubbles appear (corresponding to 0.09 V/Pt at 150 mV min1 scan rate), the current increases slightly. This contribution to agitation is the result of the motion of bubbles around their average position, in equilibrium in the pressure antinode of the acoustic wave. On the contrary, in a random manner or triggered by an external event (impact on the vessel, electrode motion in the field, etc.), the strength maintaining the bubbles in equilibrium is broken and a large flow is directed toward the electrode. This phenomenon is similar to what observed by PIV (Fig. 3). This corresponds to a global bubble motion leading to a significant increase in current average level (global convective flow) and to current spikes indicating that a strong cavitation event has occurred. The transition between the two modes of cavitation is totally independent of the electro-

chemical measurement, thus it is possible to switch from the stationary cavitation mode to the motion of cavitation bubbles mode. It can occur at any value of the potential. It is well known at low frequencies (20–60 kHz) that mass-transfer limited currents under ultrasonic agitation included a steady state and timedependent component (oscillating around the average plateau current value) [18,19,23,25]. These peaks are more difficult to observe at high frequencies, because cavitation is usually less violent [30]. Moreover, this leads some authors to prefer high frequencies as mechanical effects are reduced [5,6], while chemical effects remain at high levels [31]. HIFU therefore ensures a broader range of magnitude of bubble dynamics, from stationary bubbles (available only at high frequencies) to moving bubbles with very high velocities (possible in both HIFU and low frequencies) [1] 3.4.2. Distribution of the Sherwood number in the sonoreactor This operating mode with stationary bubbles is interesting, as it may be useful for several applications where the destructive effects of cavitation must be avoided. Agitation was systematically

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Fig. 5b. Average normal and tangential velocity components in the reactor axis determined by PIV in presence of an electrode at various distances from the emitting surface (Tf3000: 20 W).

Fig. 6. Voltammetry study of different cavitation modes (5 W).

mapped by moving the working electrode into the acoustic field in a plane containing the acoustic axis (distribution of agitation in our cylindrical reactor was considered as axisymmetric). All experiments were conducted with great care to prevent bubble motion, i.e. 10 W and ultrapure water. Fig. 7 shows the evolution of the agitation level in the Tfc750 field expressed in Sherwood numbers versus longitudinal and axial directions. This allows to map the complete reactor volume facing the transducer. Sherwood numbers were calculated with the value of the limited current density j~ jD j obtained with mass transfer measurement. The stirring lim

effects are distributed with the same global shape as predicted by the previous method, and maximum agitation is observed before the acoustic focal just as for the PIV measurements. More original is the experimental detection of the marked agitation decrease at 60 mm from the transducer on the propagation axis, due to destructive interferences. This point will be described in

detail in the comparison between equivalent velocities and Eckart’s theoretical velocities. 3.4.3. Equivalent velocity To simplify the comparison between theoretical and experimental values, previous results were expressed in equivalent velocities (Fig. 8). Theoretical Eckart’s velocities U were calculated from the modeling [13,29] with the acoustic intensity distribution calculated in a previous work [1] with the Rayleigh’s integral (Ultrasim module of Matlab developed at the University of Oslo). This equation contains a geometrical factor G(r) dependent on the acoustic beam Rb and the vessel (Rv = 46mm) radii. The absorption coefficient is estimated experimentally.

U¼

aIa r2t GðrÞ gc

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Fig. 7. Mapping of the distribution of Sherwood number on a half-plane adjacent to the transducer acoustic axis (Tfc750: 10 W).

Fig. 8. Comparison between the equivalent velocity determined by electrochemistry and the theoretical Eckart’s velocity at the stationary cavitation mode (Tfc750: 10 W).

With        2 2 R2 for 0 6 r 6 Rt GðrÞ ¼ 12 1  Rr 2  1  2Rb2 1  Rr 2  log RRvb v v b       2 R2 for Rt 6 r 6 Rv And GðrÞ ¼ 1  2Rb2 1  Rr 2  log Rrv v

v

The acoustic beam radius is calculated as a function of z (distance of a point on the acoustic axis to the transducer’s center) and r = 0 (on the acoustic axis). Fig. 8 shows that close to the transducer, the effects of ultrasound are not significant, and a noticeable velocity can be detected only beyond 20 mm from the transducer. A marked decrease then occurs at 60 mm, resulting from the destructive interferences due to the phase shift between each transducer component. Beyond this point, it then increases again up to a maximum at the acoustic focal. Equivalent velocities were calculated from electrochemical measurements and plotted vs transducer to electrode distance. Both curves present the same global pattern in the prefocal zone (0–70 mm from the transducer). It is important to note that velocity calculated from Eckart’s equation are strongly dependant of the absorption coefficient (not easy to evaluate in presence of cavitation), and therefore should be considered cautiously from the point of view of their absolute values. Nevertheless, the evolu-

tion of simulated velocities fit surprisingly well with the experimental equivalent ones in the propagation axis; in particular, the presence of the destructive interferences predicted by theory is experimentally confirmed. On another hand, the experimental maximum velocity is shifted toward the transducer. This has been already observed in a previous work ([1] – Fig. 12a), where the light emitted by sonochemiluminescence SCL was recorded at different locations in the reactor. The highest SCL values were obtained in a zone centered on 73 mm of the emitting surface, slightly upstream from the acoustic focal (we had named this zone: the sonochemical focal). For powers upper than 10 W, there is an absence of SCL at the focal and in the post-focal zone, immediately downstream from the focal. Our first assumptions were that the high concentration of bubbles in this zone would favor interactions between them, such as coalescence or clustering in the case of stationary cavitation, or, on the contrary, when they reach high speeds in a viscous fluid, that their deformation would induce asymmetric collapses. Some authors [32] have recently shown that gentle additional agitation in the cavitation field minimizes this quenching. This tends to prove that SCL absence at the focal is linked to clustering or coalescence of bubbles. In fact, this cloud of bubbles directly at the focal is a possible reason for the shift

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toward the transducer since it acts as a reflector [33]. This displacement of inertial cavitation is comparable to what happens when, for flat high frequency transducers, the activity is located just below the water/air interface, where the acoustic wave is reflected. We also observe the presence of a peak on the curve of equivalent velocities (around 80 mm from the focal), a peak that was inexistent on the curve of theoretical Eckart’s velocities. Distortion of the wave observed at the focal leads to harmonics of higher frequency (due to shock wave presence) [1]. Thus, energy transfer between the wave and the propagation media is increased, resulting in an increase in acoustic flow speed, as they are both proportional to the absorption coefficient (which is also dependent on the square of the frequency). This observation is original and supports the assumption of the translation of all phenomena occurring at the focal. Finally, after reaching its maximum, the experimental curve decreases more rapidly than the theoretical one, confirming once again that the presence of the bubbles cloud forms an obstacle to wave propagation (the decrease in cavitation activity is proportional to the decrease in acoustic activity). It was observed that the velocity values represented on these curves have an order of magnitude far beyond those measured by PIV (around a few hundred mm s1 instead of ten mm s1). This is consistent with previous observations at low frequency where agitation close to the electrode vicinity is essentially due to oscillation/collapse of cavitation bubbles (up to 90%) instead of acoustic streaming (Rayleigh and Langevin) [7]. 4. Conclusion In the present paper, Particle Image Velocimetry measurements have enabled us to map hydrodynamic phenomena in presence or absence of an obstacle in the acoustic field. It is interesting to note that maximum velocity is not located at the focal, but is slightly shifted in the transducer direction, and that this shift is greater for high powers. The two cavitation modes described in previous work [1] (‘‘stationary bubbles” and ‘‘moving bubbles”) greatly affect the hydrodynamic behavior of our sonoreactors. The results obtained by electrochemical measurements show the same low hydrodynamic activity in the transducer vicinity, the same shift of the active focal toward the transducer, and the same absence of activity in the post-focal axial zone. The comparison with theoretical Eckart’s velocities (acoustic streaming in non-cavitating media) confirms a very high activity at the ‘‘sonochemical focal”, accounted for by wave distortion, which induced greater absorption coefficients. Future prospects are determination of the size of the bubbles generated by HIFU, and control of the cavitation mode by modulating the excitation signal. Acknowledgements The authors would like to extend their gratitude to the ‘‘Région Franche-Comté”, the DIRRECTE (French ministry for industry), and C&K and IMASONIC for their technical and financial support as part of the ‘‘ULTRASUR Project” (pôle de compétitivité Microtechniques). References [1] L. Hallez, F. Touyeras, J.-Y. Hihn, J. Klima, J.-L. Guey, M. Spajer, Y. Bailly, Characterization of HIFU transducers designed for sonochemistry application: cavitation distribution and quantification, Ultrasonics 50 (2) (2010) 310–317. [2] R.A. Fowler, S.L. Fossheim, J.L. Mestas, J. Ngo, E. Canet-Soulas, C. Lafon, Noninvasive magnetic resonance imaging follow-up of sono-sensitive liposome tumor delivery and controlled release after high-intensity focused ultrasound, Ultrasound Med. Biol. 39 (12) (2013) 2342–2350. [3] P. Gelat, G. ter Haar, N. Saffari, The optimization of acoustic fields for ablative therapies of tumours in the upper abdomen, Phys. Med. Biol. 57 (24) (2012).

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