The effects of ultrasound on micromixing

Accepted Manuscript The effects of ultrasound on micromixing Jeroen Jordens, Bram Bamps, Bjorn Gielen, Leen Braeken, Tom Van Gerven PII: DOI: Reference:

S1350-4177(16)30060-8 http://dx.doi.org/10.1016/j.ultsonch.2016.02.020 ULTSON 3136

To appear in:

Ultrasonics Sonochemistry

Received Date: Revised Date: Accepted Date:

6 October 2015 12 February 2016 18 February 2016

Please cite this article as: J. Jordens, B. Bamps, B. Gielen, L. Braeken, T.V. Gerven, The effects of ultrasound on micromixing, Ultrasonics Sonochemistry (2016), doi: http://dx.doi.org/10.1016/j.ultsonch.2016.02.020

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The effects of ultrasound on micromixing Jeroen Jordensa,b, Bram Bampsa, Bjorn Gielena,b, Leen Braekenb, Tom Van Gervena* a

KU Leuven, Department of Chemical Engineering, Celestijnenlaan 200F, B-3001 Leuven, Belgium b Research group Lab4U, Faculty of Industrial Engineering, KU Leuven, Universitaire Campus gebouw B bus 8, 3590 Diepenbeek, Belgium *Corresponding author. Address: Celestijnenlaan 200F, 3001 Leuven, Belgium; E-mail address: [email protected]; tel.: +32 16 32 23 42

Abstract The Villermaux-Dushman reaction is a widely used technique to study micromixing efficiencies with and without sonication. This paper shows that ultrasound can interfere with this reaction by sonolysis of potassium iodide, which is excessively available in the Villermaux-Dushman solution, into triiodide ions. Some corrective actions, to minimize this interference, are proposed. Furthermore, the effect of ultrasonic frequency, power dissipation, probe tip surface area and stirring speed on micromixing were investigated. The power and frequency seem to have a significant impact on micromixing in contrast to the stirring speed and probe tip surface area. Best micromixing was observed with a 24 kHz probe and high power intensities. Experiments with different frequencies but a constant power intensity, emitter surface, stirring speed, cavitation bubble type and reactor design showed best micromixing for the highest frequency of 1135 kHz. Finally, these results were used to test the power law model of Rahimi et al. This model was not able to predict micromixing accurately and the addition of the frequency, as an additional parameter, was needed to improve the simulations.

Highlights • • • • •

Sonication can interfere with Villermaux-Dushman reaction; Ultrasonic energy dissipation and frequency should be included in micromixing model; Best micromixing was achieved with a 24 kHz probe and high power settings; Enhanced micromixing was achieved by both stable and transient cavitation bubbles; High frequencies produce best micromixing in the case of transducers when all other parameters are kept constant.

Keywords

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Micromixing, process intensification, sonochemistry, Villermaux-Dushman, microstreaming, sonolysis, modeling, cavitation.

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1. Introduction Mixing on a molecular scale (micromixing) plays an important role in several chemical reactions like precipitation, neutralization, combustion or polymerization reactions [1–4]. It increases the selectivity of competitive reactions where the reaction rate of interest is limited by diffusion. Additionally, micromixing improves the reaction rate of mixing sensitive reactions by reducing the micromixing time below the reaction time [5,6]. Ultrasound has shown drastic improvements of this micromixing, up to ca. 50 % compared to silent conditions [2,7–10]. Three main mechanisms are proposed to explain these enhancements. First, the collapse of cavitation bubbles is thought to create micro-jets, shockwaves and micro-streaming which generate turbulence in the liquid and hence improve mixing on the molecular scale [2,5,8,10,11]. These effects are mainly attributed to transient cavitation bubbles as these implode more violently compared to stable ones [8]. Secondly, micromixing can be improved by oscillating stable cavitation bubbles. These bubbles will vibrate around their resonance radius and hence cause convective circulation in the surrounding liquid which creates turbulences in the liquid and consequently improve micromixing [10]. Finally, the mechanism of acoustic streaming is proposed in literature [8,12,13]. This macroscopic streaming is generated when ultrasound energy is dissipated by viscous stress and results in steady vortices and time independent circulation which improve micromixing [14]. This effect is more pronounced at higher acoustic frequencies as attenuation of sound waves will be higher at these frequencies and hence more energy is dissipated compared to lower frequencies [15]. It is still not clear to which extent these mechanisms contribute to micromixing and if there is a dominant one. Although ultrasound showed significant enhancements compared to silent conditions, the ultrasonic parameters which optimize micromixing are not clear. Lee et al. for example observed less micromixing with a 647 kHz plate transducer compared to a 20 kHz probe [4]. Also, Monnier et al. had a similar observation; a 20 kHz probe created better micromixing compared to 540 or 955 kHz transducers [1]. Rahimi et al., Parvizian et al. and Faryadi et al. in contrast, found that their 1.7 MHz transducers created better results than a 24 kHz probe [10,11,13]. Furthermore, they compared their results with the ones of Monnier et al. and observed that, at a constant ultrasonic intensity per unit volume, their 1.7 MHz reactor created better micromixing than the 20 kHz probe and cup probe of Monnier et al. [11]. No explanation for this discrepancy was given. However, from their papers one could notice that several parameters differ during their experiments. First, the reactor geometry used among the different papers varies considerably. Monnier et al., Lee et al., Rahimi et al. and Parvizian et al. used reactors of respectively 100, 165, 360 mL and 2L [4,5,10,11]. From literature, it is known that the reactor geometry significantly influences the ultrasound field [7,16]. Hence, different levels of acoustic streaming or cavitation characteristics can be created which consequently impact micromixing. Secondly, ultrasonic probes with small diameters of 12 to 20 mm are compared with ultrasonic transducers with larger diameters up to 45 mm. The former are more likely to create a non-uniform acoustic field and transient cavitation bubbles while the latter favor a 3

uniform acoustic field and stable bubbles [13,17–19]. Again, these differences can impact micromixing behavior. Furthermore, the ultrasonic power is not always compared in a similar way. Monnier et al., Parvizian et al. and Rahimi et al. applied a constant electrical power to the ultrasound sources while Lee et al. kept the power inside the reactor constant. The latter was done by calorimetric measurements which allow, according to literature, a much fairer comparison between different frequencies [20–23]. Finally - besides these different geometries, bubble types and power levels - also the positioning of the ultrasonic source differs. All probes are introduced from the top of the reactor while most transducers are placed at the bottom. Therefore, the direction of the ultrasound waves will be opposite and the acoustic properties like the proportion of standing and travelling waves and reflected power will differ [24]. These acoustic properties influence the cavitation structures and therefore also micromixing [16,25]. All these parameters together make it difficult to investigate solely the effect of frequency on micromixing and do not allow to draw a univocal conclusion. The effect of ultrasonic power or intensity on micromixing, in contrast, is very clear. Higher ultrasonic powers lead to better micromixing [2,5,8,10,26]. This is straightforward as higher powers lead to more violent collapse of cavitation bubbles and more acoustic streaming. Rahimi et al. even proposed a model to simulate the effect of ultrasonic energy dissipation (ε) on the micromixing time (tm) [26]. The following power law was used to correlate both parameters to each other: Eq. 1


 =  

In this equation, a and b are fitting parameters which need to be defined experimentally. The micromixing times were plotted in function of the energy dissipation ratios (W/kg) for each operating condition. Power law trend lines were fitted through these points and from the equations of these trend lines, the values for a and b were obtained. Different trend lines, and therefore different values for a and b, were obtained for acid concentrations of 0.5, 0.75 and 1 M and sonicated and silent conditions. The power law model was used to predict the micromixing time under silent and sonicated conditions for a given acid concentration in their reactor setup. It showed a very good correlation between simulated and measured values with errors of less than 8%. This model was, however, developed for their reactor configuration and frequency of 42 kHz. The Villermaux-Dushman or iodide-iodate reaction is one of the most used techniques to characterize micromixing due to its easy implementation, cheap reagents and well established reaction kinetics [1,2,5,6,8,10,26–30]. The degree of micromixing is measured by the amount of triiodide (I3-) produced by the iodide-iodate reaction. The worser the micromixing, the more I3- produced. The reader is referred to section 2.2 for a detailed description of the reactions and reagents. This Villermaux-Dushman method is also commonly used to study the effect of ultrasound on micromixing [1,2,4,5,8,11,26]. All of the papers referred to in the previous paragraph, for example, used this method. However, when looking deeper in literature, one can find that potassium iodide, which is excessively available in the 4

Villermaux-Dushman buffer solution, is oxidized by reactive species such as •OH radicals and hydrogen peroxide formed by collapsing cavitation bubbles [31,32]. The generation of these reactive species in sonicated water is often referred to as the sonolysis of water. These reactive species will oxidize the available iodide ions to iodine which subsequently reacts with the excess of iodide to triiodide according to the following reaction scheme [31,32]: ∙  +  →  +   +  →  2 →  + 2  +  →  In fact, these reactions are commonly used in the field of sonochemistry during the "Iodine release method" to characterize the cavitational activity [33]. This sonolysis reaction can, however, interfere with the Villermaux-Dushman reaction as both reactions produce triiodide ions. In this way, the amount of triiodide produced by the Villermaux-Dushman reaction will be overestimated and hence the micromixing underestimated. To the authors' best knowledge, no reports are present in literature which investigated this possible interference or proposed any corrective actions. In the present work, the effect of sonolysis on the Villermaux-Dushman reaction will be studied and some corrective actions will be proposed. Furthermore, the effect of ultrasonic frequency on micromixing will be studied in a single reactor geometry with a constant probe tip surface area, similar power dissipations, the same stirring speed and cavitation bubble type. Moreover, the effect of stirring speed, ultrasonic intensity and power on the micromixing efficiency will be investigated. Finally, the power law model of Rahimi et al. will be tested among different frequencies and ultrasonic powers. The addition of the frequency, as an additional parameter, in the micromixing model will be investigated as well.

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2. Materials and methods 2.1. Experimental setup Figure 1 shows the experimental setup which consists of a jacketed glass cylinder without top or bottom plate and an ultrasound transducer. This transducer is placed at the bottom of the reactor and clamped to the cylinder to allow proper sealing of the reactor. By clamping different transducers to the bottom, each operating at their own resonance frequency, it is possible to use the same reactor over a wide frequency range. The temperature was fixed at 25°C by a Julabo MP thermostatic bath. A Cole Parmer ultra compact mixer with axial blade impeller of 30 mm diameter was used to stir the solution at different stirring rates. The stirrer was always placed in the center of the reactor at 1 cm from the bottom. An Ismatec REGLO-Z Digital gear pump was used to add the sulphuric acid solution to the reactor. The tubing from this pump had an inner diameter of 1 mm, was located at a radial distance of 2 cm from the impeller and was immersed 3 cm in the reactor solution. This location was fixed during all experiments. The tubing was immersed just before the addition of the acid and a check valve was installed between the outlet of the pump and the tubing to avoid release of acid before the start of the experiment. Also, the height of the pump and reactor were adjusted to minimize hydrostatic pressure differences which could lead to uncontrolled acid release. Two ultrasonic probes and three ultrasonic transducers were used to test a frequency range of 24 till 1135 kHz. Table 1 shows the specifications of these ultrasonic sources. The ultrasonic probes were introduced from the top in the solution while the transducers are placed at the bottom of the reactor. Tips with diameters of 7 till 40 mm were placed on the UP 200S ultrasonic probe to test a range of probe tip surface areas. The 24 kHz probes were always introduced in the center of the reactor without any impeller and immersed 1 cm in the solution. The 30 kHz probe was introduced together with the mixer and was therefore not placed in the center but at 2 cm from the impeller and 4 cm from the acid injection location. This probe was also immersed 1 cm below the liquid surface. The power inside the reactor was changed by varying the input power level from 20 to 100 %. Calorimetric power calibrations were performed to assure that the power inside the reactor was constant for all different ultrasonic sources. Correlations between the input power (Pin) and the calorimetric power (Pcal) can be obtained. These correlations are provided in Table 1 and show, in all cases, a linear relationship between the power transferred to the transducer or probe and the calorimetric power, with a linear correlation coefficient (R²) of at least 0.97. The importance of calorimetric measurements during sonochemical experiments is already emphasized in literature [20,22]. Beside the probes, three ultrasound transducers were used: one with resonance frequencies of 41 and 94 kHz, another with a frequency of 165 kHz and a third with frequencies of 577, 860 and 1135 kHz. The first two transducers were glued to a glass plate to avoid corrosion and erosion of the transducer surface. The last one was a transducer with titanium diaphragm which could directly be used. The ultrasonic frequency and power of these transducers were controlled by a Picotest G5100A waveform generator which was connected to an E&I 1020L

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RF power amplifier. Pin was defined as the difference between the forward and reflected power which could be obtained from this amplifier.

2.2. Reactions description The Villermaux-Dushman reaction system was used to study the micromixing efficiency. This reaction consists of two parallel competing reactions [6,27].   +  ⇌  

(Reaction 1: quasi-instantaneous neutralization reaction)

5 +  + 6  ⇌ 3 + 3 

(Reaction 2: very fast reaction)

When an excess of iodide is present, all iodine will be transformed to triiodide according to the following reaction: I + I ⇌ I

(Reaction 3: quasi instantaneous equilibrium)

The Villermaux-Dushman procedure implies the addition of a small quantity of protons (by means of sulphuric acid) to a mixture of iodate, iodide and borate ions (further referred to as the buffered solution). The amount of acid added is in stoichiometric deficiency to make sure reactions 1 and 2 will go in competition. In perfect mixing conditions, the acid is immediately dispersed and consumed by the instantaneous reaction (reaction 1). When non-ideal mixing conditions occur, the mixing time is in the same range or higher than the characteristic reaction time of reaction 2 [5,30]. A local overconcentration of the acid will exist and the acid will react with iodide and iodate to yield iodine. Therefore, the selectivity of iodine is a measure for the segregation state of the mixture. Due to the excess of iodide, all iodine is transformed into triiodide according to reaction 3. The concentration of these triiodide ions can be measured and directly introduced in the definition of the segregation index Xs (-) which is given in Eq. 2 [6,27]. Eq. 2



 = 



In Eq. 2, Y (-) is the ratio of the amount of protons consumed by reaction 2 over the total amount of protons added to the buffered solutions as depicted in Eq. 3. Eq. 3

=

 !"#$ %&'()&'*+ )"$ , -./ "#-$. &0 1)2

Here, Vreactor is the volume of the reactor (190 mL), Vinjection the volume of the acid injection (0.19 mL), (H+)0 the concentration of the acid solution before addition to the buffered solution (0.5 M) and (I2) the concentration of iodine in the reactor after addition and reaction of the acid with the buffered solution. Due to the excess of iodide, all iodine is assumed to be transformed in triiodide and the concentration of iodine can be assumed zero. (I3-)corr is the corrected I3- concentration calculated by Eq. 4. Eq. 4

& )3455 = & )678569 − & )4;4<=> 7

Here, & )678569 is the triiodide concentration measured by UV spectroscopy and & )4;4<=> the triiodide concentration produced by sonolysis. The importance of the latter will be discussed more in depth in section 3.1. YST is the value of Y in the case of total segregation and given by Eq. 5. A&'B*+)2

?@ = AC'B+D

Eq. 5

+ * 2 C0(EB* D 2

In Eq. 5, (IO-3)0 and (H2BO-3)0 refer to the initial concentrations of resp. iodate (0.002 M) and borate ions (0.091 M) in the buffered solution. The value of Xs ranges between 0 for perfect micromixing and 1 for total segregation.

2.3.Experimental procedure sonolysis effect First, the buffered solution was prepared according to the concentrations provided in Table 2. The potassium iodide and potassium iodate powders and sodium hydroxide grains are bought from BDH Prolabo Chemicals and have purities of 99.7%, 99% and 99% respectively. The orthoboric acid is bought from Ph. Eur. and has a purity of 99.8%. To prepare the buffered solution, each chemical is dissolved in ultrapure water (18.2 MOhm.cm). Subsequently, the buffer is prepared by mixing the orthoboric acid and sodium hydroxide solutions. Afterwards, the potassium iodide and potassium iodate solutions are added to the buffer. The pH of the solution should be kept between 8.5 and 9.5 to avoid the thermodynamical formation of iodine [34,35]. A pH of 9.3 was obtained for the buffered solution prepared with the chemicals summarized in Table 2. After preparation of the buffered solution, 190 mL of this solution is added to the reactor. The stirrer was set at 50 rpm and ultrasound is turned on at the desired frequency and power. Next, samples of 1 mL were taken from the solution at defined time intervals and the absorbance was measured via offline UV/VISspectrophotometry (Shimadzu UV 1601) at 353 nm. The triiodide concentration was calculated based on Eq. 6. Eq. 6

& ) =

F GH

With D the absorbance (-), ε the molar extinction coefficient (M-1∙cm-1) and L the optical length (cm). Calibration experiments were performed prior to the micromixing experiments to correlate the absorbance and triiodide concentration with each other. A linear correlation with a R2 of 0.9995 was found.

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2.4.Experimental procedure Villermaux-Dushman reaction The same buffered solution as described in section 2.3 was used. Next, the 0.5 M sulphuric acid solution was prepared according to the concentration given in Table 2. Sigma-Aldrich is the supplier of the sulphuric acid with a purity between 95% and 97%. After preparation of these solutions, 190 mL of the buffered solution is added to the reactor. The stirrer was set at the desired rotation speed and ultrasound is turned on. At the start of the experiment, 0.19 mL of the 0.5 M sulfuric acid solution was added to the reactor within 13 s (flow rate of 0.88 mL/min). This time is above the critical feed time of 8 s to ensure that only micromixing was measured. The critical feed time was defined according to the procedure provided in literature [6,27]. When the acid was added to the solution, the reaction system is given 1 min to fully react and homogenize. Finally, samples of 1 mL were taken and analyzed according to the same procedure as described in section 2.3.

2.5. Sonoluminescence experiments In order to check the type of cavitation bubbles, sonoluminescence (SL) quenching measurements were performed. Several papers in literature showed already the potential to define the dominant cavitation bubble type with this technique [17,36,37]. The degree of quenching of SL signals, by adding volatile components, depends on the bubble type. Propanol will quench SL signals of stable cavitation bubbles but not of transient ones. Acetone, on the contrary, will quench SL signals of both stable and transient bubbles and is added to ensure that these SL signals originate from cavitation bubbles. Ultrapure water (18.2 MΩ.cm) was used as the bulk medium and propanol (≥ 99.5% Sigma Aldrich) and acetone (≥ 99.8% Sigma Aldrich) are added, in separate experiments. Both alcohols were added in increasing concentrations up to 500 mM in steps of 50 mM till stable SL signals were obtained. These final SL values were used to determine whether stable or transient bubbles are present. Sonoluminescence signals (SL signals) were recorded for 30 sec with a gate time of 100 msec, using a photon counting head (Hamamatsu, H11890 series). These SL signals were corrected for dark counts so that only the increase in photon counts caused by the sonoluminescence was taken as the SL value. Results are shown in this paper on a relative basis compared to the SL signal of ultrapure water (SL0). The threshold between transient and stable bubbles, also defined as the 50% cut-off value, was set at 50% of this relative SL-signal [36–38]. Stable cavitation bubbles are dominant when the final relative SL signal of propanol is less than 50%. Oppositely, when the final SL signal of propanol remains above 50 %, mainly transient bubbles are present. Only these final conclusions, transient or stable bubbles, will be displayed in this paper. The procedure described above was performed for each frequency and power setting to obtain this conclusion.

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3. Results and discussion First, the effect of sonolysis on the segregation index will be discussed and some corrective actions will be proposed. Next, the effect of stirring speed, ultrasonic frequency, intensity and power dissipation ratio on the micromixing efficiency will be investigated. Finally, the power law model of Rahimi et al. will be tested and improvements will be proposed.

3.1. Influence of sonolysis on segregation index As discussed in the introduction, ultrasound may interfere with the segregation index measurements via the production of triiodide ions in the buffer solution. This hypothesis is tested in this section. First, the triiodide production in the buffer solution by means of sonication was measured. Next, the effect of this triiodide production on the segregation index was checked and finally some corrective actions were proposed. The triiodide concentration in the Villermaux-Dushman buffer solution was measured under sonication according to the procedure described in section 2.3. Figure 2 shows the evolution of this triiodide concentration in time for different frequencies at a constant calorimetric power of 9 W. From this graph it becomes clear that, depending on the applied frequency, ultrasound is indeed able to generate I3- ions in the buffer solution. This production of I3- can be explained by the sonolysis reaction as discussed in the introduction. The frequency seems to play an important role in this process. No I3- production can be detected at frequencies of 30 and 41 kHz. Higher frequencies, in contrast, show a significant increase in triiodide concentration over time. The steepest increase in concentration was detected at 577 kHz. After 15 min of sonication, the concentration has risen from 2.7E-7 mol/L to 1.5E-5 mol/L. The triiodide production is maximized at 577 kHz while it is negligible at 30 and 41 kHz. These results correlate with the sonolysis yield as function of frequency. This sonolysis reaction takes place in the bulk of the solution and consists of two steps. First •OH, H• and HOO• radicals are formed within the cavitation bubble by the sonolysis of H2O and O2. Secondly, these radicals move outside the bubble to the bulk solution to react with the potassium iodide or they will recombine inside the bubble to form H2O or H2O2. The sonolysis yield depends on the frequency as the frequency impacts the amount of radicals formed and released into the liquid. On the one hand, the cavitation effects are more violent at low frequencies, leading to a higher production of radicals inside the bubble. On the other hand, most radicals will recombine inside the cavitation bubbles at these low frequencies due to the long lifetime of collapse. At higher frequencies, the energy released upon collapse is reduced and consequently the yield for formation of radicals inside the bubble diminishes. However, the collapse occurs more rapidly and more radicals are able to escape from the bubble before they recombine. An optimum exists typically at a frequency between 200-600 kHz [24,42,43]. The frequency of 577 kHz lies within this optimum which explains why it entails a higher I3- production compared to higher or lower frequencies. These results suggest that, depending on the applied frequency, ultrasound can significantly impact the I3production and hence segregation indices. Moreover, these results indicate that the effect will not be the same for all frequencies as the I3- production is frequency dependent. 10

To study the effect of this triiodide production by sonolysis on the segregation indices, a second set of experiments was performed. First, sonolysis experiments were performed for 20 minutes at a frequency of 577 kHz at three different power levels of 5, 9 and 15 W. The concentration of triiodide ions produced by sonolysis, & )4;4<=> , were obtained from these experiments. Next, the Villermaux-Dushman reaction was performed under the same conditions. Two series of segregation indices were calculated from these experiments: corrected and uncorrected ones. The former was obtained by using Eq. 4 for correction of & )4;4<=> . The latter was calculated with the same equation but & )4;4<=> was now assumed to be zero. Figure 3 shows the corrected and uncorrected segregation indices as function of the sonication time. From this graph it can be seen that uncorrected segregation indices increase in time. The higher the applied power, the steeper the rise in segregation index. This makes sense as it was already proven in literature that higher power levels result in more radical production [41,42]. The higher the radical production, the larger the triiodide production, the more the Y-value in Eq. 3 will increase and the higher the segregation index will be. Furthermore, Figure 3 shows a significant difference between the corrected and uncorrected segregation indices, especially for sonication times of 5 min or above. After 20 min of sonication, this difference raised up to 69 % for the highest power level. The corrected segregation indices, in contrast, remain almost constant in time. These results show that Eq. 4 is adequate to correct for the triiodide production by sonolysis. As a conclusion one can state that ultrasound is able to influence the segregation index by sonolysis of the buffer solution. Uncorrected segregation indices obtained after more than 5 min sonication can result in an overestimation of the segregation index and hence an underestimation of the micromixing efficiency. Therefore, it is suggested to use corrected segregation indices which correct the triiodide produced by sonolysis based on Eq. 4 or to minimize the sonication time below 5 min. The latter technique was chosen for all further segregation indices used in this paper. A sonication time of 1 min was selected as this minimizes the sonolysis error and still allows to observe the micromixing effects of ultrasound.

3.2.Effect process parameters on micromixing The effect of stirring speed, ultrasonic frequency, power dissipation ratio and intensity on the segregation index will be investigated. Based on these results, the input parameters for the enhanced power law, which will be discussed in section 0, are selected.

3.2.1.

Stirring speed

Figure 4 displays the segregation index as function of the stirring speed for silent conditions and frequencies of 94 and 577 kHz. Under silent conditions, a lower segregation index and 11

hence better micromixing is obtained by increasing the stirring speed. This is straightforward as higher stirring speeds induce higher fluid velocities and hence better mixing on both macro- and micro scale. Ultrasound seems to diminish this effect as almost no difference in segregation index can be observed between the tests at 0, 50 and 200 rpm during sonication at 94 and 577 kHz. These results suggest that, whenever ultrasound is applied in combination with mechanical stirring, ultrasound seems to dominate the mixing on a molecular scale. The effect of stirring on micromixing seems negligible when sonication is applied. Furthermore, comparable segregation indices under silent and sonicated conditions were observed at 200 rpm. This means that when mechanical mixing is sufficiently high, sonication is not able to improve mixing any further. It was also noted that at 50 rpm, there is a significant difference in segregation index obtained at 94 and 577 kHz. This effect of frequency on the segregation index will be investigated more in depth in the next paragraph.

3.2.2.

Ultrasonic frequency

Figure 5 shows the segregation index as function of the applied frequency for a constant power dissipation ratio of 47 W/kg and stirring speed of 50 rpm. The dominant cavitation type was defined for each frequency according to the procedure described in section 2.5. From Figure 5 it becomes clear that, when stable cavitation bubbles are created, the applied frequency has a significant effect on the segregation index. For stable cavitation, the higher the frequency, the smaller the segregation index and hence the better micromixing becomes. These results are in agreement with the papers of Parivizian et al. and Rahimi et al. [2,10,11]. In these papers, lower micromixing times and thus faster micromixing were achieved with a 1.7 MHz sonoreactor compared to a 20 kHz one at the same power level. This was explained by the occurrence of more acoustic streaming and a higher amount of cavitation bubbles and thus convective circulation at higher frequencies. Although a clear trend is visible among the frequencies of 94 till 1135 kHz, one cannot state as a general rule that higher frequencies will create better micromixing. The data point at 30 kHz clearly deviates from this trend, since a similar segregation index to the one at 1135 kHz was obtained. However, the ultrasound source and cavitation type are different from all other points. At 30 kHz, the majority of the cavitation bubbles are transient ones in contrast to stables ones for all other frequencies. These transient bubbles will implode more violently and are thus able to generate stronger shock waves which enhances micromixing more [2,5,8,10,11]. However, it is not clear what the degree of acoustic streaming is compared to the other frequencies as the probe tip surface area was considerably smaller than with the transducers. Also, an ultrasonic probe was used instead of an ultrasonic transducer. This probe was inserted from the top of the reactor while the ultrasonic transducers were placed at the bottom. As described in the literature section, this can change the acoustic properties and therefore the degree of micromixing. Therefore, we could state that good micromixing can be achieved by both stable and transient bubbles but we cannot draw any conclusions about the driving mechanism. However, the results hint that the mechanism of imploding cavitation bubbles cannot be the only one because similar micromixing efficiencies 12

were observed at 1135 kHz compared to 30 kHz where mostly stable bubbles are present which implodes very weakly. The results in Figure 5 are, in contrast to previous papers in literature, performed on a single reactor with a constant power dissipation and stirring speed. Moreover, the dominant cavitation type was checked and also the emitting area was kept almost constant for all stable bubbles. These parameters can explain why other papers in literature observed better micromixing at lower frequencies [1,4]. In these papers plate transducers were compared with probe ones, where the former was inserted from the top and the latter at the bottom. Furthermore, the cavitation type was not checked and the probe tip surface areas were not kept constant as explained in the introduction section. All these variations can influence the acoustic properties and hence impact the micromixing efficiency. Moreover, none of these papers report corrective measures for the sonolysis effect of ultrasound. This effect can, as explained in section 3.1, cause an overestimation of the segregation indices of frequencies between 165 and 1135 kHz. This overestimation of the segregation indices compared to low ultrasonic frequencies will again make comparison between the different frequencies questionable. As a conclusion one can state that higher frequencies generate better micromixing when stable bubbles are generated, a single reactor geometry is used and the probe tip surface area, stirring speed and energy dissipation are kept constant. Changing these parameters can have a significant impact on the micromixing as the data point of 30 kHz showed. From a practical point it was not possible to test more frequencies for transient cavitation bubbles or probes.

3.2.3.

Power dissipation and intensity

Some authors state that the probe tip surface area has a significant impact on the segregation index while others claim that the energy dissipation ratio (ε) is more important [1,4,26]. To investigate which factors impact the segregation index, a series of experiments was performed with varying power dissipation ratios and emitter sizes. In this paper, the energy dissipation ratio (in W/kg) is defined as the calorimetric power divided by the mass of solvent. The power intensity (in W/cm²) is the calorimetric power divided by the probe tip surface area. Figure 6 shows the segregation index as function of the energy dissipation ratio for different frequencies. From this graph it becomes clear that the power dissipation ratio has a significant impact on the segregation index for all studied frequencies. Higher values of ε result in lower segregation indices. Best micromixing was achieved at the highest energy dissipation of 142 W/kg. Also Monnier et al. and Parivizian et al. observed better micromixing for higher power ratios for both low (20 kHz) and high (1.7 MHz) frequencies [2,5]. They explain these results by three phenomena. First, increasing ultrasonic powers lead to more violent collapse of cavitation bubbles. Secondly, more oscillating cavitation bubbles will be formed at higher powers and thus more convective streaming will be created. Finally, elevated power levels increase acoustic streaming and hence turbulence. All three phenomena are possible mechanisms for ultrasonic enhanced micromixing. 13

Lee et al. explained the observed differences in segregation index between the 20 kHz probe and 647 kHz transducer by the variations in probe tip surface area, 12 and 45 mm respectively [4]. It was hypothesized that a smaller probe tip surface area generates higher acoustic intensities (11 W/cm² compared to 2.8 W/cm²), thus more intense shear effects and hence enhanced micromixing. This hypothesis was tested by a series of experiments where the energy dissipation ratio and frequency were kept constant at 142 W/kg and 24 kHz respectively. The ultrasonic intensity was varied between 2 and 70 W/cm² by using probe tips with different diameters. Figure 7 shows the results and it can be seen that very marginal differences in segregation index are present when diameters of 7 till 40 mm are used. Only the point of 2 W/cm² (40 mm) has a slightly higher segregation index compared to the other two. Furthermore, the differences in segregation indices are less pronounced compared to Figure 6 where the energy dissipation ratio was varied. These results suggest that no correlation exists between the probe tip surface area or ultrasonic intensity and the corresponding segregation indices within the range of 2 till 70 W/cm². The results observed by Lee et al. should therefore be explained by other factors like position of the ultrasonic sources or differences in cavitation type or amount of acoustic streaming. It should, however, be noted that outside the range of 2 till 70 W/cm², the power intensity can still have a significant impact. In Figure 6, a drastic reduction of segregation index can be observed from 0 till 2 W/cm². It is possible that micromixing is impacted significantly by a change in energy density within this range. It was, however, impossible, with the current setup, to test energy intensities between 0 and 2 W/cm² while keeping all other parameters constant. The segregation indices of all tested frequencies and powers are combined in Figure 8. The 24 kHz horn shows the lowest segregation indices, and hence best micromixing of all tested conditions. However, one cannot conclude that the frequency of 24 kHz is better than higher frequencies as not all settings like power intensity, probe diameter, probe position, cavitation bubble type etc. are constant. The ultrasound field can therefore vary significantly and result in different cavitation and hence mixing effects. The energy intensity of the transducers lies for example in the range of 0.02 till 0.36 W/cm² compared to 2 till 70 W/cm² for the 24 kHz horn, as can be seen in Table 3.

From these results one can conclude that the ultrasonic frequency and energy dissipation ratio show strong correlation with the segregation index. One could therefore state that the energy dissipation and frequency should be both included in a micromixing model. The probe tip surface area and stirring speed, in contrast, seem to have less impact within the studied conditions.

14

3.3.Enhanced power law model Rahimi et al. proposed the power law model of Eq. 1 to simulate micromixing based on the energy dissipation ratio solely [26]. This model was tested against all experimental results obtained in the previous sections. The segregation index (Xs) was used instead of the micromixing time tm. This should yield similar results as the t m is linearly correlated with Xs in the paper of Rahimi et al [26]. The fitting parameters a and b will have different values but the trend between Xs and ε will be similar. In the present research, parameters a and b have values of 0.944 and -0.443 respectively. Table 3 shows the measured and calculated segregation indices as well as the absolute relative errors (ARE%). These ARE% were calculated by the same procedure as in the paper of Rahimi et al. Calculated segregation indices can be considered reliable when ARE% < 10% [26]. From Table 3 one can see that the ARE% values for the majority of the frequencies and energy dissipation ratios are above 10 %. Therefore, the power law model of Eq. 1 is considered unreliable to predict Xs over different frequencies and ultrasonic sources. These results indicate that other parameters, beside the energy dissipation ratio, should be included in the model as well. The results of section 3.2 suggested already, as discussed before, that also the frequency plays an important role. The power law of Eq. 1 was therefore adapted to incorporate the effect of frequency, as an additional parameter. First, a graph of Xs in function of ε was made for each frequency individually. These results are plotted in Figure 8 together with the power law equations of the corresponding trend lines. From these equations, significant variations in fitting parameters a and b can already be observed among the different frequencies. Next, these fitting parameters are correlated with the frequency in Figure 9. Because of the limited number of frequencies tested for ultrasonic probes, the model was only tested for transducers. Significant increasing and decreasing trends can be observed for parameters a and b respectively. As a first approach, simple linear correlations for both fitting parameters and the frequency were used. These correlations resulted in the power law equation shown in Eq. 7. Eq. 7  = &0.0002L + 0.3251) & N.NNNOP N.NQRQ) Here, f is the ultrasonic frequency (kHz) and ε the energy dissipation ratio (W/kg). Finally, this enhanced power law was tested against all measured segregation indices for transducers provided in Table 3. The simulated Xs values from the enhanced power law show considerable smaller ARE% values compared to the ones of Rahimi et al. The majority of all ARE% are below 10% and the maximum error was 36% compared to 47% for the model of Rahimi et al. These results support the hypothesis that the frequency should be added, besides the energy dissipation, as a parameter in a micromixing model. The model in Eq. 7 is still far from perfect to model micromixing. The purpose was, however, to investigate the effect of adding the frequency as an additional parameter. Further improvement of the model is needed to make it applicable for different reactor designs and ultrasonic sources. 15

4. Conclusion First, it was shown that ultrasound can interfere with the segregation indices obtained by the Villermaux-Dushman reaction through sonolysis. This effect is more prominent for longer sonication times and frequencies around 850 kHz. Frequencies below 165 kHz do not show any significant effect. A correction procedure was proposed to allow fair comparison between frequencies. Next, the effect of stirring speed, frequency, ultrasonic intensity and power dissipation ratio on the segregation index was investigated. The segregation index showed a strong correlation with the energy dissipation ratio and the frequency. These parameters were therefore considered in the model for prediction of the segregation index. Finally, the power law model of Rahimi et al. was tested against different frequencies and ultrasonic sources. Very weak correlations between simulated and experimental segregation indices were obtained. The addition of the frequency as an additional parameter was tested and significantly better simulations were obtained. Therefore, one can assume that the frequency should be included, besides the energy dissipation, in the micromixing model for ultrasonic transducers.

17

Tables Table 1 Specifications of the ultrasound sources Ultrasound source

Type

Frequency Diameter Linear equation Pcal R²-value kHz mm 24 7 0.225 P in + 6.645 0.98

Hielscher UP200S

Probe

Hielscher UP200S

Probe

24

14

0.735 P in + 8.249

0.97

Hielscher UP200S

Probe

24

40

0.881 P in + 9.405

0.99

Hielscher UP50H

Probe

30

7

0.105 P in + 1.681

0.99

Ultrasonics World MPI-7850D-20_40_60H Transducer

41

78

0.493 P in + 0.187

0.99

Ultrasonics World MPI-7850D-20_40_60H Transducer

94

78

0.454 Pin - 0.067

1.00

Ultrasonics World MPI-4538D-40_100H

Transducer

165

40

0.331 P in + 1.681

0.99

Meinhardt E/805/T/M

Transducer

577

75

0.489 Pin - 0.215

1.00

Meinhardt E/805/T/M

Transducer

860

75

0.464 P in + 0.186

0.99

Meinhardt E/805/T/M

Transducer

1135

75

0.459 P in + 0.143

0.99

Table 2 Concentrations of the buffered and sulphuric acid solutions Solution

Buffered solution

Acid solution

Chemical Potassium iodide (KI) Potassium iodate (KIO3) Orthoboric acid (H3BO3) Sodium hydroxide (NaOH) Sulphuric acid (H2SO4)

Concentration (M) 0.012 0.002 0.091 0.091 0.500

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Table 3 Measured and calculated segregation indices (Xs) with the corresponding absolute relative errors (ARE%) for different frequencies (f), probe tip surface areas (A), energy dissipations () and energy intensities (I).The values with grey background originate from experiments with transducers while all others were performed with ultrasonic probes. The measured segregation indices correspond to the average of two experiments.

f kHz 24 24 24 24 24 24 24 30 30 30 94 94 94 94 577 577 577 577 860 860 860 860 1135 1135 1135 1135

A mm² 38 154 1257 38 154 38 154 38 38 38 4778 4778 4778 4778 4418 4418 4418 4418 4418 4418 4418 4418 4418 4418 4418 4418

ε W/kg 142 142 142 101 405 63 432 19 33 49 9 12 19 90 4 14 27 50 5 16 26 53 4 14 26 50

I W/cm² 70.16 17.54 2.15 50.00 50.00 31.18 53.27 9.38 16.21 24.39 0.04 0.05 0.07 0.36 0.02 0.06 0.12 0.22 0.02 0.07 0.11 0.23 0.02 0.06 0.11 0.21

Measured Model Rahimi et al. Enhanced power law Xs Xs ARE % Xs ARE % 0.06 0.11 75% 0.06 0.11 82% 0.09 0.11 11% 0.09 0.12 30% 0.05 0.07 22% 0.11 0.15 31% 0.06 0.06 9% 0.31 0.26 17% 0.26 0.20 24% 0.23 0.17 27% 0.29 0.35 22% 0.30 2% 0.28 0.32 15% 0.29 5% 0.24 0.26 8% 0.28 19% 0.24 0.13 47% 0.25 6% 0.36 0.51 42% 0.38 4% 0.32 0.29 9% 0.32 1% 0.28 0.22 22% 0.30 8% 0.27 0.17 39% 0.28 3% 0.37 0.45 22% 0.39 5% 0.34 0.28 19% 0.33 3% 0.27 0.22 18% 0.31 15% 0.23 0.16 30% 0.28 20% 0.36 0.49 35% 0.43 18% 0.28 0.29 6% 0.35 26% 0.23 0.22 4% 0.32 36% 0.23 0.17 26% 0.28 25%

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Figures

Figure 1: Reactor setup.

1.8E-05 30 kHz

41 kHz

94 kHz

165 kHz

577 kHz

860 kHz

1135 kHz

Concentration I3- (Mol/L)

1.5E-05

1.3E-05

1.0E-05

7.5E-06

5.0E-06

2.5E-06

0.0E+00 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Time (min)

Figure 2: Evolution of triiodide concentration during sonication as function of time at a constant calorimetric power of 9 W. 20

1.0 0.9

Corrected - 5W

Corrected - 9W

Corrected - 15W

Not corrected - 5W

Not corrected - 9W

Not corrected- 15W

0.8 0.7

Xs (-)

0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

5

10

15

20

25

Time (minutes)

Figure 3: Corrected and uncorrected segregation indices (Xs) as function of the sonication time at 577 kHz and 50 rpm.

0.60 Silent

94 kHz

577 kHz

Segregation index (-)

0.50

0.40

0.30

0.20

0.10

0.00 0

50

100

150

200

250

Stirring speed(rpm) Figure 4 Segregation index as function of stirring speed for different frequencies at constant ε of 47 W/kg.

21

0.40 Silent

Stable bubbles

Transient bubbles

Segregation index (-)

0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0

200

400

600

800

1000

1200

Frequency (kHz) Figure 5: Segregation index as function of the applied frequency at constant power dissipation ratio (47 W/kg) and stirring speed (50 rpm). The symbols indicate the average value over three repetitions and the error bars the standard deviation.

22

0.60 Silent

24 kHz

30 kHz

577 kHz

860 kHz

1135 kHz

Segregation index (-)

0.50

0.40

0.30

0.20

0.10

0.00 0

20

40

60

80

100

120

140

160

ε(W/kg) Figure 6: Segregation index as function of the energy dissipation ratio (ε) for different frequencies. No stirring was applied. The symbols indicate the average value over three repetitions. The standard deviations of all data points are smaller than the symbol sizes and are therefore not displayed.

0.60 Silent

7 mm probe

14 mm probe

40 mm probe

Segregation index (-)

0.50 0.40 0.30 0.20 0.10 0.00 0

10

20

30

40

50

60

70

80

Intensity (W/cm²)

23

Figure 7: Segregation index as function of the intensity at a constant energy dissipation ratio of 142 W/kg without stirring.

Segregation index (-)

1.00

0.10

0.01 1

10

100

1000

ε (W/kg) 24 kHz Xs

= 0.411ε-0.338 R² = 0.604

30 kHz Xs = 0.760ε-0.305 R² = 0.995

94 kHz Xs = 0.326ε-0.074 R² = 0.575

577 kHz Xs = 0.427ε-0.118 R² = 0.958

850 kHz Xs = 0.549ε-0.207 R² = 0.893

1135 kHz Xs = 0.482ε-0.205 R² = 0.953

Figure 8: Segregation index as function of the energy dissipation ratio (ε) for different frequencies. The symbols indicate the average value over two repetitions and the error bars the standard deviation. Only the error bars of 24 kHz are visible because all other standard deviations are smaller than the symbol sizes and are therefore not displayed.

24

0.6

0 Param a transd

Param b transd

-0.05 a = 0.0002f + 0.3251

0.4 -0.1 0.3 -0.15 0.2 b = -0.0001f - 0.0575

Fitting parameter b

Fitting parameter a

0.5

-0.2

0.1 0.0 0

200

400

600

800

1000

-0.25 1200

Frequency (kHz) Figure 9: Fitting parameters a and b as function of the applied frequency.

25

Acknowledgements The research leading to these results has received funding from the European Community's Seventh Framework Program (FP7/2007-2013) under grant agreement n° NMP2-SL-2012309874 (ALTEREGO). J. Jordens acknowledges funding of a Ph.D. grant by the Agency for Innovation by Science and Technology (IWT).

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