A semi-empirical approach for determining the number density and void fraction of acoustic cavitation bubbles in sono-reactors

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A new semi-empirical technic has been established relying on the linkage between the chemistry in the bulk liquid and that taking place in the acoustic cavitation bubble. The open-source COPASI software has been used for the optimization of number density according to the total yield of a single bubble and the fitting of the experimental yield of hydrogen peroxide in the sonicated solution. It was observed that the number density is increased with the rise of ultrasound frequency from 200 to 1140 kHz, independently of the saturating gas nature (O2, Ar or air).

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Nội dung Text: A semi-empirical approach for determining the number density and void fraction of acoustic cavitation bubbles in sono-reactors

Received: 18 November 2022 Revised: 15 February 2023 Accepted: 5 May 2023 DOI: 10.1002/vjch.202200207 RESEARCH ARTICLE A semi-empirical approach for determining the number density and void fraction of acoustic cavitation bubbles in sono-reactors Aissa Dehane Slimane Merouani Laboratory of Environmental Process Engineering, Department of Chemical Abstract Engineering, Faculty of Process Engineering, A new semi-empirical technic has been established relying on the linkage University Constantine 3 Salah Boubnider, Constantine, Algeria between the chemistry in the bulk liquid and that taking place in the acoustic cavitation bubble. The open-source COPASI software has been used for the opti- Correspondence mization of number density according to the total yield of a single bubble and the Aissa Dehane, Laboratory of Environmental fitting of the experimental yield of hydrogen peroxide in the sonicated solution. It Process Engineering, Department of Chemical was observed that the number density is increased with the rise of ultrasound fre- Engineering, Faculty of Process Engineering, University Constantine 3 Salah Boubnider, P.O. quency from 200 to 1140 kHz, independently of the saturating gas nature (O2 , Ar Box 72, 25000 Constantine, Algeria. or air). Within this range of wave frequencies, i.e. from 200 to 1140 kHz, the num- Email: aissaleon15@gmail.com; ber of active bubbles goes up from 9.35 × 107 to 3.65 × 1015 L−1 s−1 . On the other aissaleon@yahoo.com side, it has been demonstrated that the number density obtained under air atmo- Funding information sphere is greater than that resulting either under argon or oxygen-saturating gas. Ministry of Higher Education and Scientific Interestingly, with respect to the saturating gas nature (O2 , Ar, air) and the range of Research of Algeria, Grant/Award Number: ultrasound frequency (200–1140 kHz), it was observed that the increase of num- A16N01UN250320220002; General Directorate of Scientific Research and Technological ber density was not necessarily accompanied by a proportional increase of void Development (GD-SRTD) fraction (total volume of bubbles). KEYWORDS COPASI software, number density, saturating gas, semi-empirical method, ultrasound frequency, void fraction 1 INTRODUCTION In = 1 W/cm2 ) determined the bubble size distribution in an actual sonochemical reactor using the Fraunhofer Within the sono-irradiated field, the collapse of micron- laser diffraction (LD) method with temporal separation of sized bubbles produces enormous pressures (several hun- the acoustic wave disturbance (pulsed sonication). More- dred atmospheres) and temperatures (thousands of degree over, they also reported the effects of surfactant in the Kelvin). A range of industrial and scientific applications ben- equilibrium state and the effect of pulse length. A com- efit from the advantageous physical and chemical effects paratively smaller bubble size range was achieved, which produced by these critical conditions.1–10 However, the is found to be closer to the resonance size range of the control and optimization of cavitation systems are chal- cavitation bubbles, at short pulse length, lower pulse num- lenging and have been the subject of various research ber, and in the presence of low concentrations of SDS. because of the chaotic nature of acoustic cavitation bub- Additionally, an optimal number density was found in rela- bles. In general, the analysis of size distribution, bubbles tion to the turn-on period, while the number of bubbles coalescence, bubble deformation, void fraction (total vol- increased as the surfactant concentration rose. But since ume of bubbles), secondary Bjerknes force and other laser diffraction and the phase Doppler method are based phenomena were the subjects of numerous theoretical on measuring scattered laser light from bubbles, these and experimental works. Iida et al.11 (freq = 443 kHz, methods are highly sensitive to a variety of phenomena © 2024 Vietnam Academy of Science and Technology and Wiley-VCH GmbH. Vietnam J. Chem. 2024;62:141–150. wileyonlinelibrary.com/journal/vjch 141
25728288, 2024, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200207 by Readcube (Labtiva Inc.), Wiley Online Library on [01/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 142 DEHANE and MEROUANI (acoustic wave disturbance, bubble deformation coales- reflection etc.) could be combined with theoretical tools, cence, degassing bubbles etc.) observed in the irradiation such as acoustic bubbles and CFD (computational fluids field. On the other hand, a capillary approach was employed dynamics) modeling, for a deeper analysis of their inter- by Lee et al.12 (freq = 515 kHz, PE = 20 W) to assess actions with the acoustic distribution in the sonicated the impact of surface-active solutes on the coalescence of solution. bubbles in the sonicated solution. The addition of surface- A number of theoretical attempts have been made to active solutes was shown to reduce the total volume of assess the size distribution of active bubbles in a son- bubbles (total void of bigger gas bubbles) through the icating medium, primarily based on the single bubble inhibition of bubbles coalescence. Using a pulsed mode hypothesis. These have been accomplished by measuring of sonication, Lee et al.13 evaluated the range of the the amount of produced molecular hydrogen (H2 )21,22 or sonochemically active bubbles at 515 kHz through the oxidants (• OH, HO2 • , O3 , and H2 O2 ).23,24 Additionally, the Epstein–Plesset equation and the bubbles’ total dissolu- impact of CCl4 and methanol (in water) on the range of tion time. It was shown that the cavitation bubble size active bubbles was studied in an argon environment.25,26 goes down and the bubble size distribution narrows a low However, only few studies have focused on quantifying concentration of SDS is added to the analyzed solution. the number density of active bubbles in the irradiation The bubble population density was centralized around the solution. mean radius. Additionally, it was concluded that the pulsed Using a steady-state approach, Merouani et al.27 have SL (sonoluminescence) technique could be adopted for the recently developed a semi-empirical method based on the evaluation of size distribution of SL bubbles in the sono- material balance equations of • OH, HO2 • , and H2 O2 in the irradiated aqueous solutions. In single- and dual-frequency bulk liquid. As a result, the expression of the number den- systems (355 and 20 kHz), Brotchie et al.14 used the same sity as a function of the molar yield of • OH, HO2 • , and H2 O2 methodology as Lee et al.13 in the purpose to link the within the bubble was provided utilizing the production ultrasonic pulse separation with the size of acoustic cav- rates of these species (• OH, HO2 • , and H2 O2 ) in conjunction itation bubbles. As a function of the pulse mechanism, with the experimentally established H2 O2 production rate they showed an increase in bubble density, coalescence in the liquid phase. Only the impact of ultrasonic frequency rate, and bubble size; however, the continuous operation was assessed in this investigation; the mathematical model demonstrated the opposite tendency (decrease). Further- used ignored mass and heat transfers in addition to reac- more, Brotchie et al.14 demonstrated a direct correlation tion heat. On the other side, Kerboua’s study28 was founded between the increase in sonochemical activity and the on an energetic examination of the microscopic (one bub- relative coalescence extent in a dual-frequency system. ble) and macroscopic (control volume) systems exposed It should be noted that the characterization of bubble to the ultrasonic field. According to Kerboua’s analysis,28 population through the evaluation of void fraction has the relationship between the microscopic system (acous- been treated in several works using different experimen- tic cavitation bubble) and the macroscopic system (dV) is tal approaches such as Phase Doppler,15 Laser diffraction,16 wholly theoretical. The overall energy fluctuates for the sound speed variation,17 electromagnetic reflection,18,19 control volume (dV) throughout a time slot dt. This com- and capillary technique.20 It is worth mentioning that prises the acoustic energy, internal energy, macro-kinetical according to the various experimental works, the void frac- energy, and macro-potential energy. The number density tion (an indicator of number density) has been evaluated was thus expressed using a first order non-linear differen- as a time-averaged value, whereas, according to the recent tial equation. In order to obtain this differential equation, works of Iida et al. (443 kHz, 1 W/cm2 )20 and Burkin et al. it was assumed that the acoustic intensity term [I(x)] will (120 kHz, 3.04 W/cm2 ),17 this parameter (void fraction) has remain constant over the distance dx (travelled by an ultra- been estimated at collapse. sonic disturbance). Finally, a series of equations (evaluating Additionally, all the experimental investigations15–20 the bubble radius, wall velocity etc.) are solved in parallel were performed at constant operating conditions of ultra- with the mathematical statement expressing the number of sound frequency, acoustic power, liquid temperature, and cavities. for a single saturating gas. Moreover, despite the vari- Based on the above discussion, in the current work, a new ous experimental techniques proposed in literature, the semi-numerical method was suggested for calculating the final judgement of the efficacy of these methods needs volume fraction and number of sonic bubbles produced more investigations under different operating conditions inside a sono-reactor. This method relies on the relation- (acoustical conditions, variation of saturating gas nature, ship between the chemistry of a single bubble and the presence of additives, varying liquid temperature and vol- surrounding liquid. The impacts of ultrasound frequency ume etc.) for which the sensitivity (and performance) of (200 to 1140 kHz), and saturating gas nature (air, oxygen, each of these techniques will be accurately evaluated. and argon) on the number density (number of bubbles) and Additionally, the experimental quantification of void frac- void fraction (total volume of bubbles) were investigated. tion and number density with respect to the different Additionally, our findings are confronted with the literature physical probing means (laser, sound, electromagnetic works for accuracy.
25728288, 2024, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200207 by Readcube (Labtiva Inc.), Wiley Online Library on [01/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License DEHANE and MEROUANI 143 2 THEORETICAL PACKAGE Where, λL and L are the thermal conductivity of water and the latent heat of vaporization, respectively. The mathemat- 2.1 The microreactor system ical formula of λL is given in ref. [48] as a function of TL (liquid temperature) and PL (liquid pressure) in the range of 273.15 The adopted mathematical model for the single bubble K < TL < 623 K and Psat < PL < 50 MPa. The latent heat of process was detailed in our prior studies.25,29 Relying on evaporation of water (L) is given by:49 a system of ordinary differential equations, this model ( )0.358 includes heat exchange across the bubble interface, water ( ) 5 673.43 − 9 (T − 273.15) evaporation and condensation at the acoustic cavitation L J∕kg = 2.44281 × 10 5 wall, liquid compressibility and viscosity, and chemical reactions heats. (2) The model’s governing equations are summarized in Table S1. The interactions between bubbles are According to Equation (1), for the calculation of the inter- disregarded.25 This assumption has been made due to facial temperature (Tint ), two gradients of temperature are the complicated nature of multibubble systems (clus- assumed on both sides of the bubble wall; therefore, at the ters) which makes the process modeling more and more inner thermal layer 𝛿g (Table S1), the temperature changes complex (until now not well understood). linearly from T (internal temperature of the bubble) to Tint Many leading research groups in sonochemistry have (interfacial temperature). Within the outside thermal layer used the single bubble approach to explain the over- (𝛿L ) of bubble, the temperature changes linearly from Tint to all reported sonochemical effects (sonoluminescence and T∞ (the ambient temperature of liquid). As a result, the tem- sonochemistry) in aqueous solutions in connection to influ- perature gradient on the outside layer of the bubble wall encing factors.23,27,30–45 The reaction pathways employed 𝜕T is given as: l = (T∞ −Tint )/𝛿L . As in the case of the inside for the internal chemistry of argon, oxygen, and air bub- 𝜕r thermal layer (Table S1), δL is estimated by√ considering the bles are shown in Tables S2–S4, respectively. Briefly, Table R R𝜒 S1 regroups the following main equations: time scale of bubble motion: 𝛿L = min{ , ̇ L }, with the 𝜋 R thermal diffusivity 𝜒L = 𝜆L ∕(𝜌L CpL ). In the present paper, 1. Equation (S1) (the modified Keller–Miksis equation46 ) the thermal conductivity, and the viscosity of liquid water describes the radial dynamics of the bubble during its are calculated as functions of liquid temperature and pres- oscillation in a compressible medium (water) saturated sure, whereas the surface tension and the saturated vapor with a specified gas (Ar, O2 , or air). pressure of water are calculated as functions of liquid tem- 2. The internal bubble pressure and temperature during perature as in ref. [49]. The density and the heat capacity of oscillation are given by Equations (S3) and (S4), respec- liquid water are obtained from ref. [50] tively. It is worth mentioning that due to the consideration of 3. Equation (S5) (the Hertz–Knudsen formula47 ) describes the interfacial bubble temperature, the equations of mass ̇ the mass flux, “m”, of water evaporation and condensa- transfer (evaporation and condensation of water) and heat tion at the bubble interface. exchange (see Equations (S5) and (S6) in Table S1) are esti- ̇ 4. Heat exchange (heat dissipation by diffusion33 ), “Q”, out- mated as functions of the interfacial temperature (Tint ). In side and inside the acoustic cavitation bubble is given by addition, in the present paper, the thermal conductivity of Equations (S6–S8). the gas (inside the bubble) is evaluated through its depen- 5. Equation (S9) describes the bubble’s internal energy’s dency on the temperature and the density of gas and vapor temporal variation. mixture (see Equation (S8), Table S1). On the other hand, the 6. Equations (S10–S15) describe the temporal variation, accommodation coefficient of Equation (S5) is calculated as during oscillation, of the water quantity and all other follows:51 species (k) within the bubble. ⎧𝛼 = 0.35 if Tint < 350 K, It is to indicate that in the present work, the main ⎪𝛼 = 0.35 − 0.05k(1) − 0.05k(2) + 0.025k(3) if 350 ≤ Tint improvements of the mathematical model are given as ⎪ ≤ 500 K, follows: ⎨ 0.05 ( ) ⎪𝛼 = Tc − 500 if 500 K ≤ Tint ≤ Tc , ⎪ Tc −500 1. For the calculation of the interfacial bubble tempera- ⎩𝛼 = 0.0 if T ≥ Tc , ture (Tint ), energy balance at the interface is obtained (3) through the continuity of energy flux at the bubble wall: with k(m) = k(k − 1) … .[k − (m − 1)], and k = Tint − 70. 50 𝜕Tl | | ( ) Lastly, the uptake coefficient (Θ) is used to compute the 𝜆L |r = R = 𝜆g 𝜕T | r = R + m∕MH O L ̇ (1) 𝜕r | 𝜕r | rate of dissolution (rd,i ) of chemical compounds from the | | 2
25728288, 2024, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200207 by Readcube (Labtiva Inc.), Wiley Online Library on [01/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 144 DEHANE and MEROUANI inside of the bubble into the surrounding liquid:52 uid) of the acoustic cavitation bubble. It should be noted that due to the inhomogeneous distribution of bubbles in √ the sono-irradiated solution, an average value (based on Tkb ni rd,i = Θ ⋅ × 4𝜋R2 (4) a mean ambient bubble radius) of the number density is 2𝜋mi V determined in the present paper. With the assumption of a constant flux (L−1 s−1 ) of sono-active bubbles generated where i denotes the chemical species (I = OH, H, H2 , HO2 in the irradiated liquid, the chemistry in the surround- etc.); kb is the Boltzmann constant, and T is the tempera- ing solution is triggered by the generated species at the ture inside the bubble. The uptake coefficient is assumed as strong collapse of bubbles. Therefore, with the fitting of Θ = 0.001.52 mi is the molecular mass of the species, ni is the the experimental data of the instantaneous production of number of moles inside a bubble, V is the bubble volume, hydrogen peroxide in the bulk liquid, the flux (L−1 s−1 ) of and R is the bubble radius. active bubbles was optimized by considering the effects The process for solving the set of differential equations of acoustical circumstances (frequency, intensity, and static shown in Table S1 was thoroughly described in our previ- pressure), and the solution conditions (temperature, pH and ous publications.25,53 On the other side, a mean (typical) volume). ambient bubble radii were chosen to reflect the ambient The kinetic modeling of the reaction schemes of Tables bubble population size because of the relatively narrow S5 and S6 has been performed using the open-source bubble size distribution at higher ultrasound frequen- COPASI software [version 4.34 (Build 251)]. In addition cies (>100 kHz).13,54 This method is frequently employed by to the possibility of resolving complex reaction mecha- researchers in theoretical sonochemistry.21–24,55,56 There- nisms, COPASI software allows the determination of known fore, to cover the entire range of wave frequency (from 200 rate constants using different optimization methods such to 1140 kHz) discussed in this study, a collection of ambi- as genetic algorithm, differential evolution, evolutionary ent radii (mean radii, R0 ’s) is used. These radii were chosen programming, and evolution strategy (SRES) etc. based on the experimental findings of Chen et al.,57 Lee The reactions in Tables S5 and S6, along with their rate et al.,13 and Brotchie et al.,54 which show that they vary constants and concentrations of initial substances, serve as mostly in terms of frequency. The ambient radii that are the software’s input parameters. For the determination of being used are as follows: 1.4 μm for 1140 kHz, 2.7 μm for number density, the experimental profile of H2 O2 forma- 800, 817, and 860 kHz, 3 μm for 500 and 585 kHz, 3.2 μm tion (function of time) was introduced to the software and for 300 and 362 kHz, and 3.9 μm for 200 kHz. According to then fitted by setting the number of active bubbles, i.e. the different theoretical studies21–24,55,56 of a single bubble constant flux (L−1 s−1 ), as an optimizable parameter. The sonochemistry, these ambient radii were verified. The satu- genetic algorithm approach was chosen to carry out this ration gas effect on the selection of each R0 is discussed in optimization. Test S1 of the SM. The generated species for a single bubble were intro- On the other hand, outside the acoustic cavitation bub- duced to the COPASI software based on the saturating gas ble (in the solution), the evolving chemistry is controlled nature: by the reaction pathways depicted in Tables S5 and S6 for argon/oxygen-bubble and air-bubble, respectively. As it is ∙ Under argon/oxygen atmosphere (with respect to the shown in Tables S5 and S6, the chemistry in the surround- chemistry in Table S5): ing liquid is directly related to the nature of the saturating gas (i.e. Ar, O2 or air). Production of a single bubble (mol) = xOH∙ OH + xH∙ H + xO O + xO2 O2 + xH2 O H2 O 2.2 Determination of the number of ∙ active bubbles and void fraction + xH2 H2 + xHO HO2 + xH2 O2 H2 O2 + xO3 O3 (5) 2 Due to the complex interactions (e.g. coalescence, sec- Where xi is the number of moles of species i (OH, H, O…). ondary Bjerknes force etc.) between bubbles in the soni- ∙ Under air atmosphere (with respect to the chemistry in cated liquid, and for purpose of simplifying our task, in the Table S6): present work, the population of active bubbles is repre- sented by a single ambient radius, which is the mean ambi- Production of a single bubble (mol) ent radius (see previous section). This approach has already ∙ ∙ been employed in previous theoretical studies.27,58,59 Addi- = xOH OH + xH H + xO O + xO2 O2 + xH2 O H2 O tionally, it is supposed that the acoustic bubble is frag- ∙ +xH2 H2 + xHO HO2 + xH2 O2 H2 O2 + xO3 O3 + xN2 N2 mented at the first collapse, i.e. when the minimum radius 2 (Rmin ) is attained. As a result, the determination of the +xN N + xNO NO + xNO2 NO2 + xHNO2 HNO2 number density was based on the linkage between the chemistry both inside and outside (in the surrounding liq- +xHNO3 HNO3 + xN2 O N2 O + xHNO HNO (6)
25728288, 2024, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200207 by Readcube (Labtiva Inc.), Wiley Online Library on [01/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License DEHANE and MEROUANI 145 Finally, in addition to the constant flux of active bub- bles, the concentration profiles of the different substances are generated over the formation period of hydrogen peroxide. On the other hand, relaying on the previous assumptions for the determination of number density, the void fraction “ɛ” (fraction of the total volume of bubbles) is simply deter- mined over the strong compression phase by the following expression: ( ) 𝜀 = N × 4∕3𝜋R3 min (7) It should be noted that in the above expression, the num- ber density (N) is recalculated over the lifetime period of a single bubble (until the end of the collapse phase). Finally, our findings (in terms of number density and void fraction) are confronted with the theoretical outcomes of Merouani et al.,27 Kerboua et al.,28 and the experimental findings of Iida et al.20 and Birkin et al.17 for critical analysis. 3 RESULTS AND DISCUSSION 3.1 Model validation and aqueous phase sonochemistry To validate our numerical model, the fitted curves of H2 O2 production (in deionized water) were compared to those obtained experimentally under the operational condi- tions of Ferkous et al. (sat. gas = air, freq. = 585 kHz, In = 3.628 W/cm2 ),60 Okitsu et al. (sat. gas = Ar, freq. = 200 kHz, In = 1 W/cm2 ),61 and Pétrier and Fran- cony (sat. gas = O2 , freq. = 200 kHz, In = 2.388 W/cm2 ),62 as in Figure 1(a)–(c). As it can be seen in Figure 1(a)–(c), independently of the experimental conditions, our numer- ical findings (fitted curves) are in good agreement with the experimental results of hydrogen peroxide production. F I G U R E 1 Experimental [(a): Ferkous et al. (sat. gas: air, Under these best data fitting, the optimized flux of bubbles freq. = 585 kHz, In = 3.628 W/cm2 , Tliq = 25 ◦ C).60 (b) Okitsu et al. (sat. gas: is 6.67 × 1010 , 3.39 × 108 and 9.35 × 107 L−1 s−1 according Ar, freq. = 200 kHz, In = 1 W/cm2 , Tliq = 20 ◦ C)61 and (c): Pétrier and to the conditions of Ferkous et al. (Figure 1(a)), Okitsu Francony (sat. gas: O2 , freq. = 200 kHz, In = 2.388 W/cm2 , Tliq = 20 ◦ C).62 ] and modeling of hydrogen peroxide sono-production under air, oxygen, et al. (Figure 1(b)), and Pétrier and Francony (Figure 1(c)), and argon atmosphere. respectively. These values of bubble number density are in the same order of magnitude as those predicted by several researchers, as it will be discussed later. In = 2.338 W/cm2 , sat. gas: O2 ), Merouani et al.27 (f = 300– In light of the above results, the established chemical 1140 kHz, In = 2 W/cm2 , sat. gas: air), Okitsu et al.61 schemes of Tables S5 and S6 (in addition to the mathemati- (freq = 200 kHz, In = 1 W/cm2 , sat. gas: Ar), Pflieger et al.63 cal model of Table S1) could be adopted with confidence for (freq = 362 kHz, In = 1.52 W/cm2 , sat. gas: Ar), Ferkous more exploration of the effect of operational circumstances et al.64 (freq = 585 kHz, In = 3.628 W/cm2 , sat. gas: Ar) upon the number density and void fraction. and Vajnhandl et al.65 (freq = 817 kHz, In = 2 W/cm2 , sat. gas: Ar) were compared to those obtained by Merouani et al.27 (under different conditions, see Figure 2) and Ker- 3.2 Impact of wave frequency and boua et al.28 (f = 20–800 kHz, In = 0.77 W/cm2 , sat. gas: saturating gas on the number density O2 ). At first sight, it can be observed that over the cov- ered ultrasound frequency range (from 200 to 1140 kHz), In Figure 2, our numerical results under the operational our findings (number of active bubbles) are quantitatively conditions of Pétrier and Francony62 (freq = 200–800 kHz, situated between those reported by Merouani et al.27
25728288, 2024, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200207 by Readcube (Labtiva Inc.), Wiley Online Library on [01/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 146 DEHANE and MEROUANI air and oxygen-saturating gases. A similar tendency of the effect of saturating gas on the triodide formation (in KI solu- tion) was obtained in the experimental works of Pétrier et al. (under oxygen and argon atmospheres) at 514 kHz (20 W) and 20 kHz (30 W)66 and Wayment and Casadonte (under air and argon atmospheres)68 at 300 and 20 kHz (0.8 W). In general, the effects of saturating gases on the sonoactivity of liquid could be explained in light of their physical properties: (i) solubility, (ii) thermal conductivity, and (iii) polytropic index (Cp/Cv). A saturating gas with a relatively high solubility (i.e. high nucleus’ number in the irradiated solution), low thermal conductivity (i.e. reduced heat energy dissipation outside the bubble) and high poly- F I G U R E 2 Comparison of our results [red line (air-atmosphere), green line (O2 -atmosphere), and brown line (Ar-atmosphere)] to those tropic index (i.e. generation of high maximal temperature obtained by Merouani et al. [black line (Merouani’s conditions), dashed and molar yield in the acoustic cavitation), is expected to yellow line (Pétrier and Francony’ conditions), and pink line (Jiang et al. increase the sonoefficiency of the sonicated solution as well conditions))27 and Kerboua et al. (blue line)28 as function of ultrasound as that of a single bubble. The opposite trend is obtained frequency. for gases with low solubility, polytropic index, and high thermal conductivity. In the present paper, the thermal con- ductivity of gases varies with bubble temperature (Equation and Kerboua et al.28 groups. The observed discrepancies (S8), Table S1), where that of argon is lower than those between our findings and those of Kerboua’s group28 and of air and oxygen gases (are in the same range).69 There- Merouani’s team27 (Figure 2) can be attributed to the fore, the dissipation of heat energy in air and O2 -bubbles various approaches each group used to determine the is greater than that in argon bubbles. On the other hand, number density (see Section 1). However, at the present, oxygen and air gases have the same heat capacity ratio it is impossible to make a conclusive judgement on the of 1.39 (at 25 ◦ C), which is lower than that of argon gas effectiveness of these methods based on reliable exper- (1.67 at 25 ◦ C). The solubility (in mole fraction at 25 ◦ C) imental results (not available). Moreover, it is found that of these gases is in the order: Ar (2.5306 × 10−5 ) > O2 the number of active bubbles increased with the rise of (2.3009 × 10−5 ) > air (1.402 × 10−5 ).70 This order indi- frequency (Figure 2). According to the present study, the cates that the coalescence process is more probable in increase in number density is from 6.34 × 108 L−1 s−1 the same solubility order (Ar > O2 > air), because, more (300 kHz) to 3.65 × 1015 L−1 s−1 (1140 kHz), from 9.35 × 107 nucleus are created in the presence of gases with high sol- L−1 s−1 (200 kHz) to 1.82 × 1013 L−1 s−1 (800 kHz) and ubility (increases the number of bubbles). This mechanism from 3.39 × 108 L−1 s−1 (200 kHz) to 8.11 × 1013 L−1 s−1 (coalescence) is accentuated with the increase or decrease (817 kHz), for air, O2 , and Ar atmosphere, respectively. of acoustic intensity and wave frequency, respectively. By The influence of ultrasonic frequency on cavitation can considering effect of thermal conductivities and polytropic explain the increase in bubble density as wave frequency ratios of gases (Ar, O2 , and air), the expansion ratio and increases. As frequency increases, oscillating cavities’ max- the implosion intensity in argon bubble are expected to imum radii and lifetimes decrease. This is because the be greater than those in O2 and air bubbles (Tmax and acoustic period shortens with increasing frequency. Higher Rmax,Ar > Tmax and Rmax_O2 , air ) at fixed frequency and acous- acoustic frequencies hence generate a significant num- tic power. Moreover, taking into account the impact of ber of active bubbles per unit of time compared to lower gases solubility (increased coalescence probability in the ones. Additionally, the increase of number density (at high order: Ar > O2 > air), more acoustic cavities are expected frequency) could be reinforced by the fact that at high to be generated in the order: air > O2 > Ar. These findings frequencies (with fixation of acoustic intensity) the molar show that the variation of number density as a function of yield of a single bubble goes down, thus, with respect saturating gases nature is the outcome of the combined to the increased total production in the sonicated liquid effects of solubility, thermal conductivity and polytropic at high frequency,66,67 more active bubbles are expected ratios of these gases. to be existing under these conditions. Furthermore, the Returning to our results in Figure 2, due to the adopted increase in the number of bubbles at high frequencies is technique in the present work, the number of active bub- supported by the plausible decrease in coalescence mech- bles is directly related to the number of generated species anism with the formation of small bubbles (expansion at the strong collapse (Section 2.2). As a result, since the ratio goes down). Interestingly, it is observed that in our amount of chemicals created decreases with lower bubble work, the number density obtained under air atmosphere is temperatures, it follows that there would be more active greater than that retrieved under argon and oxygen atmo- bubbles (Figure 2) at lower molar yield. This could be easily spheres (Figure 2). Merouani et al.27 have obtained the corroborated according to the peak temperatures attained same behavior (for the number of active bubbles) under at the end of collapse for a single bubble. For example, the
25728288, 2024, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200207 by Readcube (Labtiva Inc.), Wiley Online Library on [01/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License DEHANE and MEROUANI 147 maximal temperatures retrieved at 585, 500, and 585 kHz under air, O2 and Ar atmospheres are 3010, 3698, and 5831K, respectively (results not shown). It should be noted that some exceptions are observed at around 200 kHz for all the saturating gases and around 800 kHz for oxygen and argon atmospheres. These discrepancies may be ascribed to the different operational conditions (acoustic frequency, acoustic intensity, liquid temperature, solution pH) as well as the probable experimental errors made during the mea- surement of H2 O2 concentration in the indicated works of Figure 2. Conditions: Our results were obtained according to the operating circumstances of: Pétrier and Francony62 (freq = 200–800 kHz, In = 2.338 W/cm2 , sat. gas: O2 , Tliq = 20 ◦ C, green line), Merouani et al.27 (freq = 300– 1140 kHz, In = 2 W/cm2 , sat. gas: air, Tliq = 25 ◦ C, red line), Okitsu et al.61 (freq. = 200 kHz, In = 1 W/cm2 , sat. gas: Ar, Tliq = 20 ◦ C, brown line), Pflieger et al.63 (freq = 362 kHz, In = 1.52 W/cm2 , sat. gas: Ar, Tliq = 20 ◦ C, brown line), Ferkous et al.64 (freq = 585 kHz, In = 3.628 W/cm2 , sat. gas: Ar, Tliq = 25 ◦ C, brown line) and Vajnhandl et al.65 (freq = 817 kHz, In = 2 W/cm2 , sat. gas: Ar, Tliq = 25 ◦ C, brown line). Merouani’s group results: black line (Mer- ouani’s conditions: freq = 300–1140 kHz, In = 2 W/cm2 , sat. gas: air, Tliq = 25 ◦ C), dashed yellow line (Pétrier and Francony’ conditions: sat.gas: O2 , freq = 20–800 kHz, In = 2.338 W/cm2 , Tliq = 20 ◦ C), and pink line (Jiang et al. conditions: sat. gas: O2 , freq = 20–800 kHz, In = 2.338 W/cm2 , Tliq = 20 ◦ C).27 Kerboua et al. condi- tions: (freq = 20–800 kHz, In = 0.77 W/cm2 , sat. gas: O2 , F I G U R E 3 Number density and void fraction function of ultrasound Tliq = 20 ◦ C).28 frequency (200–1140 kHz) and saturating gas nature [(a): air, (b): Ar, and (c): O2 ] under the operational conditions of Merouani et al.27 [(a), freq. = 300–1140 kHz, In = 2 W/cm2 , sat. gas: air, Tliq = 25 ◦ C], Okitsu et al.61 [(b), freq. = 200 kHz, In = 1 W/cm2 , sat. gas: Ar, Tliq = 20 ◦ C], 3.3 Effect of wave frequency and Pflieger et al.63 [(b), freq. = 362 kHz, In = 1.52 W/cm2 , sat. gas: Ar, saturating gas on void fraction Tliq = 20 ◦ C], Ferkous et al.64 [(b), freq. = 585 kHz, In = 3.628 W/cm2 , sat. gas: Ar, Tliq = 25 ◦ C], and Vajnhandl et al.65 [(b), freq. = 817 kHz, In = 2 W/cm2 , sat. gas: Ar, Tliq = 25 ◦ C], and Pétrier and Francony62 [(c), In this section, with respect to the evolution of number (freq. = 200–800 kHz, In = 2.338 W/cm2 , sat.gas: O2 , Tliq = 20 ◦ C]. density, the variation of void fraction was visualized over the wave frequency from 200 to 1140 kHz, under differ- ent saturating gases, Figure 3(a)–(c). As it can be seen in On the other hand, under an oxygen atmosphere, Figure 3(a),(b), the increase in number density was not Figure 3(c) shows that the void fraction goes up with always accompanied by a similar increase in the void frac- the number density in the wave frequency range from tion. For example, under air atmosphere (Figure 3(a)), the 200 to 800 kHz; a similar tendency was obtained by Lee rise of the wave frequency from 860 to 1140 kHz gives et al.71 under air atmosphere, where the void rate was an increase of 5.19% in number density, whereas, for the monotonously increased (from 2.8 to 8.2 μL/s) with the rise same frequency range, the void fraction goes down from of acoustic frequency from 168 to 726 kHz. The harmo- 2.15 × 10−6 to 1.94 × 10−7 (−90.97%). The same behavior nious increase of void fraction with the number density (for void fraction) was obtained under an argon atmosphere (under O2 atmosphere) may be explained by the rela- (Figure 3(b)) in the frequency range from 200 (2.56 × 10−12 ) tively larger frequency steps (compared to Figure 3(a),(b)) to 585 kHz (6.81 × 10−13 ). These findings are in line with existing over the analyzed frequency range (200, 500, and those obtained by Kerboua et al.28 under oxygen atmo- 800 kHz). From Figure 3(a)–(c), based on the analysis of sphere. In addition, these results indicate that no correlation number density and void fraction with respect to the ultra- exists between the number of bubbles and the void frac- sound frequency variation and the nature of saturating gas, tion, which means that the determination of number den- it can be deduced that the adoption of void fraction for an sity from the void fraction could not be directly performed accurate determination of number density is not enough without more information about the bubbles population without considering more information about the bubble (size distribution, bubble-bubble interactions etc.). population.
25728288, 2024, 2, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200207 by Readcube (Labtiva Inc.), Wiley Online Library on [01/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 148 DEHANE and MEROUANI (200–1140 kHz), it was observed that the increase of num- ber density was not always accompanied by a proportional increase of void fraction. This means that no correlation exists between both parameters (i.e. number of bubbles and void fraction). As a result, the use of void fraction for the determination of number density could be performed with the consideration of more information about the bubble population, through a deep understanding of the different interactions in the irradiated solution. Performance anal- ysis of the present semi-empirical technique shows the possibility of using our method for the determination of F I G U R E 4 Comparison of our results in terms of void fraction (under number density (and void fraction) in other environments, the experimental conditions of Merouani et al.27 (freq. = 300–1140 kHz, especially where nonvolatile and hydrophilic species are In = 2 W/cm2 , sat. gas: air, Tliq = 25 ◦ C) to those obtained by Iida et al (freq. = 443 kHz, In = 1 W/cm2 , sat. gas: air, Tliq = NI)20 and Burkin et al. present in the bulk liquid. Finally, in light of the findings (freq. = 120 kHz, In = 3.04 W/cm2 , sat. gas: air, Tliq = 25 ◦ C).17 of the present work, the increase in number density was obtained monotonously with the rise in wave frequency Additionally, as it can be seen in Figure 4, in terms of independently of the saturating gas nature. However, for a void fraction, our findings are found to be in acceptable maximal sonoactivity in the irradiated solution, the saturat- accordance with those determined experimentally (at col- ing gas nature (oxygenated mediums are recommended) lapse phase) by Iida et al. (443 kHz, 1 W/cm2 )20 and Burkin and acoustical circumstances (optimum frequencies and et al. (120 kHz, 3.04 W/cm2 )17 under air atmosphere. The acoustic powers are recommended) should be adequately observed differences between our findings (8.07 × 10−13 – selected. In addition, more understanding of the sono- 2.14 × 10−6 ) and those of Iida (4.14 × 10−11 ) and Burkin chemical medium could be achieved by combining the (5.2 × 10−9 ) teams could be ascribed to the adopted tech- acoustic bubble modeling with the computational fluid niques (Iida et al.: Capillary technique, Burkin et al.: sound dynamics (CFD) simulations. speed variation, present paper: semi-numerical technique) for the determination of void fraction. F U N D I N G I N F O R M AT I O N This study was funded by The Ministry of Higher Edu- cation and Scientific Research of Algeria (project No. 4 CONCLUSION A16N01UN250320220002) and the General Directorate of Scientific Research and Technological Development (GD- In the current study, a new semi-empirical technic has been SRTD). proposed for the determination of number density and the void fraction of bubbles. This method was principally based C O N F L I C T O F I N T E R E S T S TAT E M E N T on the combination of the solution’s chemistry with that The authors declare no conflicts of interest. taking place inside the acoustic cavitation bubble. This link was performed using COPASI software, where the number of active bubbles was optimized with respect to the gen- ORCID erated species (at the collapse phase) of a single bubble Aissa Dehane https://orcid.org/0000-0001-8384-2526 and the fitting of the experimental evolution of H2 O2 con- centration in the surrounding liquid. 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