Insight into the role of dissolution mechanism in the sonochemistry of acoustic cavitation bubble

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The present paper is focused on the impact of the dissolution mechanism of the different species (formed within a single bubble) on bubble chemistry. This process is analyzed on a range of ultrasound frequencies from 140 to 515 kHz, at an acoustic intensity of 1 W/cm². The obtained findings are compared to the results available in the literature.

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Nội dung Text: Insight into the role of dissolution mechanism in the sonochemistry of acoustic cavitation bubble

Cite this paper: Vietnam J. Chem., 2023, 61(5), 632-645 Research article DOI: 10.1002/vjch.202300115 Insight into the role of dissolution mechanism in the sonochemistry of acoustic cavitation bubble Aissa Dehane*, Slimane Merouani Laboratory of Environmental Process Engineering, Department of Chemical Engineering, Faculty of Process Engineering, University Constantine 3 Salah Boubnider, P.O. Box 72, 25000 Constantine, Algeria Submitted March 22, 2023; Revised June 3, 2023; Accepted June 16, 2023 Abstract Using a detailed numerical model, in the present work, the dissolution process of the different species generated by the acoustic cavitation bubble was investigated through the analysis of bubble chemistry over a range of wave frequencies from 140 to 515 kHz. It has been observed that during the first bubble collapse, at 140 and 213 kHz, significant amounts of ●OH, O, H●, H2, and O2 molecules (from ~ 2.110-20 to 4.8610-18 mol) are dissolved into the bulk liquid (2.84-0.067%). However, with the rise of ultrasound frequency (>213 kHz), the number and the quantity of the dissolved substances are decreased ( H● (4.4110-18-7.7610-19 mol) > O (1.810-18-2.7510-19 mol) > ●OH (4.6810-19-1.9110-19 mol) > O2 (8.4310-20- 2.110-20 mol). Nevertheless, at 355 kHz, the dissolution of the main substances is in the order: H ● (1.1610-20 mol) > ● OH (5.1310-21 mol)>H2 (3.5910-21 mol). Despite the low dissolution percentages of the different species (compared to the total yield) during the first bubble collapse (< 3%), it has been observed that the corresponding molar amounts (depending on the applied frequency) are of great importance (≤ 4.8610-18 mol). On the other hand, independently of the number of acoustic cycles (1, 2 or 3), the dissolution tendency of the different species, at 140 and 213 kHz, is in the order: H2 > H● > O > O2 > ●OH > O3 > HO2● > H2O2. Nevertheless, above 213 kHz, this ranking starts to be disturbed with the dominance of the main species, i.e. H2, H●, O, ●OH, and O2 molecules. According to the obtained findings in the present paper, the importance of the dissolution mechanism (into the bubble chemistry) is clearly evidenced; therefore, for an accurate simulation of the chemistry of an acoustic cavitation bubble, the consideration of the dissolution process should be taken into account throughout the bubble’s oscillation. Keywords. Numerical model, dissolution process, ultrasound frequency, bubble chemistry, bubble collapse, acoustic cycles. 1. INTRODUCTION cleaning,[5] nanoparticle and polymer synthesis,[6-8] pollutants mineralization,[9,10] biomedical uses[11-13] An enormous amount of energy can spontaneously and food science.[14,15] be concentrated when an ultrasonic irradiation Due to the prominent role of the acoustic travels through a fluid, which can result in the cavitation bubble in the different scientific emergence of several chemical species (•OH, HO2•, applications, a large number of experimental and O, H2O2, O3, H2…etc.) as well as the possible theoretical works has been deduced for a deeper production of light bursts (depending on acoustical understanding of its behaviour in a single or conditions). All of these chemical (substances multibubble system. These studies include the effect formation) and physical (light emission) events take of many operational parameters, e.g. ultrasonic place inside the acoustic cavitation bubble.[1-3] At the frequency,[16,17] acoustique power,[16-19] saturating end of the collapse phase, spectacular circumstances gas,[20-22] ambient pressure[23,24] and solution are developed (~5000 K and ~ 500 bar[4]), leading to temperature,[25-28] on the sonoactivity of the acoustic the decomposition of bubble content and the bubble. In addition, the impact of transport generation of the different radicals and molecules phenomena (mass and heat),[29] gas diffusion,[30,31] (depending on the initial composition of the bubble). viscosity, depth, and surface tension of liquid,[32–34] Based on the acoustical cavitation phenomenon, reactions heat,[35] vapour and gases segregation[36] ultrasound offers a wide range of technical and other parametric conditions and mechanisms applications, including surface, including surface were investigated. On the other hand, the 632 Wiley Online Library © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Aissa Dehane et al. concentration of reactive and non-reactive species argon-saturated water under an ultrasonic formed inside the bubble varies considerably from irradiation. Some improvements are made in the the bubble interior (the gas phase) to the surrounding present study. This section covers the most liquid, where oxidation/reduction processes may important aspects of the model. Our model, which is occur due to diffused species. According to certain based on a set of ordinary differential equations, investigations, only a small percentage of •OH considers non-equilibrium vaporization and radicals may escape the liquid boundary zone and condensation of water molecules at the bubble wall, reach the liquid's bulk.[37,38] However, data on the heat transfer both inside and outside the bubble, and influence of processing conditions (frequency, chemical processes. The governing equations of our power, ambient pressure, etc.) and transfer numerical model are listed in table 1. The phenomena on the dissolution mechanism of the interactions between bubbles are disregarded. Table different species are very scarce. 2 shows the chemical routes for Ar-bubble, which In the theoretical work of Yasui et al.[39] for a can be used to investigate the interior bubble single acoustic cavitation bubble, the dissolution chemistry. Table 1 provides the following main mechanism effect on the different chemical species equations: has been investigated under a single frequency and a 1. The radial dynamics, R(t), of the bubble constant acoustic amplitude (52 kHz, 1.52 bar). It during its oscillation in a compressible has been concluded that important quantities are medium (water) saturated with argon are dissolved into the surrounding liquid either in the described by Eq. 1 (the modified Keller- case of SBSL or for an air bubble. Moreover, it was Miksis equation[41]). found that not only hydroxyl radicals are produced 2. During oscillation, Eqs. 3 and 4 supply the by a bubble but also O atoms and H2O2. It has been internal bubble pressure and temperature, suggested that an appreciable quantity of O atom is respectively. produced by bubbles within a standing-wave-type 3. The mass flow (dm/dt) of water evaporation sonochemical reactor in which oxygen is dissolved and condensation at the bubble-liquid in water. Despite the interesting results obtained by interface is described by Eq. 5 (the Hertz- Yasui’s group, much scarcity is observed in the Knudsen formula[42]). literature regarding the analysis of the dissolution mechanism in relation to the variation of the 4. The heat exchange (dQ/dt ) within and outside ultrasound frequency. Therefore, more work is the bubble during oscillation is described by required in order to enhance our understanding Eq. 6 (heat dissipation by conduction[43]). toward this process (dissolution mechanism). 5. Eq. 9 depicts the temporal fluctuation of the To this end, the present paper is focused on the bubble's internal energy. impact of the dissolution mechanism of the different 6. During bubble oscillation, the temporal species (formed within a single bubble) on bubble variation of H2O and all other species ‘k’ chemistry. This process is analyzed on a range of amounts are described by Eqs. 10 and 11. ultrasound frequencies from 140 to 515 kHz, at an The resolution approach of the differential acoustic intensity of 1 W/cm². The obtained findings equations in table 1 is detailed in depth in our are compared to the results available in the literature. previous papers.[40,44] The molar amount of every As it is known, the chemistry within the oscillating species (excluding argon, which is chemically inert) bubble is very sensitive to the variation of the in the bubble, as well as the development of the operating circumstances (wave frequency, acoustic bubble temperature, pressure, radius, and wall power, liquid temperature, saturating gas, etc.), velocity, are all outputs of these equations, which additionally, the simulation of this complex medium are applied throughout the bubble’s lifetime. Since (bubble interior) needs an accurate consideration of the active bubble range at higher ultrasound all the possible mechanisms taking place inside the frequencies (> 100 kHz) is limited, the mean bubble. As a result, the present work aims at the (average) ambient bubble radii (R0) were evaluation and the revealing of the importance of the determined empirically to represent the ambient dissolution process (of the different species) during bubble size of the active population.[17,45] This the simulation of the bubble chemistry. approach is extensively used in theoretical sonochemistry research.[29,35,46–49] The typical Model ambient bubble radii (R0) at the investigated frequencies are 5 µm at 140 kHz,[50] 3.9 µm for 213 Early on,[40] a comprehensive mathematical model kHz,[17] 3.2 µm for 355 kHz[17] and 3 µm for 515 was created for a single spherical bubble vibrating in kHz.[45] © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 633
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Insight into the role of dissolution mechanism… Table 1: Principal equations of the model (see detail in Refs. [40,63])* 1. Bubble dynamics Ṙ ṁ 3 2 Ṙ 2ṁ (1- + ) RR̈ + Ṙ (1- + ) C CρL 2 3C 3CρL 1 𝑅̇ 𝑅 𝑚𝑅 ̈ 𝑅̇ 𝑚 ̇ = (1 + ) [𝑃 𝐵 (𝑡) − 𝑃 𝐴 𝑠𝑖𝑛 (2𝜋𝑓 (𝑡 + )) − 𝑃∞ ] + (1 − + ) 𝜌𝐿 𝐶 𝐶 𝜌𝐿 𝐶 𝐶𝜌 𝐿 𝑚̇ 𝑚 ̇ 𝑅̇ 𝑚 ̇ 𝑅 𝑑𝑃 𝐵 + (𝑅̇ + + )+ (Eq. 1) 𝜌𝐿 2𝜌 𝐿 2𝐶𝜌 𝐿 𝐶𝜌 𝐿 𝑑𝑡 - Pressure at the external bubble wall: 2𝜎 4𝜇𝑅̇ 𝑃 𝐵 (𝑡) = 𝑃(𝑡) − − (Eq. 2) 𝑅 𝑅 - Bubble pressure and Temperature: nRg T an² P(t) = + (Eq. 3) V-nb V² an² (E+ V ) T= (Eq. 4) Cv nt 2. Mass transfer (water vapor and methanol condensation and evaporation): {Psat,H2O [R]-𝑃 𝐻2𝑂 } ṁ = α (Eq. 5) 2πT 𝑖𝑛𝑡 Rg √ MH2O 3. Heat transfer (thermal conduction): (Tint -T) ̇ Q = 4πR²λg (Eq. 6) 𝛿g R 𝑅𝜒 𝑔 𝛿g = min { ,√ } (Eq. 7) π Ṙ 𝑏 (𝑛 𝐻2𝑂 +𝑛 𝐴𝑟 ) 1 λg = ( +1.2+0.755y) 𝜅0,𝑚𝑖𝑥 (Eq. 8) 𝑉 𝑦 4. Internal bubble energy: n 2 m, 𝐻2𝑂 ̇ 2 (Tint -T) 4 3 ΔE = -P(t)ΔV(t)+4πR ∆t e +4πR ∆t λg - πR ∆t ∑ ∆Hi ri ( 𝐸𝑞. 9) MH2O H2O 𝛿g 3 i=1 5. Change in species quantities (mol): - For H2O m, 𝐻2𝑂 ̇ nH2O (t+O ) = nH2O (t)+4πR2 ∆t ̇ +V ∆t UH2O (Eq. 10) MH2O - For other species k (except Ar): nk (T+∆t) = nk (T)+V ∆t Uk̇ (Eq. 11) where: I 1 dnk U̇ k = ∑(υ"-υ') ri (k=1, …, K) (Eq. 12) V dt i=1 K K ri = kfi ∏[Xk ]υ'ki -kri ∏[Xk ]υ"ki (Eq. 13) k=1 k=1 © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 634
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Aissa Dehane et al. Eafi kfi = Afi Tbfi exp (- ) (Eq. 14) Rg T Eari kri = Ari Tbri exp (- ) (Eq. 15) Rg T *Variables description: a and b (in Eqs. 3 and 4) are the Van de Waals constants (given in Ref. [64]), Rg is the universal gas constant. V is the volume of the bubble [V = 4/3(πR3)], T is the temperature inside the bubble, E is the internal bubble energy, Psat[R] is the saturated vapor pressure (calculated by using Antoine’s equation) at the interface temperature (Tint), MH2O is the molar mass of water vapor. ‘α’ is the accommodation coefficient. λg, 𝜒 𝑔 and 𝛿g are the heat conductivity, thermal diffusivity of the gas mixture and the thickness of the thermal boundary layer, respectively. [Individual λi of gases[64-66]: λH2O(T) = 9.96721310-5T - 1.170510-2, λAr(T) = 3.588710-5T + 6.8127710-3, 𝜒 𝑔 = [λg/Cp]. Cp is the heat capacity concentration (J m-3 K-1) for H2O, Ar mixture, Cv is the molar heat of gases and vapor in the bubble [Cv = (3/2)Rg for monoatomic gases (Ar, H…), (5/2)Rg for diatomic gases (O2, N2, …) and (6/2)Rg for triatomic gases]. ΔHi and ri are the enthalpy change and the rate of the ith reaction, respectively, and eH2O is the energy ̇ ̇ transported by 1 mol of an evaporating or condensing water vapor [e,H2O = Cv,H2OT], Ui (Uk ) is the production rate of th H2O (k species) within the bubble. Table 2: Kinetical mechanism within a collapsing argon bubble.[67,68] M is the third Body. Subscript “f” denotes the forward reaction and “r” denotes the reverse reaction. A is in (cm3 mol-1 s-1) for two body reaction [(cm6 mol-2 s-1) for a three body reaction], and Ea is in (cal mol-1) and ∆H in (Kcal mol-1). For some of the backward reactions, the constants are not listed. Those backward reactions are neglected during calculations Reaction Af nf Eaf Ar nr Ear ΔH 1 H2O+M ⇌ H●+●OH+M 1.9121023 -1.83 1.185105 2.21022 -2.0 0.0 121.72 17 -0.64 5 15 -0.5 0.0 2 O2+M ⇌ O+O+M 4.51510 1.18910 6.16510 120.91 3 ● OH+M ⇌ O+H●+M 9.881017 -0.74 1.021105 4.7141018 -1.0 0.0 104.36 4 H●+O2 ⇌ O+●OH 1.9151014 0.0 1.644104 5.4811011 0.39 -2.93102 16.54 5 H●+O2 +M ⇌ HO2● +M 1.4751012 0.6 0.0 3.091012 0.53 4.887104 - 49,0 6 O+H2O ⇌ ●OH+●OH 2.97106 2.02 1.34104 1.465105 2.11 -2.904103 17.37 7 HO2●+H● ⇌ H2+O2 1.661013 0.0 8.23102 3.1641012 0.35 5.551104 - 57.34 8 HO2●+H● ⇌ ●OH+●OH 7.0791013 0.0 2.95102 2.0271010 0.72 3.684104 - 38.82 9 HO2●+O ⇌ ●OH+O2 3.251013 0.0 0.0 3.2521012 0.33 5.328104 - 55.47 10 HO2●+●OH ⇌ H2O+O2 2.891013 0.0 -4.97102 5.8611013 0.24 6.908104 - 72.83 11 H2+M ⇌ H●+H●+M 4.5771019 -1.4 1.044105 1.1461020 -1.68 8.2102 106.33 12 O+H2 ⇌ H●+●OH 3.821012 0.0 7.948103 2.667104 2.65 4.88103 1.97 13 ● OH+H2 ⇌ H●+H2O 2.16108 1.52 3.45103 2.298109 1.40 1.832104 - 15.4 14 H2O2+O2 ⇌ HO2●+HO2● 4.6341016 -0.35 5.067104 4.21014 0.0 1.198104 41.95 15 H2O2+M ⇌ ●OH+●OH+M 2.9511014 0.0 4.843104 1.01014 -0.37 0.0 52.13 16 H2O2+H● ⇌ H2O+●OH 2.4101013 0.0 3.97103 1.269108 1.31 7.141104 - 69.6 17 H2O2+H● ⇌ H2+HO2● 6.0251013 0.0 7.95103 1.0411011 0.70 2.395104 - 15.38 18 H2O2+O ⇌ ●OH+HO2● 9.550106 2.0 3.97103 8.66103 2.68 1.856104 - 13.42 19 H2O2+●OH ⇌ H2O+HO2● 1.01012 0.0 0.0 1.8381010 0.59 3.089104 - 30.78 20 O3+M ⇌ O2+O+M 2.481020 0 2.27104 - - - 26.14 21 O3+O ⇌ O2+O2 5.21018 0 4.157103 - - - - 94.77 22 O3+●OH ⇌ O2+ HO2● 7.81017 0 1.9103 - - - - 39.46 23 O3+HO2● ⇌ O2+O2+●OH 11017 0 2.8103 - - - - 29.17 24 H●+O3 ⇌ HO2●+O 91018 0.5 3.99103 - - - 32.45 25 H●+O3 ⇌ ●OH+O2 1.61019 0 0 - - - - 23.01 © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 635
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Insight into the role of dissolution mechanism… In this work, the main improvements of our where, λL and L are the thermal conductivity of previous model are given as follows: For the water and the latent heat of vaporization, calculation of the interfacial bubble temperature respectively. The mathematical formula of λL is (Tint), energy balance at the interface is obtained given in Ref. [51] as a function of TL (liquid through the continuity of energy flux at the bubble temperature) and PL (liquid pressure) in the range wall: 273.15 K < TL< 623 K and Psat < PL < 50 MPa. The 𝜕𝑇 𝜆 𝐿 𝑙| 𝜕𝑇 = 𝜆𝑔 | + ̇ 𝑚 L (Eq. 16) latent heat of evaporation of water (L) is given by 𝜕𝑟 𝑟=𝑅 𝜕𝑟 𝑟=𝑅 𝑀 𝐻2 𝑂 Ref. [52]: 0.358 𝑗 9 𝐿 ( ) = 2.44281 × 10−5 (673.43 − (𝑇 − 273.15)) (Eq. 17) 𝐾𝑔 5 According to Eq. 16, for the calculation of the water are calculated as functions of liquid interfacial temperature (Tint), two gradients of temperature and pressure, whereas the surface temperature are assumed on both sides of the bubble tension and the saturated vapour pressure of water wall, therefore, at the inner thermal layer 𝛿g (table are calculated as functions of liquid temperature as 1), the temperature changes linearly from T (internal in Ref. [52]. The density and the heat capacity of temperature of the bubble) to Tint (interfacial liquid water are obtained from Ref. [53]. temperature). Within the outside thermal layer (𝛿L ) It should be noticed here that due to the of the bubble, the temperature changes linearly from consideration of the interfacial bubble temperature, Tint to T∞ (the ambient temperature of liquid). As a the equations of mass transfer (evaporation and result, the temperature gradient on the outside layer condensation of water) and heat exchange (Eqs. 5 𝜕𝑇 (𝑇 −𝑇 ) and 6 in table 1) are estimated as functions of the of bubble wall is given as: 𝜕𝑟 𝑙 = ∞ 𝛿 𝑖𝑛𝑡 . As in the L interfacial temperature (Tint). In addition, in the case of the inside thermal layer (table 1), 𝛿L is present paper, the thermal conductivity of the gas estimated by considering the time scale of bubble (inside the bubble) is evaluated through its R 𝑅𝜒 dependency on the temperature and the density of motion: 𝛿L =min { π ,√ Ṙ 𝐿 }, with the thermal gas and vapor mixture (Eq. 8 of table 1). On the diffusivity 𝜒 𝐿 = 𝜆 𝐿 /(𝜌 𝐿 𝐶𝑝 𝐿 ). In the present paper, other hand, the accommodation coefficient of Eq. 5 [54] the thermal conductivity, and the viscosity of liquid is calculated as follows : 𝛼 = 0.35 𝑖𝑓 𝑇𝑖𝑛𝑡 < 350𝐾, 𝛼 = 0.35 − 0.05𝑘 − 0.05𝑘 + 0.025𝑘 (3) 𝑖𝑓 350 ≤ 𝑇𝑖𝑛𝑡 ≤ 500 𝐾, (1) (2) 0.05 (Eq. 18) 𝛼= (𝑇 𝑐 − 500) 𝑖𝑓 500𝐾 ≤ 𝑇𝑖𝑛𝑡 ≤ 𝑇 𝑐 , 𝑇 𝑐 −500 { 𝛼 = 0.0 𝑖𝑓 𝑇 ≥ 𝑇 𝑐 , 𝑇 𝑖𝑛𝑡 with 𝑘 (𝑚) = 𝑘(𝑘 − 1) … . [𝑘 − (𝑚 − 1)], and 𝑘 = 50 − 70. Finally, the rate of dissolution (rd,i) of chemical 3.1. Dissolution mechanism for one acoustic cycle products into the surrounding liquid from the interior of the bubble is calculated using the uptake First and foremost, to illustrate the importance of the coefficient (Θ)[39]: dissolution mechanism, the evolution of hydroxyl radicals was investigated at a frequency of 213 kHz, 𝑇𝑘 𝑏 𝑛𝑖 𝑟 𝑑𝑖 = Θ√  4R2 (Eq. 19) where the dissolution rate, the molar yield and the 2 𝑚 𝑖 𝑉 migrated amount of hydroxyl radicals outside the where i denotes the chemical species (i = ●OH, H●, bubble are followed for a period of 1.29 µs of the H2, HO2●, …). kb is the Boltzmann constant, and T is bubble’s lifetime (figure 1(a)). The variation of the the temperature inside the bubble. The uptake bubble radius and temperature are shown in figure coefficient is assumed as Θ = 0.001.[39] mi is the 1(b). As it can be seen in figure 1(a), at the end of molecular mass of the species, ni is the number of the compression phase of the bubble (t ~ 3.48 µs), moles inside a bubble, V is the bubble volume and R the molar production of ●OH radicals is rapidly is the bubble radius. increased up to around 1.3210-16 mol, then, this yield is drastically reduced with the decrease of 3. RESULTS AND DISCUSSION bubble temperature (lower than 5752 K, figure 1(b)) for t > 3.48 µs. On the other hand, the rapid increase © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 636
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Aissa Dehane et al. of ●OH formation is accompanied by an important bouncing bubble into the surrounding water is increase in the dissolution rate (outside the bubble) mainly due to the high inner pressure of the bubble of this species with a maximum value of 2.9810-10 during the collapse phase in addition to the molar mol/µs at 3.48 µs. This means that 4.6810-19 mol of concentration of each substance. As a result, over hydroxyl radicals is dissolved in the surrounding the rapid compression phase, the combustion liquid during a period of 3.48 µs (until the end of the products (●OH, ●HO2, H2O2, ●H, etc.) generated compression phase). It is worth mentioning that the inside the bubble are forced to be migrated outside dissolution process of the different species from the the bubble toward the surrounding liquid. Figure 1: Temporal evolution of (a) dissolution rate, integral of ●OH flux and the molar yield of hydroxyl radicals, and (b) the bubble temperature and instantaneous radius, for one acoustic cycle (Conditions: frequency = 213 kHz, In = 1 W/cm², R0 = 3.9 µm, Tliq = 20°C, Psta = 1 atm) Even though only ~0.35% of ●OH radicals could be analyzed in terms of the whole bubble’s (4.6810-19 mol) is dissolved in only 3.48 µs (from population, therefore, even when the dissolved the beginning of bubble oscillation to the end of the amount for a single bubble is low, the synergy of compression phase, figure 1(a)), this quantity is millions of acoustic cavities substantially enhances considered important with respect to the overall the effect of this mechanism (dissolution) on the production of a single bubble. Furthermore, as it will overall chemistry of the sonicated solution. be seen later, the effect of the dissolution process However, due to the bubble-bubble coalescence, the could be intensified with the variation of the dissolved amount of the different species may be operating conditions, thus, the chemistry of bubble is affected, which complicates the chemistry of the substantially affected by this mechanism. It is worth irradiated solution. The weightiness of the mentioning that the impact of the dissolution process dissolution mechanism (in a sonochemical process) © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 637
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Insight into the role of dissolution mechanism… is clearly asserted according to the obtained results radicals (4.4710-19 mol) and that of Yasui et al. for one acoustic cycle (4.69 µs, figure 1(a)). As can (1.09510-18 mol) is obviously ascribed to the lower be seen at 4.69 µs, the dissolved amount of hydroxyl ultrasound frequency used by Yasui’s group (52 radicals is 4.4710-19 mol compared to the formed kHz); therefore, more time is available for hydroxyl quantity of 4.2510-19 mol. This means that 51.26% radicals to be dissolved outside the bubble. of hydroxyl radicals (compared to the total yield of For more clarification of the impact of the ● OH for one cycle) is dissolved in the bulk liquid for dissolution process, the chemistry of the bubble, in one acoustic cycle at 213 kHz. A similar trend was terms of dissolved quantity, inner production and retrieved by Yasui et al.[39] under the experimental total yield of the different species, is visualized conditions of Didenko and Suslick[55] for SBSL during one acoustic cycle (including the first bubble in a steady state (52 kHz, 1.52 bars and 3°C) collapse) over a frequency range from 140 to 515 for one cycle, where 1.09510-18 mol is dissolved kHz for a fixed acoustic intensity of In = 1 W/cm². during one acoustic cycle (i.e. 19.2 µs). The The obtained results were depicted in figures 2(a)- discrepancy between our dissolved amount of ●OH (d). © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 638
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Aissa Dehane et al. Figure 2: The effect of ultrasound frequency (140, 213, 355, and 515 kHz) on the dissolved amount, internal production and the total yield of the different species (●OH, H, O, HO2●, H2O2, H2, O2, and O3) during (a) the compression phase and (c) one acoustic cycle. Percentages of the dissolved quantity (compared to the total production) of the different species are shown in (b) for the collapse phase, and in (d) for one acoustic cycle (conditions: In = 1 W/cm², R0 = 5.0 µm at 140 kHz, 3.9 µm at 213 kHz, 3.2 µm at 355 kHz and 3.0 µm at 515 kHz, Tliq = 20°C, Psta = 1 atm). The selected R0 values are typical ambient bubble radii (means) of the population of active bubbles at each frequency At first sight, from Figs. 2 (a) and 2(c), it is retrieved at 140 and 213 kHz. However, with the observed that the dissolution, the inner formation increase of the applied wave frequency (greater than and the total production of the different species are 213 kHz), the number and the amount of the increased with the decrease of ultrasound frequency dissolved substances are drastically decreased until (from 515 to 140 kHz). This tendency is largely it is nullified at 515 kHz (figure 2(a)). Over the first observed in many experimental and theoretical collapse (figure 2(a)), at 140 and 213 kHz, the works.[16,56–59] These outcomes are ascribed to dissolution capacity is in the order: H2 > H● > O > ● theincrease of bubble lifetime with the reduction of OH > O2. However, at 355 kHz, the dissolution of the wave frequency; therefore, more water vapour is the main substances is in the order: H● > ●OH > H2. encapsulated within the oscillating bubble at the end For example, at 140 kHz (213 kHz), the migrated of the expansion phase. Consequently, at the end of amounts of ●OH, O, H●, H2 and O2 outside the the implosion regime, harsh collapses are retrieved bubble during the first collapse are 4.6810-19 under these circumstances (low frequencies), thus, (1.9110-19), 1.810-18 (2.7510-19), 4.4110-18 huge amounts of chemical species are produced (7.7610-19), 4.8610-18 (9.4410-19) and 8.4310-20 (within the acoustic cavitation bubble) with the (2.110-20) mol, respectively. In contrast, at 355 dissolution of important quantities of these kHz, the dissolved quantities are reduced to substances in the surrounding liquid. It should be 5.1310-21, 1.1610-20 and 3.5910-21 mol, noted that some exceptions are retrieved for some respectively for ●OH, H● and H2 (figure 2(a)). cases, where the maximum yield of ●OH, H2O2, O3, Despite the important quantities dissolved during the O2 at the end of bubble collapse is obtained at 213 first collapse of the bubble (figure 2(a)), the findings kHz, whereas this maximum is shifted toward 355 of figure 2(b) show that these amounts are of very kHz for ●OH and H2O2 over one acoustic cycle (2.81 low percentages (< 3%) compared to their total µs, figures 2(a) and 2(c)). These findings are in good production within the acoustic cavitation bubble. agreement with the different works indicating a The analysis of figure 2(c) indicates that over one maximum yield of oxidants at around 300 kHz in a acoustic, the dissolution of the different species multibubble system.[38,60–62] On the other hand, (●OH, O, H●, H2 and O2) is remarkably increased according to figure 2(a), it can be observed that with the migration (outside the bubble) of relatively significant amounts of ●OH, O, H, H2, and O2 lower amounts of O3 and HO2● at 140 and 213 kHz. molecules are dissolved into the bulk liquid during As it can be seen in figure 2(c), the dissolved the first collapse of a single bubble. This is clearly quantity of O, H● and H2 is at around 110-16 mol at © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 639
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Insight into the role of dissolution mechanism… 140 kHz, compared to approximately 110-18 mol cycles etc.) the higher number of dissolved species for ●OH, H● and H2 at 355 kHz. In contrast, (more time is available for species migration). This 8.1110-22 mol of H● atoms is dissolved at 515 kHz. process is intensified especially at lower ultrasound Similarly, to the case of the first collapse (figure frequencies with the improvement of bubbles 2(a)), at 140 and 213 kHz, the dissolution of the collapse. various species for one acoustic cycle (figure 2(c)) is in the order: H2 > H● > O > O2 > ●OH > O3 > HO2●, 3.2. Dissolution mechanism for multiple acoustic whereas this order at 355 kHz is given as: H2 > ●OH cycles > H● > O > O2 (figure 2(c)). The importance of the dissolution mechanism is clearly asserted In this section, the investigation of the dissolution accordingly to Fig. 2(d) for one acoustic cycle, process is extended for multiple acoustic cycles (3 where significant percentages are observed periods), where the results are shown in figures 3 especially for ●OH, H●, H2 and HO2● for wave (a)-(c). First, as it is shown in figure 3(b), the molar frequencies of 140, 213 and 355 kHz. It is obvious yield of all species is improved with the decrease of that the longer the bubble lifetime (one, two, three ultrasound frequency (from 515 to 140 kHz) as it Figure 3: Variation of (a) the dissolved amount (in mol), (b) the internal production (total- dissolved) and (c) the percentage of the dissolved quantity of the different species (●OH, H●, O, HO2●, H2O2, H2, O2, and O3) as functions of the wave frequency (140, 213, 355 and 515 kHz) for three acoustic cycles (conditions: In = 1 W/cm², R0 = 5.0 µm at 140 kHz, 3.9 µm at 213 kHz, 3.2 µm at 355 kHz and 3.0 µm at 515 kHz, Tliq = 20°C, Psta = 1 atm). The selected R0 values are typical ambient bubble radii (means) of the population of active bubbles at each frequency © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 640
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Aissa Dehane et al. was indicated previously for the case one acoustic seen that especially for the main dissolving species cycle. On the other hand, this molar production (of (H2, H●, O, ●OH and O2), the inner production (i.e. all substances) is either stabilized, decreased or total yield minus the dissolved amount) may be increased over the three acoustic cycles (figure 3 exceeded by the dissolved amount, particularly with (b)). This is evidently governed by the developed the increase of the number of acoustic cycles (>one temperature inside the oscillating bubble as it is cycle) and the decrease of ultrasound frequency. depicted in figures 4(a)-(d). Additionally, the According to these findings, the importance of the generation of different species (inside the bubble) is dissolution mechanism is clearly evidenced either also affected by the concentration of the various with the decrease in wave frequency or with the substances over the compression period. Moreover, increase in the bubble’s lifespan (i.e. increase in it is worth mentioning that the yield of HO2● and number of cycles). H2O2 is hardly increased either with the decrease of Finally, despite the dependence of the dissolved wave frequency or with the rise of acoustic cycles’ amount’s percentage on the total production of each number (figure 3(b)). On the other side, relatively species, figure 3(c) shows again the significance of greater amounts of O3 (compared to those of HO2● the dissolution process in the bubble chemistry and H2O2) are formed at the different conditions of especially with the decrease of ultrasound frequency ultrasound frequency and number of acoustic cycles, or with the rise of acoustic cycles (> 1 cycle). To (figure 3(b)). According to figure 3(a), the amount illustrate, at 355 kHz, the dissolved amount (in %) of of the dissolving species is monotonically increased hydroxyl radicals goes up from 8.13 (one cycle) to with the rise of the bubble’s lifespan (1, 2 and 3 38.50% (over three cycles) of its total production. cycles). At 140 and 213 kHz, and independently of For the same species (●OH), this percentage is the number of acoustic cycles (1, 2 or 3 periods), the increased from 57.71 (one cycle) to 88.43% (for three cycles) at 140 kHz. In light of the above, the dissolved amount (in moles) of the different species inclusion of the dissolution mechanism into the is in the order: H2 > H● > O > O2 > ●OH > O3 > HO2● chemistry of acoustic bubble is of great significance > H2O2. Nevertheless, over 213 kHz (at 355 and because of its capability of improving our 515), this ranking starts to be disturbed with a clear understanding toward the chemistry inside or at the dominance of the main species, i.e. H2, H●, O, ●OH, interface of acoustic cavitation bubble and even in and O2 molecules, dissolved outside the bubble. the surrounding solution. Interestingly, according to Figs. 3(a)-(b), it can be Figure 4: Temporal evolution of bubble radius and temperature at the different ultrasound frequencies (140, 213, 355, and 515 kHz) for three acoustic cycles (conditions: In = 1 W/cm², R0 = 5.0 µm at 140 kHz, 3.9 µm at 213 kHz, 3.2 µm at 355 kHz and 3.0 µm at 515 kHz, Tliq = 20°C, Psta = 1 atm). The selected R0 values are typical ambient bubble radii (means) of the population of active bubbles at each frequency © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 641
25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Insight into the role of dissolution mechanism… 4. CONCLUSIONS Algeria and the General Directorate of Scientific Research and Technological Development (GD- Through the analysis of a single bubble SRTD) for their support in conducting the RFU sonochemistry and dynamics, the dissolution process project named “Développement, scale-up et during the oscillation of an acoustic cavitation intensification de procédés innovants d’oxydation et bubble (for one or multicycles) is investigated on a de réduction (POA/PRA) pour la destruction rapide range of wave frequency from 140 to 515 kHz (In = de micropolluants emergeants des effluents aqueux 1 W/cm²). First, it has been observed that the industriels”. dissolution, the inner production and the total yield (inside the bubble) of the different species are Funding. This work received financial support from monotonically increased with the decrease of wave The Ministry of Higher Education and Scientific frequency (from 140 to 515 kHz). Moreover, it was Research of Algeria (project code: observed that during the first collapse, at 140 and A16N01UN250320220002) and the General 213 kHz, significant amounts (from ~2.110-20 to Directorate of Scientific Research and 4.8610-18 mol) of ●OH, O, H●, H2, and O2 Technological Development (GD-SRTD). molecules are dissolved into the bulk liquid. However, with the rise of ultrasound frequency (> Competing interests. The authors declare no 213 kHz), the number and the quantity ( H● > O > manuscript itself. ● OH > O2. Nevertheless, at 355 kHz, the dissolution of the main substances is in the order: H● > ●OH > REFERENCES H2. Despite the low dissolution percentages of the different species (compared to the total yield) during 1. K. S. Suslick, Y. Didenko, M. M. Fang, T. Hyeon, K. the first bubble collapse (< 3%), it has been J. Kolbeck, W. B. McNamara III, M. M. Mdleleni, M. Wong. 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25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202300115 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 Vietnam Journal of Chemistry Aissa Dehane et al. Nomenclature Af (Ar) Pre-exponential factor of the forward (reverse) reaction, [(cm3 mol-1 s-1) for two body reaction and (cm6 mol-2 s-1) for three body reaction]. bf (br) Temperature exponent of the forward (reverse) reaction. c Speed of sound in the liquid medium (m s-1). Cp Heat capacity concentration inside the bubble (J/m3 K). Eaf (Ear) Activation energy of the forward (reverse) reaction (cal mol-1). f Frequency of ultrasonic wave (Hz). Ia Acoustic intensity of ultrasonic irradiation (W m-2). kf (kr) Forward (reverse) reaction constant, [(cm3 mol-1 s-1) for two body reaction and (cm6 mol-2 s-1) for three body reaction]. MH2O Molar mass of water (Kg/mol). • m Evaporation-condensation rate of water (Kg/m² s). n Molar amount (mol). p Pressure inside a bubble (Pa). pmax Maximum pressure inside a bubble (Pa). p∞ Ambient static pressure (Pa). PA Amplitude of the acoustic pressure (Pa). Pv Vapor pressure of water (Pa). PB Liquid pressure on the external side of the bubble wall. (Pa). Q Energy transferred by heat exchange (J/s). R Radius of the bubble (m). Rmax Maximum radius of the bubble (m). R0 Ambient bubble radius (m). Rg Ideal gas constant (J/mol K). t Time (s). T Temperature inside a bubble (K). Tmax Maximum temperature inside a bubble (K). T∞ Bulk liquid temperature (K). V Volume of the bubble (m3). x Thermal diffusivity inside the bubble (m²/s). Greek letters α Accommodation coefficient. mix Thermal conductivity of the mixture (W m-1 K). i Thermal conductivity of species i (W m-1 K). µ Dynamic viscosity (Pa s). υki Stoichiometric coefficient of the kth chemical species in the ith reaction. l Density of liquid water (kg m-3). g Density inside the bubble (kg m-3). H2O Density of water vapor inside the bubble (Kg/m3). sat,H2O Saturated vapor density (Kg/m3).  Surface tension of liquid water (N m-1). • Uk Production rate of the kth species (mol/s m3). © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH www.vjc.wiley-vch.de 645