Multibubble Sonoluminescence from a Theoretical Perspective

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Review Multibubble Sonoluminescence from a Theoretical Perspective

Kyuichi Yasui

National Institute of Advanced Industrial Science and Technology (AIST), Nagoya 463-8560, Japan; [email protected]

Abstract: In the present review, complexity in multibubble sonoluminescence (MBSL) is discussed. At relatively low ultrasonic frequency, a cavitation bubble is ﬁlled mostly with water vapor at relatively high acoustic amplitude which results in OH-line emission by chemiluminescence as well as emissions from weakly ionized plasma formed inside a bubble at the end of the violent bubble collapse. At relatively high ultrasonic frequency or at relatively low acoustic amplitude at relatively low ultrasonic frequency, a cavitation bubble is mostly ﬁlled with noncondensable gases such as air or argon at the end of the bubble collapse, which results in relatively high bubble temperature and light emissions from plasma formed inside a bubble. Ionization potential lowering for atoms and molecules occurs due to the extremely high density inside a bubble at the end of the violent bubble collapse, which is one of the main reasons for the plasma formation inside a bubble in addition to the high bubble temperature due to quasi-adiabatic compression of a bubble, where “quasi” means that appreciable thermal conduction takes place between the heated interior of a bubble and the surrounding liquid. Due to bubble–bubble interaction, liquid droplets enter bubbles at the bubble collapse, which results in sodium-line emission.

Keywords: vaporous bubble; gaseous bubble; OH chemiluminescence; plasma; ionization potential lowering; Na-line emission; bubble–bubble interaction; acoustic ﬁeld; sulfuric acid; applications

Citation: Yasui, K. Multibubble Sonoluminescence from a Theoretical Perspective. Molecules 2021, 26, 4624. 1. Introduction https://doi.org/10.3390/ Multibubble sonoluminescence (MBSL) is the light emission phenomenon from cavi- molecules26154624 tation bubbles in liquid irradiated by strong ultrasound (Figure1)[ 1–3]. Cavitation is the appearance of bubbles in liquid by strong decrease in local instantaneous pressure by strong Academic Editor: Gregory Chatel ultrasound or by some hydrodynamic motion such as that around a ship propeller [4]. In cavitation, a bubble collapses very violently after bubble expansion under some conditions. Received: 21 June 2021 There are two reasons for the violent bubble collapse [5]. One is the spherical geometry of a Accepted: 28 July 2021 Published: 30 July 2021 bubble collapse. According to the continuity of the liquid, the speed of the bubble collapse increases as the bubble radius decreases because the surface area of a bubble decreases.

Publisher’s Note: MDPI stays neutral The other is the inertia of the surrounding liquid. Due to the inertia of the ingoing liquid, with regard to jurisdictional claims in the bubble collapse becomes very violent. The violent bubble collapse is called Rayleigh published maps and institutional afﬁl- collapse [5,6]. iations. At the end of the violent bubble collapse, temperature and pressure inside a bubble signiﬁcantly increase to more than 4000 K and 300 bar (1 bar = 105 Pa = 0.987 atm), respectively [7,8], due to quasi-adiabatic compression of a bubble, where “quasi-“ means the appreciable amount of thermal conduction takes place between the heated interior of a bubble and the surrounding liquid. As a result, water vapor inside a bubble is thermally Copyright: © 2021 by the author. Licensee MDPI, Basel, Switzerland. dissociated and OH radicals are formed, which is called sonochemical reactions [5,9]. This article is an open access article Furthermore, faint light of sonoluminescence (SL) is emitted from a bubble. Duration of distributed under the terms and high temperature and pressure inside a bubble is only less than 1–10 ns. Thus, the SL pulse conditions of the Creative Commons width from a bubble is less than 1 ns [1,6,10]. Attribution (CC BY) license (https:// MBSL was discovered in 1933 by Marinesco and Trillat [11] who observed the fog- creativecommons.org/licenses/by/ ging of the photographic plate immersed in the liquid irradiated by ultrasound. MBSL 4.0/). was recognized as the light emission from the cavitating liquid in 1934 by Frenzel and

Molecules 2021, 26, 4624. https://doi.org/10.3390/molecules26154624 https://www.mdpi.com/journal/molecules Molecules 2021, 26, x FOR PEER REVIEW 2 of 36

was recognized as the light emission from the cavitating liquid in 1934 by Frenzel and Schultes [12]. Significant development in SL research has been brought about after the discovery of single-bubble sonoluminescence (SBSL) in 1990 by Gaitan and Crum [13] (The first report on SBSL was in 1962 by Yosioka and Omura [14]. However, the work was Molecules 2021, 26, 4624 2 of 34 not confirmed.) SBSL is SL from a stably pulsating bubble trapped at pressure antinode of a standing ultrasonic wave [1,2,6]. In 1991, Barber and Putterman [15] reported in Nature that SBSL pulse width is less than 100 ps, which attracted many researchers’ attention. SchultesAfter that, [12 there]. Significant has been developmentsignificant development in SL research in SL has research. been brought Before the about discovery after the of discoverySBSL in 1990, of single-bubble MBSL, which sonoluminescence was simply called (SBSL) SL, had in been 1990 considered by Gaitan and to originate Crum [13 mainly] (The firstin the report recombination on SBSL was of infree 1962 radicals by Yosioka insideand a bubble Omura [16]. [14 ].The However, development the work of the was SBSL not confirmed.)research has SBSL been isreviewed SL from by astably Brenner, pulsating Hilgenfeldt, bubble and trapped Lohse at[6]. pressure antinode of a standingAnother ultrasonic significant wave finding [1,2,6]. in In 1991,SL research Barber is and the Putterman evidence of [15 (thermal)] reported plasma in Nature for- thatmation SBSL inside pulse a bubble width in is lesssulfuric than acid 100 in ps, optical which spectra attracted of SBSL many by researchers’Flannigan and attention. Suslick Afterin 2005 that, [17]. there has been significant development in SL research. Before the discovery of SBSLIn in the 1990, present MBSL, review, which wascomplexity simply calledin MBSL SL, is had discussed been considered based onto the originate understanding mainly indeveloped the recombination after the discovery of free radicals of SBSL. inside Furthermore, a bubble unsolved [16]. The problems development in MBSL of the are SBSL also researchdiscussed. has been reviewed by Brenner, Hilgenfeldt, and Lohse [6].

FigureFigure 1. PhotographicPhotographic image image of of MBSL MBSL from from Ar-saturated Ar-saturated SDS SDS solution solution at an at anacoustic acoustic power power of 4 ofW [3]. Ultrasound at a frequency of 148 kHz was irradiated from the bottom of the beaker. Copyright 4 W [3]. Ultrasound at a frequency of 148 kHz was irradiated from the bottom of the beaker. Copyright 2015, with the permission from Elsevier. 2015, with the permission from Elsevier.

2. TheoreticalAnother significant Model finding in SL research is the evidence of (thermal) plasma formation insideFirstly, a bubblemodel of in bubble sulfuric dynamics acid in optical developed spectra in of studies SBSL by of FlanniganSBSL is reviewed. and Suslick Some in 2005bubbles [17]. in MBSL are nearly isolated and spherical, which are similar to SBSL bubbles [18]. Furthermore,In the present bubble review, dynamics complexity model developed in MBSL is for discussed SBSL can based be modified on the understanding for MBSL bub- developedbles taking afterinto account the discovery the effect of of SBSL. bubble–bubble Furthermore, interaction unsolved [19]. problems in MBSL are also discussed.There are two types in models of bubble dynamics for SBSL [2]. One is the shock wave model that a spherical shock wave converges at the bubble center where extremely 2.high Theoretical temperature Model plasma is formed. The other is the hot-spot model that nearly the whole bubbleFirstly, is heated model by of quasi-ad bubbleiabatic dynamics compression, developed where in studies ‘quasi-‘ of SBSL means is appreciable reviewed. Some ther- bubblesmal conduction in MBSL takes are nearly place isolatedbetween and the spherical,heated bubble which interior are similar and tothe SBSL surrounding bubbles [ 18liq-]. Furthermore,uid. bubble dynamics model developed for SBSL can be modified for MBSL bubblesNumerical taking into simulations account theof bubble effect ofcollapse bubble–bubble by fundamental interaction equations [19]. of fluid dynamics haveThere revealed are two that types temperature in models and of pressure bubble dynamics are nearly for spatially SBSL [uniform2]. One inside is the shocka bub- waveble and model that there that a is spherical no shock shock wave waveformatio convergesn inside ata bubble the bubble under center many where conditions extremely [20]. highThe reason temperature for no plasma shock formation is formed. is The as otherfollows is the[21]. hot-spot As the temperature model that nearly near the the bubble whole bubblewall is islower heated than by quasi-adiabaticthat near the bubble compression, center wheredue to ‘quasi-‘ thermal means conduction appreciable between thermal the conductionheated interior takes of place a bubble between and the the heated surrounding bubble interiorliquid, sound and the speed surrounding is lower liquid. near the bubbleNumerical wall. For simulations the shock wave of bubble formation, collapse a by pressure fundamental wave equationsradiated inwardly of fluid dynamics from the havebubble revealed wall should that temperature overtake previously and pressure radiated are nearly pressure spatially waves uniform which insidemove awith bubble the and that there is no shock wave formation inside a bubble under many conditions [20]. The reason for no shock formation is as follows [21]. As the temperature near the bubble wall is lower than that near the bubble center due to thermal conduction between the heated

interior of a bubble and the surrounding liquid, sound speed is lower near the bubble wall. For the shock wave formation, a pressure wave radiated inwardly from the bubble wall should overtake previously radiated pressure waves which move with the sound speed plus radial ﬂuid (gas) velocity. Typical bubble collapse is not so violent to overcome the Molecules 2021, 26, x FOR PEER REVIEW 3 of 36

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sound speed plus radial fluid (gas) velocity. Typical bubble collapse is not so violent to overcome the adverse gradient of sound speed for the shock formation. Thus, no shock adverse gradient of sound speed for the shock formation. Thus, no shock wave is formed wave is formed inside a collapsing bubble under many conditions. inside a collapsing bubble under many conditions. Thus, in the present review, the hot-spot model is discussed (Figure 2) [5,22–26]. Thus, in the present review, the hot-spot model is discussed (Figure2)[ 5,22–26]. Temperature is assumed to be spatially uniform inside a bubble except at the thermal Temperature is assumed to be spatially uniform inside a bubble except at the thermal boundary layer near the bubble wall. Thermal conduction takes place both inside and boundary layer near the bubble wall. Thermal conduction takes place both inside and outside a bubble. Non-equilibrium evaporation and condensation of water vapor takes outside a bubble. Non-equilibrium evaporation and condensation of water vapor takes placeplace at at the the bubble bubble wall. wall.

Figure 2. The model of bubble dynamics [22]. Copyright 2004, with the permission from Elsevier. Figure 2. The model of bubble dynamics [22]. Copyright 2004, with the permission from Elsevier. The radius-time curve of a bubble in liquid irradiated with ultrasound is numerically calculated by the Keller equation [5]. The radius-time curve of a bubble in liquid irradiated with ultrasound is numerically calculated . by! the Keller equation. [5].! . ! .. . R 3 2 R 1 R R dpB 1 − RR + 𝑅 R 1 −3 =𝑅 1 1 + 𝑅 [pB − ps(t) − p∞𝑅] +𝑑𝑝 (1) c c c c dt ∞ 1 − 2 𝑅𝑅+ 𝑅3 1∞ − =ρL,∞ 1 + ∞ 𝑝 −𝑝𝑡 −𝑝 + ∞ ρL,∞ (1) 𝑐 2 3𝑐 𝜌, 𝑐 𝑐𝜌, 𝑑𝑡

wherewhere RR isis bubble bubble radius, radius, do dott denotes the timetime derivativederivative (d/dt),(d/dt), c𝑐∞ is is the the sound sound speed speed in inthe the liquid liquid far far from from a bubble,a bubble,ρL ,∞𝜌,is the is the liquid liquid density density far fromfar from a bubble, a bubble,pB is 𝑝 the is liquid the p (t) liquidpressure pressure on the on external the external side of side the bubbleof the bubble wall, wall,s is 𝑝 a nonconstant𝑡 is a nonconstant ambient ambient pressure component such as a sound ﬁeld (p (t) = −A sin ωt, where A is the acoustic amplitude pressure component such as a sound fields (𝑝𝑡 =−𝐴sin𝜔𝑡, where 𝐴 is the acoustic am- and ω is angular frequency of ultrasound), and p is the undisturbed pressure. The method plitude and 𝜔 is angular frequency of ultrasound),∞ and 𝑝 is the undisturbed pressure. Theof numericalmethod of simulations numerical simulati is simplyons as is follows simply [ 5as]. follows [5]. . R𝑅(t𝑡+∆𝑡+ ∆t)==𝑅R(t𝑡)++𝑅R(t𝑡)∆∆𝑡t (2)(2) .𝑅 𝑡+∆𝑡 =𝑅. 𝑡 +𝑅.. 𝑡∆𝑡 (3) R(t + ∆t) = R(t) + R(t)∆t (3) where 𝑅.. 𝑡 in Equation (3) is calculated by Equation (1). whereIn theR(t )hot-spotin Equation model (3) [5,23–26], is calculated the by following Equation effects (1). are taken into account; non- equilibriumIn the chemical hot-spot reactions model [5 ,inside23–26 ],a bubble, the following variation effects of liquid are takentemperature into account; at the bub- non- bleequilibrium wall, dependence chemical of reactionsphysical quantities inside a bubble, such as variationsaturated ofvapor liquid pressure, temperature surface at ten- the sion,bubble etc. wall, on liquid dependence temperature of physical at the quantitiesbubble wall, such thermal as saturated ionization vapor of pressure, molecules surface and atomstension, inside etc. a on bubble liquid including temperature the effect at the of bubble ionization wall, thermalpotential ionization lowering ofdue molecules to high density,and atoms and insidelight emissions a bubble includinginside a bubble the effect including of ionization chemiluminescence potential lowering of OH, due elec- to tron-atomhigh density, and andelectron-ion light emissions bremsstrahlung, inside a bubble radiative including recombination chemiluminescence of electrons of and OH, electron-atom and electron-ion bremsstrahlung, radiative recombination of electrons and ions, radiative attachment of electrons to neutral atoms, etc. ions, radiative attachment of electrons to neutral atoms, etc. An example of calculated radius-time curve of a SBSL bubble is shown in Figure 3 An example of calculated radius-time curve of a SBSL bubble is shown in [27]. A bubble expands during the rarefaction phase of ultrasound. At the compression Figure3[ 27]. A bubble expands during the rarefaction phase of ultrasound. At the phase of ultrasound, a bubble collapses violently, which is followed by bouncing motion. compression phase of ultrasound, a bubble collapses violently, which is followed by bounc- The numbers of molecules inside a bubble are shown as a function of time in Figure 4 [27]. ing motion. The numbers of molecules inside a bubble are shown as a function of time In SBSL, nitrogen in an initially air bubble is burned and changes to NOx and HNOx which in Figure4[ 27]. In SBSL, nitrogen in an initially air bubble is burned and changes to gradually dissolve into the surrounding liquid water [28,29]. As a result, the bubble NOx and HNOx which gradually dissolve into the surrounding liquid water [28,29]. As

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content becomes mainly argon (1% of air is argon), which is called argon rectification hy- contentpothesis.a result, becomes The the bubbleargon mainly rectification content argon becomes (1% hypothesis of air mainly is argon), has argon been which (1%validated is of called air isboth argon),argon experimentally rectification which is called andhy- pothesis.theoreticallyargon rectiﬁcation The [6].argon Thus, hypothesis.rectification the calculated The hypothesis argon results rectiﬁcation hasin Figures been validated hypothesis3–7 for SBSL both has are experimentally been for an validated argon bub-and both theoreticallyble.experimentally [6]. Thus, and theoretically the calculated [6]. results Thus, in the Figures calculated 3–7 for results SBSL in are Figures for an3 –argon7 for SBSLbub- ble.are for an argon bubble.

. . FigureFigure 3. 3. TheThe calculated calculated radius-time radius-time curve curve of of an an argon argon bubble bubble in in water water for for one one acoustic acoustic cycle cycle when when Figure 3. The calculated radius-time curve of an argon bubble in water for one acoustic cycle when thethe frequency frequency and and the the amplitude amplitude of ultrasound areare 2222 kHzkHz andand 1.321.32 bar, bar, respectively respectively and and the the ambient ambi- the frequency and the amplitude of ultrasound are 22 kHz and 1.32 bar, respectively and the ambient bubble radius isµ 4 μm [27]. Copyright 2002, with the permission of AIP Publishing. entbubble bubble radius radius is 4is 4m μm [27 [27].]. Copyright Copyright 2002, 2002, with with the the permission permission of of AIP AIP Publishing. Publishing.

Figure 4. The numbers of molecules inside a bubble asa function of time for one acoustic cycle Figurein water 4. The (a) andnumbers in aqueous of molecules methanol inside solution a bubble (b)[ as27 a]. function Copyright of time 2002, for with one the acoustic permission cycle in of Figurewater (4.a) Theand numbers in aqueous of moleculesmethanol solutioninside a bubble(b) [27]. as Copyright a function 2002, of time with for the one permission acoustic cycle of AIP in AIP Publishing. waterPublishing. (a) and in aqueous methanol solution (b) [27]. Copyright 2002, with the permission of AIP Publishing.

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Figure 5. The calculated results at around the minimu m bubble radius for aqueous methanol solu- tionFigure [27]. 5. TheThe condition calculated is resultsthe same ataround as that theof Figure minimum 3. (a bubble) The bubble radius forradius aqueous and methanolthe temperature insideFiguresolution a 5.bubble. [ 27The]. The calculated (b condition) The numbers results is the same at of around molecules as that ofthe Figure insideminimu3.( a abubblem) The bubble bubble with radius radiuslogarithmic for and aqueous the vertical temperature methanol axis. Copy- solu- righttioninside 2002,[27]. a bubble.The with condition the (b permis) The is numbers sionthe sameof AIP of as molecules Publishing. that of Figure inside a3. bubble(a) The with bubble logarithmic radius and vertical the temperature axis. insideCopyright a bubble. 2002, with(b) The the permissionnumbers of of molecules AIP Publishing. inside a bubble with logarithmic vertical axis. Copy- right 2002, with the permission of AIP Publishing.

Figure 6. The energy of the emitted light per bubble collapse and the bubble temperature at the Figure 6. The energy of the emitted light per bubble collapse and the bubble temperature at the collapse as a function of the equilibrium surface concentration of methanol (Seq)[27]. The experi- collapse as a function of the equilibrium surface concentration of methanol (Seq) [27]. The experimental data of the relative sonoluminescence intensity are also shown [30]. Copyright 2002, with the mentalFigure data6. The of energythe relative of the so emittednoluminescence light per intensity bubble collapseare also andshown the [30].bubble Copyright temperature 2002, atwith the permission of AIP Publishing. thecollapse permission as a function of AIP Publishing. of the equilibrium surface concentration of methanol (Seq) [27]. The experimental data of the relative sonoluminescence intensity are also shown [30]. Copyright 2002, with the permission of AIP Publishing.

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(a) (b)

Figure 7. The calculated results under the condition of single bubble sonochemistry [24]. A SBSL bubble with R0 = 3.6 μm Figure 7. The calculated results under the condition of single bubble sonochemistry [24]. A SBSL bubble with R0 = 3.6 µm in ina steady a steady state state in inwater water at at3 °C 3 ◦ isC irradiated is irradiated by byan anultrasonic ultrasonic wave wave of of52 52kHz kHz and and 1.52 1.52 bar. bar. (a) ( aThe) The bubble bubble radius radius (b) ( bThe) The dissolution rate of OH radicals into the liquid from the interior of the bubble (solid line) and its time integral (dotted line). dissolution rate of OH radicals into the liquid from the interior of the bubble (solid line) and its time integral (dotted line). Copyright 2005. with the permission of AIP Publishing. Copyright 2005. with the permission of AIP Publishing.

3. VaporousAs seen and in Gaseous Figure4, duringBubbles the bubble expansion, intense evaporation of water vapor intoWhen the bubblethe bubble takes content place. is Asmostly a result, water near vapor the even maximum at the end bubble of the radius, bubble thecollapse, bubble suchcontent bubbles is mostlyare called water vaporous vapor. bubbles During [33]. the bubbleOn the collapse,other hand, on when the other the bubble hand, intense con- tentcondensation at the end of of the water bubble vapor collapse occurs is noncondensable at the bubble wall. gas Assuch a result,as air, thesuch bubble bubbles content are calledis mostly gaseous argon bubbles near the[33]. end In this of the section, violent difference bubble collapse. in mechanism In Figure of 4MBSLb, the emission calculated betweenresult forvaporous aqueous and methanol gaseous solution bubbles isis shown.discussed In this[25,34]. case, evaporation of methanol also occursAccording during to the numerical bubble expansion. simulations, During vaporo the bubbleus bubbles collapse, appear intense at relatively condensation high of acousticmethanol amplitudes occurs at at the relatively bubble walllow asultrasonic well as thatfrequencies of water [35]. vapor For [27 example,]. at 20 kHz and 5 barAt in the ultrasonic end of the frequency violent and bubble pressure collapse, amplitude, temperature respectively, inside ana bubble argon expands bubble in dramaticallyaqueous methanol during the solution rarefaction under thephase condition of ultrasound of Figures (Figure3 and 8a)4 increases [33]. As to a 17,000result, Kin- as tenseshown evaporation in Figure of5a water [ 27]. takes As a place result, during water the vapor bubble as well expansion as methanol into a insidebubble a in bubble order is to thermallymaintain the dissociated saturated as vapor shown pressure in Figure insi5b.de This a bubble. kind of Although reactions areintense called condensation sonochemical of reactionswater vapor [5]. takes place at the bubble wall at the bubble collapse, still the main bubble contentDue is water to the vapor endothermic even at the dissociation end of the of bubble methanol collapse inside (Figure a bubble, 8c) [33]. temperature It should inside be noteda bubble that condensation decreases as theat the methanol bubble concentrationcollapse is strongly increases in non-equilibrium, (Figure6)[ 27]. As and a result,the partialthe intensitypressure of water SBSL vapor decreases inside as a the bubble methanol is several concentration orders of magnitude increases, larger which than semi- thequantitatively saturated vapor agrees pressure with the[36]. experimental data [30]. Theoretically, the SBSL intensity is calculatedThe peak by bubble the following temperature contributions in a vaporous for light air bubble emissions in 20 from °C water thermal is always plasma about formed 6300inside K due a bubble; to the following electron-atom reason bremsstrahlung, (Figure 8b) [33,34]. electron-ion As the bremsstrahlung,bubble temperature radiative in- recombination of electrons and ions, and radiative attachment of electrons to neutral creases, water vapor is gradually dissociated mainly by H2O + M  OH + H + M and H2O particles. Electron-atom and electron-ion bremsstrahlung is light emission when electrons + H  OH + H2, where M is the third body. The endothermic vapor dissociation sup- pressesare decelerated the further by temperature collisions with increase. neutral Thus, atoms the and bubble positive temperature ions, respectively. remains In nearly general, constantwhen a(~4000 charged K) by particle this effect such just as anbefore electron the end isdecelerated, of the bubble light collapse is emitted, (Figure known 8b). As as thebremsstrahlung speed of the bubble [31]. Detailscollapse of further the equations increases, for the the endothermic calculations ofheat the of light vapor intensity dissoci- are described in Ref. [25]. ation is no longer able to keep the bubble temperature constant. This condition is similar The model of bubble dynamics including non-equilibrium chemical reactions inside for any case, which results in the nearly constant peak temperature inside a bubble at a bubble as well as SL light emission has been validated in the study of single-bubble relatively high acoustic amplitudes [34]. This is discussed again later. sonochemistry (Figure7)[ 24]. In 2002, Didenko and Suslick [32] reported experimentally Gaseous bubbles appear at relatively low acoustic amplitudes at relatively low ultra- the production rate of OH radicals from a SBSL bubble as 8.2 × 105 molecules per acoustic sonic frequencies (Figure 9) or at relatively high ultrasonic frequencies [33,35]. Under the cycle. They also reported that the number of photons emitted from a SBSL bubble per conditions, the bubble expansion is not so intense, and correspondingly, evaporation of acoustic cycle is 7.5 × 104. OH radicals are produced inside a heated bubble by the water vapor into a bubble is not so intense. Thus, intense condensation of water vapor at dissociation of water vapor (H O). In Figure7b, the calculated dissolution rate of OH the bubble collapse results in the main2 bubble content being noncondensable gas such as radicals into the liquid from the interior of a SBSL bubble is shown as a function of time air at the end of the bubble collapse (Figure 9c) [33]. As the amount of water vapor inside for one acoustic cycle as well as its time integral [24]. The simulated total amount of OH radicals dissolved into the liquid from a SBSL bubble is 6.6 × 105 molecules per acoustic

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cycle, which almost agrees with the experimental data [24,32]. Furthermore, the simulated number of photons emitted from a SBSL bubble per pulse is 8.0 × 104, which almost agrees with the exprimental data. Thus, the model has been validated.

3. Vaporous and Gaseous Bubbles When the bubble content is mostly water vapor even at the end of the bubble collapse, such bubbles are called vaporous bubbles [33]. On the other hand, when the bubble content at the end of the bubble collapse is noncondensable gas such as air, such bubbles are called gaseous bubbles [33]. In this section, difference in mechanism of MBSL emission between vaporous and gaseous bubbles is discussed [25,34]. According to numerical simulations, vaporous bubbles appear at relatively high acoustic amplitudes at relatively low ultrasonic frequencies [35]. For example, at 20 kHz and 5 bar in ultrasonic frequency and pressure amplitude, respectively, a bubble expands Molecules 2021, 26, x FOR PEER REVIEWdramatically during the rarefaction phase of ultrasound (Figure8a) [ 33]. As a result, intense8 of 36

evaporation of water takes place during the bubble expansion into a bubble in order to maintain the saturated vapor pressure inside a bubble. Although intense condensation ofa gaseous water vapor bubble takes is much place atsmaller the bubble than wallthat in at thea vaporous bubblecollapse, bubble, the still peak the main bubble bubble tem- contentperature is (7300 water K) vapor inside even a gaseous at the endbubble of the is higher bubble than collapse that (6300 (Figure K)8 c)inside [ 33]. a Itvaporous should be noted that condensation at the bubble collapse is strongly in non-equilibrium, and the bubble because water vapor considerably cools a bubble by endothermic heat of vapor partial pressure of water vapor inside a bubble is several orders of magnitude larger than dissociation. the saturated vapor pressure [36].

Figure 8. Calculated results for an air bubble in liquid water at 20 ◦C irradiated by an ultrasonic wave of 20 kHz and 5 bar inFigure frequency 8. Calculated and pressure results amplitude, for an air respectivelybubble in liquid [33]. water The ambient at 20 °C bubbleirradiated radius by an is 5ultrasonicµm. (a) The wave radius-time of 20 kHz curveand 5 forbar in frequency and pressure amplitude, respectively [33]. The ambient bubble radius is 5 μm. (a) The radius-time curve for one acoustic cycle. A bubble disintegrates into daughter bubbles by shape instability at t = 152.7 µs which is out of this one acoustic cycle. A bubble disintegrates into daughter bubbles by shape instability at t = 152.7 μs which is out of this ﬁgure. (b) The temperature inside a bubble and the bubble radius as a function of time at around the end of the bubble figure. (b) The temperature inside a bubble and the bubble radius as a function of time at around the end of the bubble µ collapsecollapse onlyonly forfor 0.10.1 μs.s. (c(c)) Numbers Numbers of of molecules molecules ofof various various speciesspecies insideinside aa bubble bubble asas a a function function of of time time with with the the same same timetime axis axis as as that that of of ( b(b).). The The vertical vertical axis axis is is in in logarithmic logarithmic scale. scale. Copyright Copyright 2005,2005, with with the the permission permission from from Elsevier. Elsevier.

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The peak bubble temperature in a vaporous air bubble in 20 ◦C water is always about 6300 K due to the following reason (Figure8b) [ 33,34]. As the bubble temperature increases, water vapor is gradually dissociated mainly by H2O + M → OH + H + M and H2O + H → OH + H2, where M is the third body. The endothermic vapor dissociation suppresses the further temperature increase. Thus, the bubble temperature remains nearly constant (~4000 K) by this effect just before the end of the bubble collapse (Figure8b). As the speed of the bubble collapse further increases, the endothermic heat of vapor dissociation is no longer able to keep the bubble temperature constant. This condition is similar for any case, which results in the nearly constant peak temperature inside a bubble at relatively high acoustic amplitudes [34]. This is discussed again later. Gaseous bubbles appear at relatively low acoustic amplitudes at relatively low ultrasonic frequencies (Figure9) or at relatively high ultrasonic frequencies [ 33,35]. Under the conditions, the bubble expansion is not so intense, and correspondingly, evaporation of water vapor into a bubble is not so intense. Thus, intense condensation of water vapor at the bubble collapse results in the main bubble content being noncondensable gas such as air at the end of the bubble collapse (Figure9c) [ 33]. As the amount of water vapor inside a gaseous bubble is much smaller than that in a vaporous bubble, the peak bub- Molecules 2021, 26, x FOR PEER REVIEW 9 of 36 ble temperature (7300 K) inside a gaseous bubble is higher than that (6300 K) inside a vaporous bubble because water vapor considerably cools a bubble by endothermic heat of vapor dissociation.

Figure 9. Calculated results when the acoustic amplitude is 1.75 bar [33]. The other conditions are the same as those in FigureFigure 9.8.( Calculateda) The radius-time results when curve the for oneacoustic acoustic amplitude cycle. A bubbleis 1.75 disintegratesbar [33]. The into other daughter conditions bubbles are by the shape same instability as those in Figureat t = 8. 39.85 (a) Theµs. radius-time (b) The temperature curve for inside one acoustic a bubble cycle. and theA bubble bubble disintegrates radius as a function into daughter of time bubbles at around by the shape end instability of the at bubblet = 39.85 collapse μs. (b only) The for temperature 0.1 µs. (c) Numbers inside a ofbubble molecules and the of various bubble species radius insideas a function a bubble of as time a function at around of time the with end the of the bubblesame timecollapse axis only as that for of 0.1 (b ).μs. The (c) vertical Numbers axis of is molecules in logarithmic of various scale. Copyright species inside 2005, a with bubble the permissionas a function from of time Elsevier. with the same time axis as that of (b). The vertical axis is in logarithmic scale. Copyright 2005, with the permission from Elsevier.

The results of numerical simulations for an argon bubble in 5 °C water irradiated by 20 kHz ultrasound are summarized in Figure 10 [34]. As already discussed, the peak bubble temperature is nearly constant at relatively high acoustic amplitudes (Figure 10a). As the liquid temperature is lower than that in Figure 8, the peak bubble temperature of vaporous bubbles in Figure 10 is higher than that in Figure 8 [25]. According to the numerical simulations, the mechanism of the SL light emission from vaporous bubbles is chemiluminescence of OH as well as emissions from weakly ionized plasma formed inside a bubble (Figure 10b) [34]. The intensity of chemiluminescence of OH is estimated by the rates of the reactions O + H + M  OH* + M and OH + H + OH  OH* + H2O, where OH* is the excited OH radical and M is the third body. The excited OH radical emits light (chemiluminescence) by OH*  OH + hν. The quenching of molecular emissions by collisional deexcitation is taken into account in the calculations [34]. Inside a bubble at the end of the bubble collapse, temperature and pressure are extremely high, which results in strong quenching of molecular emissions by collisional deexcitation. Nev- ertheless, chemiluminescence of OH is still intense in vaporous bubbles. Ndiaye et al. [37] experimentally reported that the relative vibrational population distribution of OH obtained from the MBSL spectra deviates strongly from the equilibrium Boltzmann distribution. This may be caused by the chemiluminescence origin of OH-line emissions.

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For gaseous argon bubbles, the peak temperature is as high as 20,000 K (Figure 10a) [34]. At such high bubble temperature, considerable thermal ionization occurs inside a bubble. Furthermore, ionization potential of gas molecules is considerably lowered by the extreme high density inside a bubble [25]. The density inside a bubble is nearly as high as that of condensed phase. Pressure inside a bubble at the end of the bubble collapse is as high as about 10 GPa [23]. There is some experimental evidence on the considerable ionization-potential lowering in SL bubbles [38]. The ionization potential lowering is due to overlaps of electron wavefunctions in the extremely dense gas inside a bubble [25,39,40]. It is one of the main reasons for the plasma formation inside a bubble in addition to the high bubble temperature at the end of the violent bubble collapse. With regard to the de- Molecules 2021, 26, 4624 gree of ionization potential lowering, further studies are required. 9 of 34 The degree of ionization inside a gaseous bubble is known to be 0.03~300% with ionization potential lowering by 40~75% or more [38,41–43]. It results in the dominant light emissions from plasma such as electron-atom and electron-ion bremsstrahlung, radiative The results of numerical simulations for an argon bubble in 5 ◦C water irradiated recombination of electrons and ions, radiative attachment of electrons to neutral atoms, by 20 kHz ultrasound are summarized in Figure 10[ 34]. As already discussed, the peak etc. (Figure 10b) [25,34,43]. bubble temperature is nearly constant at relatively high acoustic amplitudes (Figure 10a). As the liquid temperature is lower than that in Figure8, the peak bubble temperature of vaporous bubbles in Figure 10 is higher than that in Figure8[25].

Figure 10. Results of numerical simulations of bubble pulsations for various acoustic amplitudes ◦ and equilibrium bubble radii for an argon bubble in 5 C water irradiated by 20 kHz ultrasound [34]. (a) The bubble temperature at the collapse. The isothermal lines are from the bottom 5000, 10,000, Figure 10. Results of numerical simulations of bubble pulsations for various acoustic amplitudes and20,000, equilibrium 20,000, 10,000,bubble andradii 7000 for K.an Aboveargon bubble the isothermal in 5 °C linewater of irradiated 7000 K, the by bubble 20 kHz temperature ultrasound at the collapse is independent of acoustic amplitude and is always 7000 K. (b) The mechanism of the light emission. At large acoustic amplitudes chemiluminescence is relatively strong; OH* → OH + hν, where OH* is created by the reactions O + H + M → OH* + M and OH + H + OH → OH* +

H2O where M is the third body. At lower acoustic amplitudes emissions from plasma are dominant; electron bremsstrahlung and radiative recombination of electrons and ions. At very low acoustic amplitudes no light is emitted. The energy of the emitted light per bubble collapse is also shown. Copyright 2001, with the permission of AIP Publishing.

According to the numerical simulations, the mechanism of the SL light emission from vaporous bubbles is chemiluminescence of OH as well as emissions from weakly ionized plasma formed inside a bubble (Figure 10b) [34]. The intensity of chemiluminescence of OH is estimated by the rates of the reactions O + H + M → OH* + M and OH + H + OH → OH* + H2O, where OH* is the excited OH radical and M is the third body. The excited OH radical emits light (chemiluminescence) by OH* → OH + hν. The quenching of Molecules 2021, 26, 4624 10 of 34

molecular emissions by collisional deexcitation is taken into account in the calculations [34]. Inside a bubble at the end of the bubble collapse, temperature and pressure are extremely high, which results in strong quenching of molecular emissions by collisional deexcitation. Nevertheless, chemiluminescence of OH is still intense in vaporous bubbles. Ndiaye et al. [37] experimentally reported that the relative vibrational population distribution of OH obtained from the MBSL spectra deviates strongly from the equilibrium Boltzmann distribution. This may be caused by the chemiluminescence origin of OH-line emissions. For gaseous argon bubbles, the peak temperature is as high as 20,000 K (Figure 10a) [34]. At such high bubble temperature, considerable thermal ionization occurs inside a bubble. Furthermore, ionization potential of gas molecules is considerably lowered by the extreme high density inside a bubble [25]. The density inside a bubble is nearly as high as that of condensed phase. Pressure inside a bubble at the end of the bubble collapse is as high as about 10 GPa [23]. There is some experimental evidence on the considerable ionization-potential lowering in SL bubbles [38]. The ionization potential lowering is due to overlaps of electron wavefunctions in the extremely dense gas inside a bubble [25,39,40]. It is one of the main reasons for the plasma formation inside a bubble in addition to the high bubble temperature at the end of the violent bubble collapse. With regard to the degree of ionization potential lowering, further studies are required. The degree of ionization inside a gaseous bubble is known to be 0.03~300% with Molecules 2021, 26, x FOR PEER REVIEW 11 of 36 ionization potential lowering by 40~75% or more [38,41–43]. It results in the dominant light emissions from plasma such as electron-atom and electron-ion bremsstrahlung, radiative recombination of electrons and ions, radiative attachment of electrons to neutral atoms, etc. [34]. ((Figurea) The bubble 10b) [ 25temperature,34,43]. at the collapse. The isothermal lines are from the bottom 5000, 10,000, 20,000,There 20,000, are 10,000, mainly and two 7000 typesK. Above in the the isothermal methods line of of ultrasonic 7000 K, the irradiation bubble tempera- of liquid ture at(Figure the collapse 11)[ is33 independent]. One is of the acoustic method amplitude to use and an is ultrasonic always 7000 horn K. (b immersed) The mechanism in the liq- of the uidlight(Figure emission. 11 Ata). largeThe otheracoustic is amplitudes the method chemiluminescence of ultrasonic bath is relatively type (standing-wave strong; OH*  type) OH + hν, where OH* is created by the reactions O + H + M  OH* + M and OH + H + OH  OH* + (Figure 11b). In the horn-type, acoustic amplitude near the horn tip can be very high such H2O where M is the third body. At lower acoustic amplitudes emissions from plasma are dominant; as 10 bar. On the other hand, in the standing-wave type, bubbles are repelled from the electron bremsstrahlung and radiative recombination of electrons and ions. At very low acoustic amplitudespressure no light antinodes is emitted. when The the energy acoustic of the amplitude emitted light is higherper bubble than collapse about 1.77is also bar shown. at 20 kHz Copyrightdue to2001, the with acoustic the perm radiationission of force AIP acting Publishing. on bubbles called primary Bjerknes force [5,33,44]. In other words, many actively pulsating bubbles gather at the region where acoustic amplitude is about 1.77 bar at 20 kHz [45].

Figure 11. Two types of sonochemical reactors [33]. (a) A horn-type reactor. (b) A standing-wave

type reactor. Copyright 2005, with the permission from Elsevier. Figure 11. Two types of sonochemical reactors [33]. (a) A horn-type reactor. (b) A standing-wave type reactor.A Copyright SBSL bubble 2005, is with a gaseous the permission bubble becausefrom Elsevier. acoustic amplitude in SBSL is much lower than the threshold one for repulsion of the primary Bjerknes force [6]. ThereConsidering are mainly two the types above in discussions, the methods many of ultrasonic bubbles irradiation in the horn-type of liquid reactors (Figure are va- 11) [33].porous One bubbles.is the method On the to use other an hand,ultrason manyic horn bubbles immersed in the in standing-wave the liquid (Figure type 11a). reactors The other is the method of ultrasonic bath type (standing-wave type) (Figure 11b). In the horn-type, acoustic amplitude near the horn tip can be very high such as 10 bar. On the other hand, in the standing-wave type, bubbles are repelled from the pressure antinodes when the acoustic amplitude is higher than about 1.77 bar at 20 kHz due to the acoustic radiation force acting on bubbles called primary Bjerknes force [5,33,44]. In other words, many actively pulsating bubbles gather at the region where acoustic amplitude is about 1.77 bar at 20 kHz [45]. A SBSL bubble is a gaseous bubble because acoustic amplitude in SBSL is much lower than the threshold one for repulsion of the primary Bjerknes force [6]. Considering the above discussions, many bubbles in the horn-type reactors are vaporous bubbles. On the other hand, many bubbles in the standing-wave type reactors are gaseous bubbles. Thus, it is suggested that SL emission in the horn-type is mainly by chemiluminescence of OH and emissions from weakly ionized plasma formed inside a bubble, and that in the standing-wave type it is mainly by the emissions from plasma. Furthermore, more gaseous bubbles are present at higher ultrasonic frequencies due to less expansion of a bubble caused by shorter acoustic period, as discussed later [35]. Thus, at higher ultrasonic frequencies, emissions from plasma are much more stronger than chemiluminescence of OH compared to MBSL at lower ultrasonic frequencies. It has been actually observed experimentally (Figure 12 [46]). The emissions from plasma, which is the continuum component of the MBSL spectra, is stronger at higher ultrasonic frequencies relative to the intensity of OH-line at the wavelength of 310 nm.

Molecules 2021, 26, 4624 11 of 34

are gaseous bubbles. Thus, it is suggested that SL emission in the horn-type is mainly by chemiluminescence of OH and emissions from weakly ionized plasma formed inside a bubble, and that in the standing-wave type it is mainly by the emissions from plasma. Furthermore, more gaseous bubbles are present at higher ultrasonic frequencies due to less expansion of a bubble caused by shorter acoustic period, as discussed later [35]. Thus, at higher ultrasonic frequencies, emissions from plasma are much more stronger than chemiluminescence of OH compared to MBSL at lower ultrasonic frequencies. It has been Molecules 2021, 26, x FOR PEER REVIEW actually observed experimentally (Figure 12[ 46]). The emissions from plasma, which12 of 36 is the

continuum component of the MBSL spectra, is stronger at higher ultrasonic frequencies relative to the intensity of OH-line at the wavelength of 310 nm.

FigureFigure 12. MBSL 12. MBSL spectra spectra of water of water at 20 at kHz 20 kHz with with 33 W, 33 W,100 100 kHz kHz with with 40 40W, W, and and 362 362 kHz kHz with with 43 43 W W at ◦ at 1818 °C C[[46].46 ].The The apparent apparent broad broad peak peak around around 400–475 400–475 nm nm at 362 kHz isis anan artifactartifact duedue to to second-order second- orderlight light emission emission of of the the strong strong MBSL MBSL UV UV part. part. CopyrightCopyright 2018,2018, with the permission from from Amer- American ican ChemicalChemical Society.Society.

As alreadyAs already discussed, discussed, at relatively at relatively low lowultrasonic ultrasonic frequencies, frequencies, vaporous vaporous bubbles bubbles are are seenseen at high at high acoustic acoustic amplitudes amplitudes (Figure (Figure 13) [35]. 13)[ The35]. vapor The vaporfraction fraction inside a inside bubble a bubbleat the at end theof the end bubble of the bubblecollapse collapse increases increases as acoustic as acoustic amplitude amplitude increases increases (Figure (Figure 13b). For 13b). 20 For kHz20 and kHz 100 and kHz 100 in kHz Figure in Figure 13, the 13 bubble, the bubble temperature temperature is the is highest the highest at a atrelatively a relatively low low acousticacoustic amplitude amplitude because because at higher at higher acoustic acoustic amplitude amplitude vapor vapor fraction fraction becomes becomes higher. higher. For For300 kHz 300 kHzand 1 and MHz 1 MHzin Figure in Figure 13, on 13the, onother the hand, other vapor hand, fraction vapor fractionis always is less always than less 0.1, thanand gaseous 0.1, and bubbles gaseous are bubbles seen areeven seen at re evenlatively at relatively high acoustic high acoustic amplitudes. amplitudes. Thus, the Thus, bubblethe temperature bubble temperature increases increases as the acoustic as the acousticamplitude amplitude increases increases and becomes and becomes nearly con- nearly stantconstant at relatively at relatively high acoustic high acoustic amplitudes amplitudes (Figure (Figure13a). 13a).

Molecules 2021, 26, x FOR PEER REVIEW 13 of 36

Molecules 2021, 26, 4624 12 of 34

(a) (b)

FigureFigure 13. 13.The The calculated calculated results results as aas function a function of acousticof acoustic amplitude amplitude for for various various ultrasonic ultrasonic frequencies frequencies (20 (20 kHz, kHz, 100 100 kHz, kHz, 300300 kHz, kHz, and and 1 MHz) 1 MHz) for for the the ﬁrst first collapse collapse of anof isolatedan isolated spherical spherical air bubbleair bubble [35 ].[35]. The The ambient ambient bubble bubble radii radii are are 5 µ m5 μ form for 20 kHz,20 kHz, 3.5 3.5µm μ form for 100 100 and and 300 300 kHz, kHz, and and 1 µ m1 μ form 1for MHz. 1 MHz. (a) The(a) The temperature temperature inside inside a bubble a bubble at the at the bubble bubble collapse. collapse. (b) (b) The molar fraction of water vapor inside a bubble at the end of the bubble collapse. Copyright 2007, with the permission The molar fraction of water vapor inside a bubble at the end of the bubble collapse. Copyright 2007, with the permission of of AIP Publishing. AIP Publishing. 4. Influence of Bubble Size 4. Inﬂuence of Bubble Size The linear resonance radius of an air bubble is 10.9 μm at 300 kHz [5,43]. However, The linear resonance radius of an air bubble is 10.9 µm at 300 kHz [5,43]. However, due to the strong nonlinear nature of bubble pulsation, the expansion ratio (Rmax/R0), due to the strong nonlinear nature of bubble pulsation, the expansion ratio (Rmax/R0), where Rmax is the maximum bubble radius and R0 is the ambient bubble radius which is where R is the maximum bubble radius and R is the ambient bubble radius which the bubblemax radius when ultrasound is absent, takes0 the peak value at smaller ambient bub- is the bubble radius when ultrasound is absent, takes the peak value at smaller ambient Molecules 2021, 26, x FOR PEER REVIEW ble radius than the linear resonance radius even at acoustic amplitude14 of 36 as low as 0.5 bar bubble radius than the linear resonance radius even at acoustic amplitude as low as 0.5 bar (Figure 14) [43]. As the acoustic amplitude increases, the maximal response of a bubble (Figure 14)[43]. As the acoustic amplitude increases, the maximal response of a bubble shifts toward smaller ambient radius. At the acoustic amplitude of 3 bar, the range of am- shifts toward smaller ambient radius. At the acoustic amplitude of 3 bar, the range of bient bubble radius for higher expansion ratio than 3 is from 0.27 to 7 μm [43]. ambient bubble radius for higher expansion ratio than 3 is from 0.27 to 7 µm [43]. The shape instability of a bubble is another important factor to determine the range of ambient bubble radius for active bubbles observed experimentally [43]. When the acoustic amplitude is above the threshold for shape instability shown in Figure 15 by the dash-dotted line, a bubble disintegrates into daughter bubbles in a few acoustic cycles [43]. The method for the numerical calculations of the threshold for shape instability is described in Refs. [35,47,48]. When the acoustic amplitude is larger than the Blake threshold shown by a solid line in Figure 15, bubble expansion becomes very strong, which is called transient cavitation [5,43]. When the threshold SL intensity and that for sonochemical production of oxidants are assumed as 10−7 pJ/collapse and 108 molecules/s, respectively, they are equal to or higher than the Blake-threshold acoustic amplitude as shown in Figure 15 [43]. The typical range of ambient radius for actual active bubbles is from the SL threshold radius (or threshold for sonochemical production of oxidants) to slightly above the threshold radius for shape instability because larger active bubbles disintegrate into daughter bubbles in a few acoustic cycles. Indeed, Brotchie et al. [49] reported experimentally that the range of ambient radius for MBSL bubbles was from 2.9 to 3.5 μm at 355 kHz, which is a relatively narrow range near the threshold for shape instability. Fur- ther studies are required on this topic [18,50].

FigureFigure 14. The 14. calculatedThe calculated expansion expansion ratio (Rmax/R ratio0) as a (Rfunctionmax/R of0 )ambien as a functiont bubble radius of ambient for various bubble radius for acousticvarious amplitudes acoustic at amplitudes 300 kHz [43]. at Both 300 the kHz horizo [43].ntal Both and the vertical horizontal axes are and in logarithmic vertical axes scale. are in logarithmic Copyright 2008, with the permission of AIP Publishing. scale. Copyright 2008, with the permission of AIP Publishing.

Figure 15. The calculated thresholds for the shape instability, for SL, and for oxidant production as well as the Blake threshold in R0-pa plane [43]. Copyright 2008, with the permission of AIP Pub- lishing.

The dependence of peak bubble temperature as well as vapor fraction inside an air bubble at the end of the bubble collapse on ambient bubble radius is shown in Figure 16a

Molecules 2021, 26, x FOR PEER REVIEW 14 of 36

Molecules 2021, 26, 4624 13 of 34

The shape instability of a bubble is another important factor to determine the range of ambient bubble radius for active bubbles observed experimentally [43]. When the acoustic amplitude is above the threshold for shape instability shown in Figure 15 by the dash- dotted line, a bubble disintegrates into daughter bubbles in a few acoustic cycles [43]. The method for the numerical calculations of the threshold for shape instability is described in Refs. [35,47,48]. When the acoustic amplitude is larger than the Blake threshold shown by a solid line in Figure 15, bubble expansion becomes very strong, which is called transient cavitation [5,43]. When the threshold SL intensity and that for sonochemical production of oxidants are assumed as 10−7 pJ/collapse and 108 molecules/s, respectively, they are equal to or higher than the Blake-threshold acoustic amplitude as shown in Figure 15[ 43]. The typical range of ambient radius for actual active bubbles is from the SL threshold radius (or threshold for sonochemical production of oxidants) to slightly above the threshold radius for shape instability because larger active bubbles disintegrate into daughter bubbles in a

Figure 14. Thefew calculated acoustic expansion cycles. Indeed,ratio (Rmax Brotchie/R0) as a function et al. [49 of] ambien reportedt bubble experimentally radius for various that the range of acoustic amplitudesambient at radius300 kHz for [43]. MBSL Both bubblesthe horizo wasntal from and vertical 2.9 to 3.5 axesµm are at in 355 logarithmic kHz, which scale. is a relatively Copyright 2008,narrow with the range perm nearission the of threshold AIP Publishing. for shape instability. Further studies are required on this topic [18,50].

Figure 15. The calculated thresholds for the shape instability, for SL, and for oxidant produc-

Figure 15. Thetion calculated as well thresholds as the Blake for threshold the shape ininstab R0-pility,a plane for SL, [43 ].and Copyright for oxidant 2008, production with the as permission of well as the BlakeAIP threshold Publishing. in R0-pa plane [43]. Copyright 2008, with the permission of AIP Pub- lishing. The dependence of peak bubble temperature as well as vapor fraction inside an air The dependencebubble at theof peak end ofbubble the bubble temperature collapse as on well ambient as vapor bubble fraction radius inside is shown an air in Figure 16a bubble at thefor end ultrasound of the bubble of 20 collapse kHz and on 1.75ambient bar [bubble43]. The radius bubble is shown temperature in Figure is the16a highest for relatively low vapor fraction (gaseous bubbles) as already discussed in the previous section. The vapor fraction is correlated with the expansion ratio of a bubble shown in Figure 16b. For vaporous bubbles, the bubble temperature is around 6500 K.

Molecules 2021, 26, x FOR PEER REVIEW 15 of 36

for ultrasound of 20 kHz and 1.75 bar [43]. The bubble temperature is the highest for relatively low vapor fraction (gaseous bubbles) as already discussed in the previous section. The vapor fraction is correlated with the expansion ratio of a bubble shown in Figure 16b. For vaporous bubbles, the bubble temperature is around 6500 K. The dependence of the light intensity of each emission process in MBSL on ambient bubble radius is shown in Figure 16c for ultrasound of 20 kHz and 1.75 bar [43]. The main emission process is electron-atom bremsstrahlung. The MBSL intensity strongly depends on the ambient bubble radius through the peak bubble temperature and the emission volume. The vertical axis of Figure 16c is in logarithmic scale. For vaporous bubbles, chemiluminescence of OH as well as electron-atom bremsstrahlung and radiative attachment of electrons to OH molecules are important emission processes. For gaseous bubbles, on the other hand, electron-atom bremsstrahlung and radiative recombination of electrons and ions are much more intense than chemiluminescence of OH as already discussed in the previous section. The rate of production of each oxidant inside an air bubble is shown as a function of ambient bubble radius in Figure 16d with the logarithmic vertical axis [43]. It is seen that at relatively high bubble temperatures the amounts of oxidants produced become relatively small. It is because at high bubble temperatures oxidants are strongly consumed inside a bubble by oxidizing nitrogen [22,43,51]. As a result, the amount of HNO2, NO, Molecules 2021, 26, 4624 14 of 34 and NO2 produced inside an air bubble is relatively large under the condition.

Molecules 2021, 26, x FOR PEER REVIEW 16 of 36

(a) (b)

FigureFigure 16. The16. The calculated calculated results results for an for air an bubble air bubble as a functionas a function of ambient of ambient bubble bubble radius radius at 20 kHz at 20 and kHz 1.75 and bar 1.75 in ultrasonic bar in ultra- frequencysonic frequency and acoustic and amplitude,acoustic amplitude, respectively respectively [43]. The [43]. horizontal The horizontal axis is in axis logarithmic is in logarithmic scale. (a )scale. The peak(a) The temperature peak temper-

(solid)ature and (solid) the molarand the fraction molar fraction of water of vapor water (dash vapor dotted) (dash do insidetted) inside a bubble a bubble at the at end the of end the of bubble the bubble collapse. collapse. (b) The(b) The expansion ratio (Rmax/R0). (c) The intensity of each emission process in SL. The vertical axis is in logarithmic scale. (d) The expansion ratio (R /R ). (c) The intensity of each emission process in SL. The vertical axis is in logarithmic scale. (d) The rate of productionmax of 0each oxidant with the logarithmic vertical axis. Copyright 2008, with the permission of AIP Publish- rate of production of each oxidant with the logarithmic vertical axis. Copyright 2008, with the permission of AIP Publishing. ing. The dependence of the light intensity of each emission process in MBSL on ambient The calculated results for acoustic amplitude of 6 bar at 20 kHz for an air bubble are bubble radius is shown in Figure 16c for ultrasound of 20 kHz and 1.75 bar [43]. The shown as a function of ambient bubble radius in Figure 17 [43]. When the ambient radius main emission process is electron-atom bremsstrahlung. The MBSL intensity strongly dependsis larger on than the 0.12 ambient μm, bubblewhich is radius slightly through larger than the peakthe Blake bubble threshold temperature radius and (0.11 the μm), emissionand smaller volume. than The about vertical 10 μm, axis bubbles of Figure are vaporous 16c is in ones logarithmic with nearly scale. constant For vaporous peak tem- bubbles,perature chemiluminescence of about 6300 K of(Figure OH as 17a). well The as electron-atom maximum peak bremsstrahlung temperature andis 8700 radiative K at the attachmentambient bubble of electrons radius to of OH 50 molecules μm due to are relatively important small emission vapor processes.fraction (gaseous For gaseous bubble). bubbles,The expansion on the other ratio hand, (Rmax/R electron-atom0) takes the maximum bremsstrahlung value of and about radiative 2400 at recombination the ambient ra- of electronsdius of 0.13 and μ ionsm, which are much is three more orders intense of thanmagnitude chemiluminescence smaller than the of OH linear as alreadyresonance discussedradius of in 164 the μ previousm at 20 kHz section. due to strong nonlinearity of the bubble pulsation (Figure 17b) [43].The rate of production of each oxidant inside an air bubble is shown as a function of ambient bubble radius in Figure 16d with the logarithmic vertical axis [43]. It is seen that at relatively high bubble temperatures the amounts of oxidants produced become relatively small. It is because at high bubble temperatures oxidants are strongly consumed inside a

(a)

Molecules 2021, 26, x FOR PEER REVIEW 16 of 36

MoleculesFigure2021 16. ,The26, calculated 4624 results for an air bubble as a function of ambient bubble radius at 20 kHz and 1.75 bar in ultra- 15 of 34 sonic frequency and acoustic amplitude, respectively [43]. The horizontal axis is in logarithmic scale. (a) The peak temperature (solid) and the molar fraction of water vapor (dash dotted) inside a bubble at the end of the bubble collapse. (b) The expansion ratio (Rmax/R0). (c) The intensity of each emission process in SL. The vertical axis is in logarithmic scale. (d) The rate of production of each oxidant with the logarithmic vertical axis. Copyright 2008, with the permission of AIP Publish- ing. bubble by oxidizing nitrogen [22,43,51]. As a result, the amount of HNO2, NO, and NO2 produced inside an air bubble is relatively large under the condition. The calculatedThe calculated results for resultsacoustic foramplitude acoustic of 6 amplitudebar at 20 kHz of for 6 an bar air atbubble 20 kHz are for an air bubble shown as a function of ambient bubble radius in Figure 17 [43]. When the ambient radius are shown as a function of ambient bubble radius in Figure 17[ 43]. When the ambient is larger than 0.12 μm, which is slightly larger than the Blake threshold radius (0.11 μm), and smallerradius than is about larger 10 thanμm, bubbles 0.12 µ arem, vaporous which is ones slightly with nearly larger constant than thepeak Blake tem- threshold radius perature(0.11 of aboutµm), 6300 and K smaller (Figure than17a). aboutThe maximum 10 µm, peak bubbles temperature are vaporous is 8700 onesK at the with nearly constant ambientpeak bubble temperature radius of 50 of μm about due to 6300 relatively K (Figure small 17 vapoa).r The fraction maximum (gaseous peak bubble). temperature is 8700 K The expansionat the ambient ratio (Rmax bubble/R0) takes radius the maximum of 50 µ valuem due of about to relatively 2400 at the small ambient vapor ra- fraction (gaseous dius of 0.13 μm, which is three orders of magnitude smaller than the linear resonance bubble). The expansion ratio (Rmax/R0) takes the maximum value of about 2400 at the radius ambientof 164 μm radiusat 20 kHz of due 0.13 to strongµm, which nonlinearity is three of the orders bubbleof pulsation magnitude (Figure smaller 17b) than the linear [43]. resonance radius of 164 µm at 20 kHz due to strong nonlinearity of the bubble pulsation (Figure 17b) [43].

Molecules 2021, 26, x FOR PEER REVIEW 17 of 36

(a)

(b)

(c)

FigureFigure 17. The calculated 17. The calculated results for an results air bubble for anas a air function bubble of asambient a function bubble of radius ambient at 20 bubblekHz radius at 20 kHz and 6 bar in ultrasonic frequency and acoustic amplitude, respectively [43]. The horizontal axis is in logarithmic scale. (a) The peak temperature (solid) and the molar fraction of water vapor (dash dotted) inside a bubble at the end of the bubble collapse. (b) The expansion ratio (Rmax/R0). (c) The intensity of each emission process in SL. The vertical axis is in logarithmic scale. Copyright 2008, with the permission of AIP Publishing.

As in the case of Figure 16c, the main light emission process in MBSL is electron-atom bremsstrahlung. For vaporous bubbles, chemiluminescence of OH is another important emission process. For gaseous bubbles, emissions from plasma (electron-atom bremsstrahlung and radiative recombination of electrons and ions) are about two orders of magnitude stronger in intensity than chemiluminescence of OH as already discussed. The maximum SL intensity is 2.0 × 10 pJ per bubble collapse at the ambient radius of 60 μm. Under this condition, the degree of ionization inside an air bubble is 0.5% with the ionization potential lowering of about 50% [43].

Molecules 2021, 26, 4624 16 of 34

and 6 bar in ultrasonic frequency and acoustic amplitude, respectively [43]. The horizontal axis is in logarithmic scale. (a) The peak temperature (solid) and the molar fraction of water vapor (dash

dotted) inside a bubble at the end of the bubble collapse. (b) The expansion ratio (Rmax/R0). (c) The intensity of each emission process in SL. The vertical axis is in logarithmic scale. Copyright 2008, with the permission of AIP Publishing.

As in the case of Figure 16c, the main light emission process in MBSL is electron- atom bremsstrahlung. For vaporous bubbles, chemiluminescence of OH is another important emission process. For gaseous bubbles, emissions from plasma (electron-atom bremsstrahlung and radiative recombination of electrons and ions) are about two orders of magnitude stronger in intensity than chemiluminescence of OH as already discussed. The maximum SL intensity is 2.0 × 103 pJ per bubble collapse at the ambient radius of 60 µm. Under this condition, the degree of ionization inside an air bubble is 0.5% with the ionization potential lowering of about 50% [43].

5. Bubble–Bubble Interaction In contrast to the case of the single bubble system (SBSL), some complexity arises from the bubble–bubble interaction in multibubble system (MBSL). In a bubble cloud, bubble pulsation is strongly inﬂuenced by the pulsations of surrounding bubbles because they radiate acoustic waves into the liquid, which is called the bubble–bubble interaction [5]. The acoustic pressure (p) radiated from a pulsating bubble is given as follows [5].

ρ . 2 .. p = L,∞ 2RR + R2R (4) r

where r is the distance from a radiating bubble. Accordingly, the Keller equation (Equation (1)) is approximately modiﬁed as follows taking into account the bubble–bubble interaction [5,19].

. .. . 2 . . R 3 R 1 R R dpB 1 − RR + R 1 − = 1 + [p − ps(t) − p∞] + − c∞ 2 3c∞ ρL,∞ c∞ B c∞ρL,∞ dt . 2 .. (5) ∑ 1 2R R + R2R i ri i i i i

where ri is the distance from the bubble numbered i, Ri is the instantaneous radius of the bubble numbered i, and summation is for all the surrounding bubbles. When the radius of each bubble is assumed to be the same for all the bubbles, Equation (5) is simpliﬁed as follows [5,19,52–54].

. .. . 2 . . R 3 R 1 R R dpB 1 − RR + R 1 − = 1 + [p − ps(t) − p∞] + − c∞ 2 3c∞ ρL,∞ c∞ B c∞ρL,∞ dt . 2 .. (6) S 2RR + R2R

where S is the coupling strength of the bubble–bubble interaction and given as follows when the spatial distribution of bubbles is assumed to be uniform.

Z lmax 2 1 4πr n 2 2 2 S = ∑ = dr = 2πn lmax − lmin ≈ 2πnlmax (7) i ri lmin r

where lmax is the radius of a bubble cloud, lmin is the distance between a bubble and a nearest bubble, lmax lmin is assumed in the last equation, and n is the number density of bubbles. Cavitation bubbles under an ultrasonic horn shown in Figure 18 have been numerically analyzed using Equation (6) as shown in Figure 19[ 19]. Due to the bubble–bubble interaction, bubble expansion is strongly suppressed [5,19,53]. Molecules 2021, 26, x FOR PEER REVIEW 19 of 36

Molecules 2021, 26, x FOR PEER REVIEW 19 of 36

bubble interaction on MBSL spectra for Ar bubbles in water. Further studies are required bubbleon this interaction topic. on MBSL spectra for Ar bubbles in water. Further studies are required Molecules 2021, 26, 4624 on this topic. 17 of 34

FigureFigure 18. 18. CavitationCavitation bubbles bubbles under under an an ultrasonic ultrasonic horn horn at at 29 29 kHz kHz and and 5 5W W observed observed by by a ahigh-speed high-speed Figurevideovideo 18. camera camera Cavitation [19]. [19]. Thebubbles The frame frame under (b (b) )is an is the theultrasonic result result of of horn the the analysis analysisat 29 kHz of of andthe the bubble5 bubble W observed motion. motion. by The Thea high-speed small small circles circles videoareare thecamera the starting starting [19]. points pointsThe frame for the (b) analysisanalysis is the result andand theofthe the curves cu analysisrves are are the ofthe calculatedthe calculated bubble streamlinesmotion. streamlines The of small of bubbles. bubbles. circles In theIn the frame (a), the bubble clouds A and B are marked by circles. Copyright 2008, with the permission are framethe starting (a), the points bubble for clouds the analysis A and and B are the marked curves byare circles. the calculated Copyright streamlines 2008, with of thebubbles. permission In thefrom frame American (a), the bubble Physical clouds Society. A and B are marked by circles. Copyright 2008, with the permission from American Physical Society. from American Physical Society.

FigureFigure 19. 19. CalculatedCalculated radius radius of ofa bubble a bubble in the in thecloud cloud A in A Figure in Figure 18 as 18 a asfunction a function of time of timefor one for Figureacousticone 19. acoustic Calculatedcycle at cycle 29 radiuskHz at 29 and kHzof 2.36a bubble and bar 2.36 in in frequenc barthe incloud frequencyy andA in pressure Figure and pressure18 amplitude as a function amplitude of ultrasound, of time of ultrasound, for respec- one acoustictivelyrespectively [19].cycle The at [29 19ambient ].kHz The and bubble ambient 2.36 radiusbar bubble in isfrequenc 5 radiusμm. They isand dotted 5 µpressurem. line The isamplitude dottedthe calc lineulated of isultrasound, theresult calculated neglecting respec- result all tivelytheneglecting [19].interactions The allambient thewith interactions bubbleother bubbles radius with is(an other5 μisolatedm. bubblesThe dottedbubble). (an line isolatedThe is thedashed calc bubble).ulated line is Theresult the dashed calculated neglecting line result isall the neglecting only the interaction with the bubbles in the cloud B. The solid line is the calculated result the calculatedinteractions result with neglecting other bubbles only the(an interaction isolated bu withbble). the The bubbles dashed in theline cloud is the B. calculated The solid lineresult is the neglectingtaking into only account the interaction all the interactions with the bubbles with su inrrounding the cloud bubbles. B. The solid Copyrigh line ist the2008, calculated with the resultpermis- calculated result taking into account all the interactions with surrounding bubbles. Copyright 2008, takingsion intofrom account American all thePhysical interactions Society. with surrounding bubbles. Copyright 2008, with the permis- with the permission from American Physical Society. sion from American Physical Society. According to the high-speed video image shown in Figure 18, many bubbles move upward toward the horn tip [19]. There are three kinds of forces acting on a bubble in an acoustic ﬁeld [5,19]. One is the radiation force from an acoustic wave (ultrasound) called the primary Bjerknes force. Another is the force acting from other bubbles called the secondary Bjerkes force. The other is the buoyant force. Numerical evaluation of the three kinds of forces on a bubble has indicated that bubbles in the bubble cloud B in Figure 18 move upward toward the horn tip by the secondary Bjerknes force from bubbles in the bubble cloud A [19]. MBSL intensity in sulfuric acid is much greater than that in water [2,55–57]. One of the main reasons for the much brighter MBSL in sulfuric acid is much lower saturated vapor pressure than that of water because it results in higher bubble temperature. According to Eddingsaas and Suslick [55], large and abrupt changes in bubble–cloud dynamics, MBSL light intensity, and its spectra under an ultrasonic horn were experimentally observed Molecules 2021, 26, 4624 18 of 34

upon varying the acoustic power in concentrated (95 wt %) sulfuric acid saturated with Ar (Figure 20). There were three different MBSL regimes as a function of acoustic intensity [55]. At relatively low acoustic intensities, a wispy, ﬁlamentous MBSL with strong Ar and SO lines was observed. Above about 16 W/cm2, the cavitating bubbles suddenly formed a bulb near the horn tip, creating a small globe of MBSL with very weak Ar lines along with the broad continuum. Above about 24 W/cm2, MBSL was observed from a cone at the horn tip, and the spectra consisted only of the broad continuum without Ar lines. These behaviors may be related to stronger bubble–bubble interaction as well as stronger secondary Bjerknes force at higher acoustic power mainly due to higher number density of bubbles. An [58] has already numerically studied the inﬂuence of the bubble–bubble Molecules 2021, 26, x FOR PEER REVIEW 20 of 36 interaction on MBSL spectra for Ar bubbles in water. Further studies are required on this topic.

Figure 20. MBSL of concentrated H SO at different acoustic powers of an ultrasonic horn [55]. (A) Figure 20. MBSL of concentrated H2SO4 at different2 4 acoustic powers of an ultrasonic horn [55]. (A) PhotographsPhotographs (10 s exposures) (10 s exposures) of different of light different emitting light regimes emitting of regimes MBSL of MBSLH2SO4, of from H2SO left4, to from right, left to right, with increasingwith increasing acoustic intensity, acoustic intensity, filament ﬁlamentous,ous, bulbous, bulbous, and cone and shaped cone shapedemission; emission; (B) MBSL (B )spec- MBSL spectra tra of concentratedof concentrated H2SO4 Hat2 theSO 4threeat the acoustic three acoustic intensities intensities shown. As shown. the acoustic As the power acoustic is powerincreased, is increased, the Ar linesthe become Ar lines weaker. become Copyright weaker. Copyright 2007, with 2007, the permission with the permission from Americ froman American Chemical ChemicalSociety. Society.

6. Acoustic6. Acoustic Field Field MBSL hasMBSL been has used been to visualize used to visualize acoustic acousticfields through ﬁelds throughthe spatial the distribution spatial distribution of of active bubblesactive bubblesin SL [59–62]. in SL [Sonochemiluminesc59–62]. Sonochemiluminescenceence (SCL) has (SCL) also has been also used been to used visual- to visualize ize acousticacoustic fields, ﬁelds, where where SCL is SCL the islight the emission light emission from an from aqueous an aqueous luminol luminol solution solution by by chemical reactions of luminol with oxidants such as OH radicals and H O produced from chemical reactions of luminol with oxidants such as OH radicals and H2O2 produced2 2 from cavitationcavitation bubbles bubbles[62–65]. An [62– example65]. An exampleof the SCL of theimage SCL is imageshown is for shown a half for plane a half of planea of a × × rectangularrectangular cell (5 cm cell × 5 (5 cm cm × 14.55 cm cm) at14.5 140 cm) kHz at in 140 Figure kHzin 21 Figure [62,66]. 21 Horizontal[ 62,66]. Horizontal stripes stripes of pressureof pressure nodes and nodes antinodes and antinodes are seen are in seen the inphotograph, the photograph, where where pressure pressure antinodes antinodes are are the brightthe bright regions regions in blue in blueby SCL. by SCL.In addi Intion, addition, a vertical a vertical narrow narrow dark darkregion region is seen is seenin in the photograph of Figure 21, where acoustic amplitude is relatively low (or number density of the photograph of Figure 21, where acoustic amplitude is relatively low (or number den- bubbles is relatively low). sity of bubbles is relatively low). In Figure 21, the numerically calculated spatial distributions of acoustic fields by the finite element method (FEM) are also shown for comparison for various attenuation coefficients (α) [66]. In the FEM program, the acoustic field in a rectangular cell filled with water with a vibrating plate at the bottom is coupled with the vibration of the side wall of the cell. The vibration amplitude at the center of the vibrating plate is assumed as 0.1 μm. The calculated result with the attenuation coefficient of 2 × 10−4 m−1 corresponds to the case that there is no bubble in the liquid. In this case, strong vibration of the side wall by high acoustic amplitude influences the acoustic field in the cell significantly because the side wall strongly radiates acoustic waves into the liquid. As a result, no horizontal stripes of pressure antinodes and nodes are seen. For the attenuation coefficient of 5 m−1, the horizontal stripes of pressure antinodes and nodes are seen as well as a vertical narrow dark region, which is qualitatively similar to the spatial distribution of SCL as compared in Figure 21 [66]. For the attenuation coefficient of 0.5 m−1, some stripes of pressure antinodes are disconnected. Thus, the actual attenuation coefficient in the experiment of SCL is probably about 5 m−1. For rigid side wall with spatially uniform vibration amplitude of the vibrating plate at the bottom of the cell, the horizontal stripes of pressure antinodes and nodes are parallel

Molecules 2021, 26, x FOR PEER REVIEW 21 of 36

as shown in Figure 22 [66]. When the vibration frequency of the vibrating plate is 100 kHz, the liquid height of 13.875 cm and 14.25 cm correspond to resonance and antiresonance, respectively. For the both cases, the liquid surface is pressure node. For the resonance case, the surface of the vibrating plate coincides with pressure antinode, while it coincides with pressure node for the antiresonance case. When the glass side wall is thin (2 mm thick), the surface of the thin side wall nearly Molecules 2021, 26, 4624 coincides with vertical pressure node as seen in Figure 23 because it is nearly a free surface19 of 34 [66].

Figure 21. The calculated spatial distribution of the acoustic amplitude for glass wall (7 mm in Figure 21. The calculated spatial distribution of the acoustic amplitude for glass wall (7 mm in thick- thickness) for various attenuation coefﬁcients of ultrasound [66]. The full-width at half maximum ness) for various attenuation coefficients of ultrasound [66]. The full-width at half maximum for the Gaussianfor the Gaussian distribution distribution of the vibr of theation vibration amplitude amplitude of the vibrating of the vibrating plate at plate the bottom at the bottom is 5 cm. is 5The cm. wallThe height wall height is 20 iscm. 20 A cm. half A halfof the of width the width (the (thefull fullwidth width is 7 is cm) 7 cm) of ofthe the liquid liquid container container is isshown. shown. TheThe photograph photograph of of sonochemilumin sonochemiluminescenceescence from from an an aqueous aqueous luminol luminol solution solution is is also also shown shown for for the the correspondingcorresponding half half plane. plane. Copyright Copyright 2007, 2007, with with the the permissi permissionon from from Elsevier. Elsevier.

In Figure 21, the numerically calculated spatial distributions of acoustic fields by the finite element method (FEM) are also shown for comparison for various attenuation coefficients (α)[66]. In the FEM program, the acoustic field in a rectangular cell filled with water with a vibrating plate at the bottom is coupled with the vibration of the side wall of the cell. The vibration amplitude at the center of the vibrating plate is assumed as 0.1 µm. The calculated result with the attenuation coefficient of 2 × 10−4 m−1 corresponds to the case that there is no bubble in the liquid. In this case, strong vibration of the side wall by high acoustic amplitude influences the acoustic field in the cell significantly because the side wall strongly radiates acoustic waves into the liquid. As a result, no horizontal stripes of pressure antinodes and nodes are seen. For the attenuation coefficient of 5 m−1, the horizontal stripes of pressure antinodes and nodes are seen as well as a vertical narrow dark region, which is qualitatively similar to the spatial distribution of SCL as compared in Figure 21[ 66]. For the attenuation coefficient of 0.5 m−1, some stripes of pressure antinodes are disconnected. Thus, the actual attenuation coefficient in the experiment of SCL is probably about 5 m−1. For rigid side wall with spatially uniform vibration amplitude of the vibrating plate at Figurethe bottom 22. The of calculated the cell, the spatial horizontal distribution stripes of ofthe pressure acoustic antinodes amplitude and for nodesthe resonance are parallel liquid as heightshown (13.875 in Figure cm) and 22[ the66]. antiresonance When the vibration one (14.25 frequency cm) for the of rigid the vibratingwall [66]. The plate bottom is 100 plate kHz, the liquid height of 13.875 cm and 14.25 cm correspond to resonance and antiresonance, respectively. For the both cases, the liquid surface is pressure node. For the resonance case, the surface of the vibrating plate coincides with pressure antinode, while it coincides with pressure node for the antiresonance case. Molecules 2021, 26, x FOR PEER REVIEW 21 of 36

as shown in Figure 22 [66]. When the vibration frequency of the vibrating plate is 100 kHz, the liquid height of 13.875 cm and 14.25 cm correspond to resonance and antiresonance, respectively. For the both cases, the liquid surface is pressure node. For the resonance case, the surface of the vibrating plate coincides with pressure antinode, while it coincides with pressure node for the antiresonance case. When the glass side wall is thin (2 mm thick), the surface of the thin side wall nearly coincides with vertical pressure node as seen in Figure 23 because it is nearly a free surface [66].

Figure 21. The calculated spatial distribution of the acoustic amplitude for glass wall (7 mm in thickness) for various attenuation coefficients of ultrasound [66]. The full-width at half maximum for the Gaussian distribution of the vibration amplitude of the vibrating plate at the bottom is 5 cm. The wall height is 20 cm. A half of the width (the full width is 7 cm) of the liquid container is shown. Molecules 2021, 26, 4624 The photograph of sonochemiluminescence from an aqueous luminol solution is also shown for the 20 of 34 corresponding half plane. Copyright 2007, with the permission from Elsevier.

Figure 22.Figure The 22.calculatedThe calculated spatial spatialdistribution distribution of the of acoustic the acoustic amplitude amplitude for forthe the resonance resonance liquid liquid height height (13.875(13.875 cm) cm) and and the the antiresonance antiresonance one one (14.25 (14.25 cm) cm) for for the the rigid wall [[66].66]. TheThe bottombottom plateplate vibrates Molecules 2021, 26, x FOR PEER REVIEW spatially uniformly. The attenuation coefﬁcient is 5 m−1. Copyright 2007, with the22 permission of 36

from Elsevier.

vibrates spatiallyWhen the uniformly. glass side Th walle attenuation is thin (2 coefficient mm thick), is 5 them−1. surface Copyright of the2007, thin with side the wall permis- nearly sioncoincides from Elsevier. with vertical pressure node as seen in Figure 23 because it is nearly a free surface [66].

Figure 23. The calculated spatial distribution of the acoustic amplitude for glass wall of 2 mm − Figurein thickness23. The calculated [66]. The spatial attenuation distribution coefﬁcient of the isacoustic 5 m 1 .amplitude Copyright for 2007, glass with wall theof 2 permissionmm in thicknessfrom Elsevier.[66]. The attenuation coefficient is 5 m−1. Copyright 2007, with the permission from Else- vier. Spatial distribution of MBSL intensity strongly depends on dissolved air concentration inSpatial water distribution as shown in of Figure MBSL 24 intensity[ 59]. In Figurestrongly 24 depends, the dissolved on dissolved oxygen air concentration concentra- is tionshown in water as as an shown indicator in Figure of dissolved 24 [59]. air In concentration.Figure 24, the dissolved For air saturated oxygen concentration water irradiated is shownwithultrasound as an indicator of 448 of dissolved kHz and 1.1air conc W/cmentration.2, the spatial For air distribution saturated water of MBSL irradiated intensity withis ultrasound localized near of 448 the kHz liquid and surface 1.1 W/cm as shown2, the spatial in Figure distribution 24a. At the ofoxygen MBSL intensity concentration is localizedof 4.2 near mg/L, the which liquid correspondssurface as shown to about in Figure 50% in24a. degree At the of oxygen air saturation, concentration the spatial of 4.2 mg/L,distribution which ofcorresponds MBSL intensity to about is nearly 50% in uniform degree insideof air saturation, the liquid asthe shown spatial in distribu- Figure 24d. tionFor of evenMBSL lower intensity oxygen is nearly concentrations, uniform inside MBSL intensitythe liquid gradually as shown diminishes. in Figure 24d. For even lower oxygen concentrations, MBSL intensity gradually diminishes. What is the reason for the dependence of the spatial distribution of MBSL on dissolved air concentration? For air saturated water, there are many visible large bubbles in the liquid under ultrasound. For the degree of air saturation of about 50%, there are very few visible large bubbles in the liquid. It suggests that visible large bubbles cause Ander- son localization of an acoustic wave (ultrasonic wave) and that consequently spatial distribution of acoustic amplitude becomes strongly inhomogeneous [67]. It may result in the spatially inhomogeneous distribution of MBSL intensity in the presence of visible large bubbles. Further studies are required on this topic. Under the pulsed ultrasound irradiation, spatial distribution of MBSL intensity strongly depends on pulse-off time under a fixed pulse-on time as shown in Figure 25 [59]. For a very short pulse-off time, the spatial distribution of MBSL intensity is localized near the liquid surface as shown in Figure 25f. For the pulse-off time of 110 ms under fixed pulse-on time of 5 ms at 448 kHz, the spatial distribution of MBSL intensity is nearly homogeneous as shown in Figure 25i. Further increase in pulse-off time results in diminishing of MBSL intensity as shown in Figure 25j. As in the case of dissolved air concentration, this behavior is related to the presence and absence of visible large bubbles in the liquid. For a very short pulse-off time of 1.5 ms in Figure 25f, there are many visible large bubbles in the liquid. On the other hand, for the pulse-off time of 110 ms, there are very few visible large bubbles in the liquid. It may result in the less Anderson localization of an acoustic wave and nearly spatially homogeneous distribution of MBSL.

Molecules 2021, 26, x FOR PEER REVIEW 23 of 36

Molecules 2021, 26, 4624 21 of 34

Figure 24. Images showing the effect of dissolved oxygen concentration on the MBSL structure taken from the side of the vessel: (a) 8.5, (b) 7.0, (c) 5.6, (d) 4.2, (e) 3.4, and (f) 2.9 mg/L [59]. The white Figuredotted 24. Images lines above showing and below the effect the MBSLof dissolved structure oxygen denotes concentration the liquid surface on the and MBSL the structure transducer taken fromposition, the side respectively. of the vessel: Continuous (a) 8.5, ( sonicationb) 7.0, (c)at 5.6, a frequency (d) 4.2, ( ofe) 4483.4,kHz and and (f) a2.9 power mg/L of [59]. 1.1 W/cm The 2white dottedwas lines applied. above Exposure and below time wasthe setMBSL to collect structure 2 × 10 denotes5 acoustic the cycles. liquid The surface center axisand of the the transducer vessel position,is located respectively. on the left Continuous side of the sonication images. Copyright at a frequency 2008, with of 448 the kHz permission and a power from American of 1.1 W/cm2 was Chemicalapplied. Exposure Society. time was set to collect 2 × 105 acoustic cycles. The center axis of the vessel is located on the left side of the images. Copyright 2008, with the permission from American Chemical Society. What is the reason for the dependence of the spatial distribution of MBSL on dissolved air concentration? For air saturated water, there are many visible large bubbles in the liquid under ultrasound. For the degree of air saturation of about 50%, there are very few visible large bubbles in the liquid. It suggests that visible large bubbles cause Anderson localization of an acoustic wave (ultrasonic wave) and that consequently spatial distribution of acoustic amplitude becomes strongly inhomogeneous [67]. It may result in the spatially inhomogeneous distribution of MBSL intensity in the presence of visible large bubbles. Further studies are required on this topic. Under the pulsed ultrasound irradiation, spatial distribution of MBSL intensity strongly depends on pulse-off time under a ﬁxed pulse-on time as shown in Figure 25[59]. For a very short pulse-off time, the spatial distribution of MBSL intensity is localized near the liquid surface as shown in Figure 25f. For the pulse-off time of 110 ms under ﬁxed pulse-on time of 5 ms at 448 kHz, the spatial distribution of MBSL intensity is nearly homogeneous as shown in Figure 25i. Further increase in pulse-off time results in diminishing of MBSL intensity as shown in Figure 25j. As in the case of dissolved air concentration, this behavior is related to the presence and absence of visible large bubbles in the liquid. For a very short pulse-off time of 1.5 ms in Figure 25f, there are many visible large bubbles in the liquid. On the other hand, for the pulse-off time of 110 ms, there are very few visible large bubbles in the liquid. It may result in the less Anderson localization of an acoustic wave and nearly spatially homogeneous distribution of MBSL. Addition of sodium dodecylsulfate (SDS), which is a surfactant, to the liquid water Figurealso 25. changes Images theshowing spatial the distribution effect of increasing of MBSL puls intensitye-off time as shownon the MBSL in Figure structure 26[59]. generatedFor in saturated1 mM SDS water solution, at a frequency spatialdistribution of 448 kHz and of MBSL at a power intensity of 1.1 is W/cm nearly2: uniform(f) 1.5, (g as) 10, shown (h) 40, (i) 110, inand Figure (j) 135 26 b.ms For [59]. 10 The mM pulse-on SDS solution, time was on thefixe otherd at 5 hand, ms. The spatial white distribution dotted lines of MBSLabove and belowintensity the MBSL is localized structure near denotes the liquid the liquid surface surfac as showne and inthe Figure transducer 26c. For posi 1 mMtion,SDS respectively. solution, The centerthere axis are of the very vessel few is visible located large on the bubbles left side in of the the liquid images. because Copyrigh SDSt 2008, strongly with retards the permission the frombubble–bubble American Chemical coalescence Society. which is the main reason for the formation of visible large bubbles. For 10 mM SDS solution, on the other hand, electric negative charge of SDS on the bubbleAddition surface of sodium is neutralized dodecylsulfate by the excess (SDS), number which of positive is a surfactant, ions, which to the results liquid in the water alsobubble–bubble changes the spatial coalescence distribu undertion ultrasound of MBSL and intensity formation as ofshown visible in large Figure bubbles. 26 [59]. As in For 1 the previous cases, Anderson localization of an acoustic wave due to visible large bubbles mM SDS solution, spatial distribution of MBSL intensity is nearly uniform as shown in may be relevant to the spatial distribution of MBSL intensity in aqueous SDS solutions. Figure 26b. For 10 mM SDS solution, on the other hand, spatial distribution of MBSL intensity is localized near the liquid surface as shown in Figure 26c. For 1 mM SDS solution, there are very few visible large bubbles in the liquid because SDS strongly retards the bubble–bubble coalescence which is the main reason for the formation of visible large

Molecules 2021, 26, x FOR PEER REVIEW 23 of 36

Figure 24. Images showing the effect of dissolved oxygen concentration on the MBSL structure taken from the side of the vessel: (a) 8.5, (b) 7.0, (c) 5.6, (d) 4.2, (e) 3.4, and (f) 2.9 mg/L [59]. The white dotted lines above and below the MBSL structure denotes the liquid surface and the transducer position, respectively. Continuous sonication at a frequency of 448 kHz and a power of 1.1 W/cm2 was applied. Exposure time was set to collect 2 × 105 acoustic cycles. The center axis of the vessel is Molecules 2021, 26, 4624 located on the left side of the images. Copyright 2008, with the permission from American Chemical 22 of 34 Society.

Molecules 2021, 26, x FOR PEER REVIEW 24 of 36

Figure 25.Figure Images 25. showingImages showing the effect the of effect increasing of increasing pulse-off pulse-off time on time the onMBSL the MBSLstructure structure generated generated in bubbles. For 10 mM SDS solution, on the other hand, electric negative charge2 of SDS on in saturatedsaturated water water at a frequency at a frequency of 448 of kHz 448 kHzand andat a atpower a power of 1.1 of W/cm 1.1 W/cm2: (f) 1.5,:(f) ( 1.5,g) 10, (g) ( 10,h) 40, (h) ( 40,i) (i) 110, the bubble surface is neutralized by the excess number of positive ions, which results in 110, andand (j) 135 (j) 135 ms ms[59]. [59 The]. The pulse-on pulse-on time time was was fixe ﬁxedd at at5 5ms. ms. The The white white dotted dotted lines lines above above and and below thebelow bubble–bubble thethe MBSL MBSL structure structure coalescence denotes denotes un theder the liquid liquidultrasound surfac surfacee andand and the formation the transducer transducer of posivisible position,tion, large respectively. respectively. bubbles. The The center Ascenter in the axisaxis previous of of the the vessel vesselcases, is islocated Anderson located on on the thelocalization left left side side of ofthe of the images.an images. acoustic Copyrigh Copyright wavet 2008, due 2008, with to with visible the the permission permissionlarge from bubblesfrom American mayAmerican be Chrelevant Chemicalemical toSociety. Society.the spatial distribution of MBSL intensity in aqueous SDS solutions. Addition of sodium dodecylsulfate (SDS), which is a surfactant, to the liquid water also changes the spatial distribution of MBSL intensity as shown in Figure 26 [59]. For 1 mM SDS solution, spatial distribution of MBSL intensity is nearly uniform as shown in Figure 26b. For 10 mM SDS solution, on the other hand, spatial distribution of MBSL intensity is localized near the liquid surface as shown in Figure 26c. For 1 mM SDS solution, there are very few visible large bubbles in the liquid because SDS strongly retards the bubble–bubble coalescence which is the main reason for the formation of visible large

Figure 26. Figure 26. Images showingImages the showing effect of the SDS effect on the of MBSL SDS on structure the MBSL generated structure at generateda frequency at of a 448 frequency of 2 kHz and at448 a power kHz and of 1.1 at aW/cm power2: ( ofa) 1.1water, W/cm (b) 1:( mMa) water, SDS, (andb) 1 ( mMc) 10 SDS, mM andSDS ([59].c) 10 Exposure mM SDS [time59]. Exposure 5 was set to timecollect was 2 × set105 toacoustic collect cycles. 2 × 10 Theacoustic white cycles.dotted line Thes whiteabove dottedand below lines the above MBSL and structure below the MBSL denotes thestructure liquid surface denotes and the the liquid transducer surface andposition, the transducer respectively. position, The center respectively. axis of the The vessel center is axis of the located onvessel the left is side located of the on images. the left Copyright side of the 2008, images. with Copyright the permission 2008, with from the American permission Chemical from American Society. Chemical Society.

7. MBSL 7.Quenching MBSL Quenching It has beenIt hasexperimentally been experimentally reported reportedthat MBSL that is almost MBSL iscompletely almost completely quenched quenched above above the thresholdthe threshold acoustic acousticpower as power shown as shownin Figure in Figure 27 [68]. 27[ Initially,68]. Initially, MBSL MBSL intensity intensity in- increases creases asas acoustic acoustic power power increases. increases. However, However, above above the the threshold, threshold, MBSL MBSL is almost is almost com- completely pletely quenched.quenched. There There is isa adistinct distinct differe differencence between between the the cavitating cavitating liquid liquid below below and and above above thethe MBSL MBSL quenching quenching threshold threshold by byvisual visual observation observation as shown as shown in Figure in Figure 28 [68].28[ 68]. Just Just below the MBSL quenching threshold shown in Figure 28a, most of the cavitation bubbles are seen near the side wall of the liquid container like smokes or filaments. On the other hand, above the MBSL quenching threshold shown in Figure 28b, white “particles” larger than 1 mm are seen almost spatially uniformly inside the liquid. The “particles” move around in the liquid. The “particles” are probably clusters of bubbles shown in Figure 29 [68]. Thus, the formation of the bubble clusters may be one of the reasons for the MBSL quenching. The bubble cluster is probably a dynamic object such that bubbles in the cluster frequently coalesce each other by secondary Bjerknes force and that the coalesced bubbles subsequently disintegrate into daughter bubbles [19]. It is suggested that bubbles in the bubble clusters are inactive in MBSL. Further studies are required on the dynamics of bubble clusters.

Molecules 2021, 26, 4624 23 of 34

below the MBSL quenching threshold shown in Figure 28a, most of the cavitation bubbles are seen near the side wall of the liquid container like smokes or ﬁlaments. On the other hand, above the MBSL quenching threshold shown in Figure 28b, white “particles” larger than 1 mm are seen almost spatially uniformly inside the liquid. The “particles” move around in the liquid. The “particles” are probably clusters of bubbles shown in Figure 29[68]. Thus, the formation of the bubble clusters may be one of the reasons for the Molecules 2021, 26, x FOR PEER REVIEW 25 of 36 MBSL quenching. The bubble cluster is probably a dynamic object such that bubbles in the Molecules 2021, 26, x FOR PEER REVIEW cluster frequently coalesce each other by secondary Bjerknes force and that25 theof 36 coalesced bubbles subsequently disintegrate into daughter bubbles [19]. It is suggested that bubbles in the bubble clusters are inactive in MBSL. Further studies are required on the dynamics of bubble clusters.

Figure 27. Dependence of MBSL intensity on FG output at 132.2 kHz and changes of power input Figure 27. to the transducerDependence [68]. Reprinted of MBSL from intensity Ultrasonics, on FGoutput vol. 40, at S. 132.2 Hatanaka, kHz and K. changes Yasui, ofT. powerKozuka, input T. to Figure 27. Dependence of MBSL intensity on FG output at 132.2 kHz and changes of power input Tuziuti,the transducer and H. Mitome, [68]. Reprinted Influence from of bubble Ultrasonics, clustering vol. on 40, mult S. Hatanaka,ibubble sonoluminescence, K. Yasui, T. Kozuka, pp. T. 655– Tuziuti, to the transducer [68]. Reprinted from Ultrasonics, vol. 40, S. Hatanaka, K. Yasui, T. Kozuka, T. 660,and Copyright H. Mitome, 2002, Inﬂuencewith the permission of bubble clusteringfrom Elsevier. on multibubble sonoluminescence, pp. 655–660, Tuziuti, and H. Mitome, Influence of bubble clustering on multibubble sonoluminescence, pp. 655– Copyright 2002, with the permission from Elsevier. 660, Copyright 2002, with the permission from Elsevier.

Figure 28. Photographs of cavitation bubbles at 132.2 kHz for the FG outputs of (a) 400 mVp-p and Figure 28. Photographs of cavitation bubbles at 132.2 kHz for the FG outputs of (a) 400 mVp-p and (b) 450 mVp-p taken with a still camera with 33 ms exposure [ 68]. Reprinted from Ultrasonics, vol. (b) 450 mVp-p taken with a still camera with 33 ms exposure [68]. Reprinted from Ultrasonics, vol. Figure 28.40, Photographs S. Hatanaka, of K.cavitation Yasui, T. bubbles Kozuka, at T. 132.2 Tuziuti, kHz and for H.the Mitome, FG outputs Inﬂuence of (a) of400 bubble mVp-p clusteringand on 40, S. Hatanaka, K. Yasui, T. Kozuka, T. Tuziuti, and H. Mitome, Influence of bubble clustering on (b) 450 mVmultibubblep-p taken with sonoluminescence, a still camera with pp. 33 655–660, ms exposu Copyrightre [68]. 2002, Reprinted withthe from permission Ultrasonics, from vol. Elsevier. multibubble sonoluminescence, pp. 655–660, Copyright 2002, with the permission from Elsevier. 40, S. Hatanaka, K. Yasui, T. Kozuka, T. Tuziuti, and H. Mitome, Influence of bubble clustering on multibubble sonoluminescence, pp. 655–660, Copyright 2002, with the permission from Elsevier.

Molecules 2021, 26, x FOR PEER REVIEW 26 of 36

Molecules 2021, 26, x FOR PEER REVIEW 26 of 36 Molecules 2021, 26, 4624 24 of 34

Figure 29. A bubble cluster observed at 23 kHz for the FG output of 1500 mVp-p which is almost above the threshold for

the MBSL quenching [68]. Copyright 2002, with the permission from Elsevier. Figure 29. A bubble cluster observed at 23 kHz for the FG output of 1500 mVp-p which is almost Figure 29. A bubble cluster observed at 23 kHz for the FG output of 1500 mVp-p which is almost above the threshold for above the threshold for the MBSL quenching [68]. Copyright 2002, with the permission from Elsevier. the MBSL quenchingAnother [68]. Copyright mechanism 2002, forwith MBSL the permission quenching from is Elsevier.the repulsion of bubbles from pressure antinodes byAnother primary mechanism Bjerknes force for MBSL at excess quenchingive acoustic is the power repulsion as shown of bubbles in Figures from pressure30 Another mechanism for MBSL quenching is the repulsion of bubbles from pressure and 31antinodes [5,44,45,69]. by Initially, primary the Bjerknes MBSL force intensity at excessive increases acoustic as acoustic power power as shown increases. in Figures It 30 antinodes by primary Bjerknes force at excessive acoustic power as shown in Figures 30 correspondsand 31 to[ 5 the,44, 45photographs,69]. Initially, of cavitation the MBSL bu intensitybbles from increases (c) to (f) as acousticin Figure power 31. From increases. (g) It and 31 [5,44,45,69]. Initially, the MBSL intensity increases as acoustic power increases. It to (j) incorresponds Figure 31, the to theMBSL photographs intensity decreases of cavitation as acoustic bubbles power from (c)increase to (f) inas Figure shown 31 in. From corresponds to the photographs of cavitation bubbles from (c) to (f) in Figure 31. From (g) Figure(g) 30. toAs (j) seen in Figure in Figure 31, 31g–j, the MBSL cavitati intensityon bubbles decreases are gradually as acoustic repelled power from increase the pres- as shown to (j) in Figure 31, the MBSL intensity decreases as acoustic power increase as shown in sure antinodein Figure as 30 acoustic. As seen power in Figure increases. 31g–j, cavitationThis is an bubbles important are graduallyreason for repelled the MBSL from the Figure 30. As seen in Figure 31g–j, cavitation bubbles are gradually repelled from the pres- quenching.pressure Indeed, antinode by stirring as acoustic the liquid, power the increases. MBSL quenching This is an is importantconsiderably reason suppressed for the MBSL sure antinode as acoustic power increases. This is an important reason for the MBSL as shownquenching. in Figure Indeed, 32a [70]. by stirringIn Figure the 32b, liquid, the thequenching MBSL quenching behavior is considerablyshown for SCL suppressed in quenching. Indeed, by stirring the liquid, the MBSL quenching is considerably suppressed aqueousas shownluminol in solution. Figure 32 Althougha [70]. In the Figure quench 32b,ing the of quenching SCL and that behavior of MBSL is shown is similar, for SCL in as shown in Figure 32a [70]. In Figure 32b, the quenching behavior is shown for SCL in there isaqueous some difference luminol between solution. them Although probab thely because quenching the ofthreshold SCL and acoustic that of amplitude MBSL is similar, aqueous luminol solution. Although the quenching of SCL and that of MBSL is similar, for SCLthere is smaller is some than difference that for between MBSL [43,62]. them probably Further studies because are the required threshold on acoustic this topic. amplitude for SCLthere is smaller is some than difference that for between MBSL [them43,62 ].probab Furtherly because studies arethe requiredthreshold on acoustic this topic. amplitude for SCL is smaller than that for MBSL [43,62]. Further studies are required on this topic.

Figure 30. Dependence of MBSL intensity on FG output at 23 kHz and changes of power input to the Figure 30. Dependence of MBSL intensity on FG output at 23 kHz and changes of power input to

the transducerstransducers [69]. [69 Copyright]. Copyright 2001, 2001, with with the thepermission permission from from IOP IOP Publishing. Publishing. Figure 30. Dependence of MBSL intensity on FG output at 23 kHz and changes of power input to the transducers [69]. Copyright 2001, with the permission from IOP Publishing.

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Molecules 2021, 26, x FOR PEER REVIEW 27 of 36 Molecules 2021, 26, 4624 25 of 34

Figure 31. Photographs of cavitation bubbles taken with the still camera with the exposure of 2 ms at 23 kHz for the FG outputs of (a) 100, (b) 200, (c) 300, (d) 500, (e) 600, (f) 700, (g) 900, (h) 1000, (i) Figure 31. Photographs of cavitation bubbles taken with the still camera with the exposure of 2 ms at 1100, and (j) 1200 mVp-p, respectively [69]. Copyright 2001, with the permission from IOP Publish- ing. 23 kHz for the FG outputs of (a) 100, (b) 200, (c) 300, (d) 500, (e) 600, (f) 700, (g) 900, (h) 1000, (i) 1100, Figure 31. Photographs of cavitation bubbles taken with the still camera with the exposure of 2 ms Molecules 2021, 26, x FOR PEER REVIEW and (j) 1200 mV , respectively [69]. Copyright 2001, with the permission from IOP28 Publishing.of 36 at 23 kHz for the FGp-p outputs of (a) 100, (b) 200, (c) 300, (d) 500, (e) 600, (f) 700, (g) 900, (h) 1000, (i) 1100, and (j) 1200 mVp-p, respectively [69]. Copyright 2001, with the permission from IOP Publish- ing. instantaneous local pressure is different between the solid or liquid surface side and the other side of the bubble surface [75–77]. Due to jetting, Na atoms enter bubbles. Furthermore, the bubble temperature decreases by jetting, which may result in weaker continuum emission from jetting bubbles [74]. Thus, Na-line-emitting bubbles (orange light) may not emit continuum component (blue light). MBSL spectra from 1 M and 3 M NaCl aqueous solutions saturated with Ar are shown in Figure 35 as well as that from pure water saturated with Ar [78]. The continuum Figure 32. Dependence of intensities of sonoluminescence (SL) (a) and sonochemiluminescence (SCL) component of MBSL as well as OH-line emission in NaCl aqueous solutions is stronger (b) on power input at 99 kHz for various rotational speeds of stirrer [70]. Copyright 2006, with than that from pure water. There are two factors on the role of the salt (NaCl). One is the Figurepermission 32. Dependence from Elsevier. of intensities of sonoluminescence (SL) (a) and sonochemiluminescence retardation(SCL) (b )of on bubble–bubble power input at 99 coalescence, kHz for various which rotational results speeds in the of increase stirrer [70]. in Copyrightnumber of 2006, ac- with tive permissionbubbles8. Na-Line and from decrease EmissionElsevier. in number of visible large bubbles [5,79]. The other is the de- + crease Figureof gas MBSLsolubility,32. Dependence in aqueous which of results intensities solution in the containingof decreasesonoluminescence Nain theions total (SL) often amount (a) exhibitsand of sonochemiluminescence bubbles Na-line in emissionthe at liquid8. (SCL)Na-Lineand590 the ( nmb) increaseon Emission in power wavelength ininput the at standing-waveas 99 shownkHz for invarious Figure component rotational1 as orange speedsof an light ultrasonic of stirrer [ 3,71 ].[70]. Aswave Copyright seen [78]. in FigureFur- 2006, 1with, the ther studiespermissionorangeMBSL are regionsinrequired from aqueous Elsevier. (Na-line on solution the mechanism emitting containing regions) of MBSL Na+ are ions enhancement different often exhibits from in the NaCl Na-line blue aqueous regions emission solu- (continuum at 590 tions.nm emittingin wavelength regions) as asshown proved in Figure in Figure 1 as 33 or[ 56ange]. In light other [3,71]. words, As cavitationseen in Figure bubbles 1, the which orange8. emitNa-Line regions the Na-line Emission (Na-line are differentemitting fromregions) those are which different emit from continuum the blue component regions (continuum [72]. emittingMBSL regions) in aqueous as proved solution in Figure containing 33 [56]. Na In+ ions other often words, exhibits cavitation Na-line bubbles emission which at 590 emitnm the in Na-linewavelength are different as shown from in Figure those which 1 as or emitange continuum light [3,71]. component As seen in [72]. Figure 1, the orangeThe Na-lineregions emission(Na-line emittingin MBSL regions) originate are from different the gas from phase the insideblue regions bubbles (continuum because theemitting detailed regions) structure as of proved Na-line in strongly Figure 33 de [56].pends In on other the gaswords, species cavitation inside bubblesbubbles suchwhich as emitCO2 the[3]. Na-lineFor the Na-lineare different emission from from thos ethe which gas phaseemit continuum inside bubbles, component Na atoms [72]. should enter bubblesThe Na-line by liquid emission jets because in MBSL Na +originate ions are nonvolatile.from the gas In phase other insidewords, bubbles Na-line because emit- tingthe bubbles detailed are structure nonsph ericalof Na-line jetting strongly bubbles. de pends on the gas species inside bubbles such as COThere2 [3]. are For mainly the Na-line three mechanisms emission from in jettingthe gas of phase bubbles inside [5]. bubbles,One is the Na simultaneous atoms should collapseenter bubbles of a pair by of liquid bubbles jets as because shown Na in +Figure ions are 34 nonvolatile. [73]. This is In also other called words, bubble–bubble Na-line emit- interaction.ting bubbles The are reason nonsph forerical the jetting jetting is bubbles. the difference of instantaneous local pressure between theThere outer are andmainly inner three sides mechanisms of the bubble in jettingsurface. of Another bubbles is[5]. the One bubble is the collapse simultaneous in a traveling-wavecollapse of a pair ultrasound of bubbles [74]. as In shown a trave inling-wave Figure 34 ultrasound, [73]. This is the also instantaneous called bubble–bubble acous- ticinteraction. pressure is Thedifferent reason betw for eenthe jettingultrasound is the incoming difference and of instantaneousoutgoing sides local on thepressure bubble be- surface.tween theThe outer other and is innerthe bubble sides ofcollapse the bubble near su arface. solid Another or liquid is thesurface bubble because collapse the in a traveling-wave ultrasound [74]. In a traveling-wave ultrasound, the instantaneous acous- ticFigure pressure 33. MBSLis different spectra betw in theeen orange ultrasound region incoming below the and pressure outgoing node andsides the on blue-white the bubble one Figure 33. MBSL spectra in the orange region below the pressure node and the blue-white one around the pressure antinode [56]. Copyright 2010, The Japan Society of Applied Physics. aroundsurface. the pressure The antinode other is [56]. the Copyrigh bubblet 2010,collapse The Japannear Societya solid of or Applied liquid Physics. surface because the

Molecules 2021, 26, x FOR PEER REVIEW 28 of 36

instantaneous local pressure is different between the solid or liquid surface side and the other side of the bubble surface [75–77]. Due to jetting, Na atoms enter bubbles. Furthermore, the bubble temperature decreases by jetting, which may result in weaker continuum emission from jetting bubbles [74]. Thus, Na-line-emitting bubbles (orange light) may not emit continuum component (blue light). MBSL spectra from 1 M and 3 M NaCl aqueous solutions saturated with Ar are shown in Figure 35 as well as that from pure water saturated with Ar [78]. The continuum component of MBSL as well as OH-line emission in NaCl aqueous solutions is stronger than that from pure water. There are two factors on the role of the salt (NaCl). One is the retardation of bubble–bubble coalescence, which results in the increase in number of active bubbles and decrease in number of visible large bubbles [5,79]. The other is the decrease of gas solubility, which results in the decrease in the total amount of bubbles in the liquid and the increase in the standing-wave component of an ultrasonic wave [78]. Fur- ther studies are required on the mechanism of MBSL enhancement in NaCl aqueous solutions.

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The Na-line emission in MBSL originate from the gas phase inside bubbles because the detailed structure of Na-line strongly depends on the gas species inside bubbles such as CO2 [3]. For the Na-line emission from the gas phase inside bubbles, Na atoms should enter bubbles by liquid jets because Na+ ions are nonvolatile. In other words, Na-line emitting bubbles are nonspherical jetting bubbles. There are mainly three mechanisms in jetting of bubbles [5]. One is the simultaneous collapse of a pair of bubbles as shown in Figure 34[ 73]. This is also called bubble–bubble interaction. The reason for the jetting is the difference of instantaneous local pressure between the outer and inner sides of the bubble surface. Another is the bubble collapse in a traveling-wave ultrasound [74]. In a traveling-wave ultrasound, the instantaneous acoustic pressure is different between ultrasound incoming and outgoing sides on the Figure 33. MBSL spectra in the orange region below the pressure node and the blue-white one bubble surface. The other is the bubble collapse near a solid or liquid surface because the around the pressure antinode [56]. Copyright 2010, The Japan Society of Applied Physics. instantaneous local pressure is different between the solid or liquid surface side and the other side of the bubble surface [75–77].

Due to jetting, Na atoms enter bubbles. Furthermore, the bubble temperature decreases by jetting, which may result in weaker continuum emission from jetting bubbles [74]. Thus, Na-line-emitting bubbles (orange light) may not emit continuum component (blue light). MBSL spectra from 1 M and 3 M NaCl aqueous solutions saturated with Ar are shown in Figure 35 as well as that from pure water saturated with Ar [78]. The continuum component of MBSL as well as OH-line emission in NaCl aqueous solutions is stronger than that from pure water. There are two factors on the role of the salt (NaCl). One is the retardation of bubble–bubble coalescence, which results in the increase in number of active bubbles and decrease in number of visible large bubbles [5,79]. The other is the decrease of gas solubility, which results in the decrease in the total amount of bubbles in the liquid and the increase in the standing-wave component of an ultrasonic wave [78]. Further studies are required on the mechanism of MBSL enhancement in NaCl aqueous solutions. Molecules 2021, 26, x FOR PEER REVIEW 29 of 36

Molecules 2021, 26, 4624 Figure 34. Comparison between experiment and simulation of the cavitation of two bubbles initially 27 of 34 separated by 400 μm [73]. Copyright 2006, with the permission of AIP Publishing.

FigureFigure 35. 35.MeasuredMeasured MBSL MBSL spectra spectra under Ar under flow, Ar in ﬂow,water inand water in 1 M and and in 31 M M NaCl and aqueous 3 M NaCl aqueous ◦ solutionssolutions (362 (362 kHz, kHz, 43 W, 43 10 W, °C) 10 [78].C) Copyright [78]. Copyright 2019, with 2019, permission with permission from Elsevier. from Elsevier.

9. Ultrafine9. Ultrafine Bubbles Bubbles CavitationCavitation threshold, threshold, which is which the threshol is thed threshold acoustic amplitude acoustic for amplitude generation forof cav- generation of itationcavitation bubbles, bubbles, decreases decreases by the presence by the of presence cavitation of nuclei cavitation such as nuclei solid particles such as and solid particles tinyand gas tiny bubbles gas bubbles[5,80,81]. [In5, 80other,81]. words, In other MBSL words, can be MBSL enhanced can beby enhancedthe addition by of the an addition of appropriatean appropriate number number of solid particles of solid particlesor tiny gas or bubbles tiny gas to the bubbles liquidto [82]. the liquid [82]. UltrafineUltrafine bubbles bubbles or bulk or nanobubbles bulk nanobubbles are defi arened definedas gas bubbles as gas smaller bubbles than smaller 1 μm than 1 µm in indiameter diameter [83,84]. [83 ,It84 is]. currently It is currently a hot topic a hot because topic because ultrafineultrafine bubbles are bubbles commercially are commercially usedused in bathing, in bathing, cleaning, cleaning, washing washing machines, machines, plant cultivation, plant cultivation, etc. [84] Ultrafine etc. [84 ]bubbles Ultrafine bubbles are usually produced by hydrodynamic cavitation such as using Venturi tube, swirling are usually produced by hydrodynamic cavitation such as using Venturi tube, swirling flow, injection of pressurized water containing gas, etc. [84] Initially, the liquid water is flow, injection of pressurized water containing gas, etc. [84] Initially, the liquid water milky because it contains a lot of microbubbles. In a few minutes after stopping the production,is milky most because of microbubbles it contains disappear a lot of at microbubbles.the liquid surface In by a buoyancy. few minutes Some after of mi- stopping the crobubblesproduction, are stabilized most of as microbubbles ultrafine bubbles disappear if the surface at the of liquida bubble surface is partly by covered buoyancy. Some withof hydrophobic microbubbles impurities are stabilized [85]. Ultrafine as ultrafine bubbles bubblesare stable if for the a few surface months of aor bubblemore is partly [86].covered They are with confirmed hydrophobic as gas bubbles impurities by their [85 ].disappearance Ultrafine bubbles after freeze-thaw are stable process for a few months [86].or more [86]. They are confirmed as gas bubbles by their disappearance after freeze-thaw processHata et [ 86al.]. [82] experimentally reported that MBSL intensity increased by the addition of ultrafineHata et al.bubbl [82es] experimentallyof about 100 nm reported in diameter that with MBSL the intensitynumber concentration increased by of the addition aboutof ultrafine 106 mL−1. bubblesFurther studies of about are 100required nm in on diameter this topic. with the number concentration of about 106 mL−1. Further studies are required on this topic. 10. Brightest MBSL 10.MBSL Brightest from water MBSL saturated with air is very weak in intensity and very hard to see even in a dark room although it is easily observable by a photographic camera [62]. MBSL MBSL from water saturated with air is very weak in intensity and very hard to see from water saturated with Ar is stronger in intensity and easier to see in a dark room [87]. even in a dark room although it is easily observable by a photographic camera [62]. MBSL However, it is still too weak to see in an illuminated room. On the other hand, MBSL from from water saturated with Ar is stronger in intensity and easier to see in a dark room [87]. Xe in concentrated sulfuric acid (H2SO4) is so bright that it is observable with naked eyes evenHowever, in an illuminated it is still tooroom weak [2,55–57]. to see in an illuminated room. On the other hand, MBSL from XeKappus in concentrated et al. [88] sulfuricexperimentally acid (H reported2SO4) is sothat bright a Xe thatbubble it is in observable phosphoric with acid naked eyes (Heven3PO4), inwhich an illuminated has relatively room low saturated [2,55–57 vapor]. pressure, emitted 150 ns flash of broad- band lightKappus that exceeded et al. [10088] W experimentally in peak intensity reportedby the impact that of aa steel Xe bubble cylinder in in phosphoricwhich acid a Xe(H bubble3PO4), was which introduced has relatively against lowa solid saturated steel base. vapor pressure, emitted 150 ns flash of broad- band light that exceeded 100 W in peak intensity by the impact of a steel cylinder in which a Xe bubble was introduced against a solid steel base. Numerically, the SL intensity is predicted to exceed 60 W from a Xe bubble in mercury, which has four orders of magnitude lower saturated vapor pressure than that of water, as shown in Figure 36 using the theoretical model described in Section2[ 42]. The bight SL from a Xe bubble is due both to lower ionization potential and lower thermal conductivity than those of other gases [42]. Lower ionization potential results in higher concentration of free electrons and consequently brighter SL due to stronger light emissions from plasma. Molecules 2021, 26, x FOR PEER REVIEW 30 of 36

Numerically, the SL intensity is predicted to exceed 60 W from a Xe bubble in mercury, which has four orders of magnitude lower saturated vapor pressure than that of water, as shown in Figure 36 using the theoretical model described in Section 2 [42]. The bight SL from a Xe bubble is due both to lower ionization potential and lower thermal conductivity than those of other gases [42]. Lower ionization potential results in higher concentration of free electrons and consequently brighter SL due to stronger light emissions from plasma. Lower thermal conductivity results in higher bubble temperature and consequently the stronger light emissions from plasma. Molecules 2021, 26, 4624 MBSL intensity is determined not only by the light intensity from a bubble but also 28 of 34 by number of active bubbles in SL. The number of active bubbles in MBSL has not yet been fully studied either experimentally or theoretically [89–91]. Further studies are required on the brightest MBSL. Lower thermal conductivity results in higher bubble temperature and consequently the stronger light emissions from plasma.

(a)

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(b)

(c)

FigureFigure 36. The 36.resultThe of resultnumerical of numerical simulation simulation for a Xe bubble for ain Xe mercury bubble as in a mercuryfunction of as time a function for of time for 200 ns near the end of the bubble collapse (R0 = 10 μm, S = 105 m−1) [42]. (a) The bubble radius (dotted 200 ns near the end of the bubble collapse (R = 10 µm, S = 105 m−1)[42]. (a) The bubble radius line) and the temperature inside a bubble (solid line). (b) The0 number of atoms (ions) inside a bubble with logarithmic(dotted line) vertical and theaxis. temperature (c) The SL intensity inside a bubble(solid line) (solid and line). its time (b) Theintegral number (dotted of atomsline). (ions) inside a Copyrightbubble 2012, with with logarithmic permission by vertical the American axis. ( cPhysical) The SL Society. intensity (solid line) and its time integral (dotted line). Copyright 2012, with permission by the American Physical Society. 11. Applications of MBSL MBSL has been used to visualize an acoustic field through the spatial distribution of active bubbles in SL especially in studies on ultrasonic cleaning, sonochemical reactors, and medical applications such as cancer treatment using high-intensity focused ultrasound (HIFU) [59–62,92,93]. In the medical applications [92–95], MBSL is used to obtain the information on the existence of inertial cavitation bubbles (active bubbles in SL). In sonodynamic therapy in which certain classes of drug can be activated by ultrasound, it has been suggested that MBSL light activates photosensitive drug [96,97]. Fur- ther studies are required on this topic. From the spectra of MBSL, various information on the physical and chemical nature of the bubble interior can be obtained such as the bubble temperature and pressure, chemical species present inside a bubble, etc. [7,8,46,55,98–103] Another interesting application of MBSL as well as SCL is installation art by modern artists [104].

12. New Development and Unsolved Problems Cairos and Mettin [105] experimentally reported that bubbles that develop a liquid jet during collapse can flash intensely by high-speed recording in xenon saturated phosphoric acid. Yu et al. [106] performed numerical simulations of bubble collapse near a rigid wall and reported the spatial distribution of temperature inside a jetting bubble. Fur- ther studies are required on SL intensity from a jetting bubble including Na-line emission as well as its pulse width [107]. Lee and Choi [108] experimentally reported that a SBSL bubble is positively charged although a microbubble in the absence of ultrasound is negatively charged for pH > 4 [109–111]. They suggested that local pH near the wall of a SBSL bubble is lower than 4 because nitrite and nitrate ions are formed by chemical reactions of nitrogen inside a bubble. Further studies are required on this topic including polarization of the liquid under the pressure gradient (flexoelectric effect, which is different from that in solid crystals [112,113]) and temperature gradient (thermoelectric effect) [112].

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MBSL intensity is determined not only by the light intensity from a bubble but also by number of active bubbles in SL. The number of active bubbles in MBSL has not yet been fully studied either experimentally or theoretically [89–91]. Further studies are required on the brightest MBSL.

11. Applications of MBSL MBSL has been used to visualize an acoustic ﬁeld through the spatial distribution of active bubbles in SL especially in studies on ultrasonic cleaning, sonochemical reactors, and medical applications such as cancer treatment using high-intensity focused ultrasound (HIFU) [59–62,92,93]. In the medical applications [92–95], MBSL is used to obtain the information on the existence of inertial cavitation bubbles (active bubbles in SL). In sonodynamic therapy in which certain classes of drug can be activated by ultrasound, it has been suggested that MBSL light activates photosensitive drug [96,97]. Further studies are required on this topic. From the spectra of MBSL, various information on the physical and chemical nature of the bubble interior can be obtained such as the bubble temperature and pressure, chemical species present inside a bubble, etc. [7,8,46,55,98–103] Another interesting application of MBSL as well as SCL is installation art by modern artists [104].

12. New Development and Unsolved Problems Cairos and Mettin [105] experimentally reported that bubbles that develop a liquid jet during collapse can flash intensely by high-speed recording in xenon saturated phosphoric acid. Yu et al. [106] performed numerical simulations of bubble collapse near a rigid wall and reported the spatial distribution of temperature inside a jetting bubble. Further studies are required on SL intensity from a jetting bubble including Na-line emission as well as its pulse width [107]. Lee and Choi [108] experimentally reported that a SBSL bubble is positively charged although a microbubble in the absence of ultrasound is negatively charged for pH > 4 [109–111]. They suggested that local pH near the wall of a SBSL bubble is lower than 4 because nitrite and nitrate ions are formed by chemical reactions of nitrogen inside a bubble. Further studies are required on this topic including polarization of the liquid under the pressure gradient (flexoelectric effect, which is different from that in solid crystals [112,113]) and temperature gradient (thermoelectric effect) [112]. Boyd et al. [114] numerically suggested that relatively strong UV light is radiated by the interaction of SL light with UV plasmon modes of the metal under the condition of aspherical air bubble collapse near a gallium-based liquid-metal microparticle. This may be applied to disinfecting water contaminated by pathogens such as bacteria and viruses. Further studies are required on this topic. Fernandez Rivas et al. [115] reported MBSL from a microreactor. Further studies are required on this topic including peculiar bubble dynamics in microfluidics [116,117]. Numerical simulations discussed in Sections2–4 are based on the theoretical model of a spherical isolated bubble. Further studies are required on numerical simulations by advanced models applicable to moving and extremely strongly interacting bubbles, nonspherical bubble collapse, splitting/merging processes, liquid sprays into the bubble, collective phenomena like change of speed of sound in a cavitating liquid, nonharmonic pressure fields, nonstationary parameters in the liquid by heating and degassing due to ultrasound irradiation, and uneven bubble distribution. Non-equilibrium plasma should also be considered [37]. In other words, these are the limitations of the theoretical model discussed in Section2. Recently, Liang et al. [ 118] reported numerical simulations of SL spectra from two interacting bubbles. Molecules 2021, 26, 4624 30 of 34

13. Conclusions Active bubbles in MBSL are classified into two categories. One is vaporous bubbles which are mostly filled with water vapor even at the end of the bubble collapse. The other is gaseous bubbles which are mostly filled with noncondensable gases such as air or argon at the end of the bubble collapse. MBSL from vaporous bubbles is by chemiluminescence of OH as well as emissions from weakly ionized plasma such as electron-atom bremsstrahlung. MBSL from gaseous bubbles is by emissions from plasma formed inside a bubble at the end of the collapse such as electron-atom bremsstrahlung and radiative recombination of electrons and positive ions. The plasma formation inside a bubble is due to high bubble temperature and the ionization potential lowering caused by the extremely high density inside a bubble at the end of the bubble collapse. Vaporous bubbles are seen at relatively high acoustic amplitudes at relatively low ultrasonic frequency. A SBSL bubble is a gaseous bubble because acoustic amplitude in SBSL is much lower than the threshold one for repulsion of the primary Bjerkens force. MBSL has been used to visualize an acoustic field through spatial distribution of active bubbles in SL. Spatial distribution of MBSL is strongly influenced by the presence of visible large bubbles, which may be related to Anderson localization of an acoustic wave. Orange light due to Na-line emission in aqueous solution containing Na+ ions origi- nates in jetting bubbles by bubble–bubble interaction or by traveling-wave ultrasound. The brightest MBSL may be from Xe bubbles in sulfuric or phosphoric acid which has relatively low saturated vapor pressure. The application of MBSL in sonodynamic therapy is required to be studied further.

Funding: This research received no external funding. Acknowledgments: The author would like to thank his collaborators in his research: Toru Tuziuti, Wataru Kanematsu, Yasuo Iida, Shin-ichi Hatanaka, Judy Lee, Muthupandian Ashokkumar, Franz Grieser, Kazumi Kato, Teruyuki Kozuka, Atsuya Towata, Hideto Mitome, Sivakumar Manickam, Norio Miyoshi, Devi Sunartio, and others. Conﬂicts of Interest: The author declares no conﬂict of interest.

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