Multibubble Sonoluminescence from a Theoretical Perspective

molecules 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

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