Unsolved Problems in Acoustic Cavitation Kyuichi Yasui Contents Introduction....................................................................................... 2 MainOxidants(OHRadical,H O ,andOAtom).............................................. 3 2 2 OHLineEmissioninSonoluminescence........................................................ 11 AcousticField..................................................................................... 20 ConclusionandFutureDirections................................................................ 30 References........................................................................................ 32 Abstract It has long been believed that the main oxidant created inside a bubble at the bubble collapse in aqueous solutions under strong ultrasound is OH radical. However, numerical simulations of chemical reactions inside an air bubble in waterindicatethatthemainoxidantisnotalwaysOHradicalbutsometimesH O 2 2 orOatom.ThelifetimeofOatominthegas–liquidinterfaceregionis,however, unknown partly due to unknown temperature in the region. It has been experi- mentallyreportedthattheupperlevelsofOHvibrationareoverpopulatedinsidea sonoluminescing bubble compared to the equilibrium Boltzmann distribution from the analysis of OH line spectra in SL. However, the reason is unknown although it could be due to the excitation through chemical reactions. The acousticfieldinsideasonochemicalreactorisalsonotfullyunderstoodbecause bubblesstronglyattenuateultrasoundandradiateacousticwavesintotheliquid. The spatial distribution of bubbles is strongly inhomogeneous. The number density of bubbles temporally changes due to fragmentation, coalescence, and dissolution. The liquid surface vibrates under ultrasound. The vibration of the container’swallalsoaffectstheacousticfieldbecauseacousticwavesareradiated K.Yasui(*) NationalInstituteofAdvancedIndustrialScienceandTechnology(AIST),Nagoya,Japan e-mail:[email protected] #SpringerScience+BusinessMediaSingapore2015 1 M.Ashokkumar(ed.),HandbookofUltrasonicsandSonochemistry, DOI10.1007/978-981-287-470-2_1-1 2 K.Yasui fromthevibratingwalls.Thebubble–bubbleinteractiononpulsationofabubble isalsodiscussed. Keywords Mainoxidant•OHradical•Oatom•H O •OHlineemission•Nonequilibrium 2 2 distribution • Vibration of wall • Ultrasound attenuation • Damped standing wave•Pulsedultrasound•Liquidsurfacevibration•Bubble–bubbleinteraction• Resonancefrequency Introduction Ultrasonics are inaudible sound with its vibration frequency greater than 20 kHz (sometimes, the sound with its vibration frequency greater than 10 kHz is called ultrasonicsforconvenience).Anacousticwave(asoundwave)isapropagationof pressureoscillationinthemediumwiththevelocityofsound(Fig.1)[1].Thesound velocityinliquidwaterisabout1500m/s,whilethatinairisabout340m/s. When a liquid is irradiated by a strong ultrasonic wave, the instantaneous local pressure becomes negative at the rarefaction phase of the ultrasonic wave. The negative pressure is a tension to expand the liquid element, which never occurs in gas phase. When negative pressure occurs in liquid adjacent to a solid surface (especiallyhydrophobicsurface),gasbubblesarecreatedatthesolidsurface(solid surfacecouldbethatofmotesordustparticlesinsolution).Bubblesaremoreeasily created at crevices of the solid, because inside a crevice the gas–liquid interface is concave with regard to the gas phase. Then the Laplace pressure caused by the Fig.1 Anacousticwave(ReprintedwithpermissionfromYasuietal.[1].Copyright(2004)by Taylor&Francis[http://www.informaworld.com]) UnsolvedProblemsinAcousticCavitation 3 surfacetensionreducestheinternalgaspressure.Thusthedissolutionofgasintothe surrounding liquid is strongly retarded, and gas diffuses into the gas pocket in the creviceattherarefactionphaseofultrasoundduetotheexpansionofthegaspocket anddecreaseinthegaspressure[2]. Createdbubblesrepeatexpansionandcollapseaccordingtothepressureoscilla- tionofultrasound.Sometimesthebubblecollapsebecomesveryviolentbecauseof the spherically converging geometry and the inertia of the inwardly moving liquid [2]. The speed of such bubble collapse increases up to the sound velocity in the liquid near the bubble wall [3]. Such the bubble collapse is called the Rayleigh collapse. The creation and collapse of bubbles under ultrasound is called acoustic cavitation. AttheendoftheRayleighcollapse,thetemperatureandpressureinsideabubble dramaticallyincreaseuptoafewthousandKelvinandafewthousandatmospheric pressure or more, respectively. It is because the work done on a bubble by the surrounding liquid during the bubble collapse is mostly converted into the thermal energy inside a bubble as the bubble collapse is so fast that thermal conduction betweentheheatedinteriorofthebubbleandthesurroundingliquidisnotdominant. Asaresult,watervaporandoxygengas(ifpresent)aredissociatedinsidetheheated interiorofabubble.Then,oxidantssuchasOHradicals,Oatoms,H O ,andO are 2 2 3 createdinsideabubble.Theoxidantsdiffuseoutofthebubbleintothesurrounding liquid,andsolutessuchaspollutantsareoxidizedbythem.Suchchemistryiscalled sonochemistry.Inaddition,afaintlightisemittedfromabubbleasapulseduetothe hightemperature,whichiscalledsonoluminescence. In the present chapter, mainly three topics are discussed focusing on unsolved problems in this field. One is the main oxidants created inside a bubble in water. Numericalsimulations haveindicatedthatnotonlyOHradicalsandH O butalso 2 2 an appreciable amount of O atoms are created inside an air bubble. However, the lifetime of O atom in liquid water as well as its role in sonochemical reactions is unknownatpresent.AnotherisOHlineemissioninsonoluminescence.Thetopicis onthenon-BoltzmanndistributionofthevibrationalpopulationofOHradicals.Isit due to the nonequilibrium state of gas inside a bubble? Is it due to chemical excitation of vibrational states of OH radicals? (Is OH line emission originated in chemiluminescence?)Theotherisonanacousticfield.Whatistheinfluenceofthe attenuationofanacousticwaveduetobubblesonanacousticfield?Howaboutthe influenceofacousticradiationfromvibratingwallsofacontainer? Main Oxidants (OH Radical, H O , and O Atom) 2 2 The main oxidant created inside a bubble in water under ultrasound has long been believedasOHradical[4].HerewediscussthatthemainoxidantisnotalwaysOH radicalbutsometimesOatomandH O .InFigs.2and3,theresultsofthenumerical 2 2 simulationofthepulsationofanisolatedsphericalairbubbleinwaterirradiatedwith 300kHzand3-barultrasoundareshown[5].Abubbleexpandsduringtherarefac- tion phase of ultrasound and, violently, collapses during the initial compression 4 K.Yasui 300 kHz, 3 bar, R0=3.5 μm 20 4 15 2 e radius (μm) 10 0 Liquid pressu bl re ub (b B a r ) 5 -2 0 -4 0 1.1 2.2 3.3 Time (μs) Fig.2 Theresultofthenumericalsimulationonradius-timecurveforoneacousticcycle(3.3μs) when the frequency and pressure amplitude of an ultrasonic wave are 300 kHz and 3 bars, respectively.Theambientradiusofanisolatedsphericalairbubbleis3.5μm.Thedottedlineis theacousticpressure(plustheambientpressure)asafunctionoftime(Reprintedwithpermission fromYasuietal.[5].Copyright(2007),AIPPublishingLLC) phase(Fig.2).Attheendofthebubblecollapse(Rayleighcollapse),thetemperature increases up to 5100 K (Fig. 3a). The density at the moment reaches 650 kg/m3 which is in the same order of magnitude as that of the condensed phase (liquid density) (Fig. 3b). The pressure inside a bubble reaches 6 (cid:2) 109 Pa (=6 GPa = 60,000 bar) at the moment. Most of water vapor and many of O are dissociated 2 insidetheheatedinteriorofabubble,andmanychemicalproductsarecreatedsuch asH O ,HO ,O,O ,HNO ,HNO ,H ,andOHradical(Fig.3c).Inthiscase,the 2 2 2 3 2 3 2 mainoxidantisH O accordingtothenumericalsimulation.Inthepresentnumer- 2 2 ical simulations, nonequilibrium effect of chemical reactions is taken into account. Rates of chemical reactions arecalculated using themodifiedArrhenius equations. Ratesofbackwardreactionsarealsocalculated.Thechemicalkineticmodelusedin the present simulations has been partially validated by hydrogen flame studies [6]. Furthermore, the present model of bubble dynamics including the chemical kinetic model has been validated by the study of single-bubble sonochemistry for which direct comparison between the numerical and experimental results is possible[7]. The results of many numerical simulations of chemical reactions inside an air bubble are summarized in Fig. 4 for various ultrasonic frequencies and pressure UnsolvedProblemsinAcousticCavitation 5 Fig.3 TheresultsofthenumericalsimulationundertheconditionofFig.2ataroundtheendofthe bubblecollapse.Thehorizontaltimeaxisisonlyfor0.15μs.(a)Thebubbleradius(dottedline)and thetemperatureinsideabubble(solidline).(b)Thepressure(solidline)andthedensity(dottedline) insideabubblewithlogarithmicverticalaxes.(c)Thenumberofmoleculesinsideabubblewith logarithmicverticalaxes.(ReprintedwithpermissionfromYasuietal.[5].Copyright(2007),AIP PublishingLLC) amplitudes[5].Ratesofproductionofeachoxidantaswellastemperatureinsidean airbubbleareshownasafunctionofacousticamplitude.Theambientbubbleradius, whichisthebubbleradiuswhenultrasoundisabsent,isassumedas5μm,3.5μm, 3.5μm,and1μmfor20kHz,100kHz,300kHz,and1MHz,respectively,asthey arethetypicalvaluesforeachfrequency. For 20 kHz and 100 kHz, the bubble temperature takes a maximum value at relatively low acoustic amplitude and decreases as acoustic amplitude increases at relativelyhighacousticamplitude.Itisbecausetheamountofwatervaporinsidea bubbleincreasesduetolargerexpansionofabubble[3].Watervapordecreasesthe bubble temperature due to its endothermic dissociation as well as its larger molar heatthanthatofair.Thuswecallabubblefilledmostlywithwatervaporavaporous bubble, while a bubble with negligible amount of water vapor is called a gaseous 6 K.Yasui Fig.4 Theresultsofthenumericalsimulationsontherateofproductionofeachoxidantinsidean isolated air bubble per second estimated by the first bubble collapse as a function of acoustic amplitudewiththetemperatureinsideabubbleattheendofthebubblecollapse(thethickline):(a) 20kHzandR =5μm.(b)100kHzandR =3.5μm.(c)300kHzandR =3.5μm.(d)1MHz 0 0 0 andR =1μm(ReprintedwithpermissionfromYasuietal.[5].Copyright(2007),AIPPublishing 0 LLC) bubble.ThentheresultsinFig.4aresummarizedasfollows.Forvaporousbubbles, the main oxidant is OH radical. For gaseous bubbles, on the other hand, the main oxidantisH O whenthebubbletemperatureatthecollapserangesfrom4000Kto 2 2 6500K.Whenthebubbletemperatureishigherthan6500Kingaseousbubbles,the main oxidant is O atom. When the bubble temperature is higher than 7000 K, the oxidantsarestronglyconsumedinsideanairbubblebyoxidizingnitrogen[8]. BythethermaldissociationofH O(H O+M ! OH + H + M,whereMisthe 2 2 thirdmolecule),theamountofHatomsisexpectedtobecreatedbythesameamount asthatofOHradicals.However,theamountofOHradicalsismuchlargerthanthat ofHatoms(Fig.3c).ItisbecausetheproductionofOHradicalsisnotonlybythe thermaldissociationofH Obutalsobythefollowingreactions:H O + O ! OH + 2 2 UnsolvedProblemsinAcousticCavitation 7 Fig.5 Experimentalresults I (1MKI . 0.0005M AM) 2 ontherateofproductionof H O inpurewaterandthatof 2 2 I in1MKIsolutionor1M 2 KI+0.0005Mammonium molybdatesolutionunder variousmixturesofargonand oxygendissolvedinthe solution(Reprintedwith 2.0 permissionfromHartand Henglein[9].Copyright 1] -n (1985),AmericanChemical mi I2 (1M KI) Society) M- 4 -0 1 e [ at r 1.0 H 0 (water) 2 2 0 0 50 100 % 0 2 OH,H O + H ! OH + H andHO + H ! OH + OH[7].Inaddition,Hatoms 2 2 2 arealsoconsumedbythereactionH + H ! H . 2 In1985,HartandHenglein[9]suggestedthattheOatomcreatedinsideabubble (cid:3) mayoxidizeI ioninanaqueousKIsolutioninwhichthemixtureofargonandO is 2 dissolved. In their experimental results (Fig. 5), the amount of I production in 2 aqueousKIsolution(2OH + 2I(cid:3) ! I + 2OH(cid:3),andinthepresenceofammonium 2 molybdate as catalyst H O + 2I(cid:3) ! I + 2OH(cid:3)), is considerably larger than that 2 2 2 of H O in pure water (2OH ! H O ). Thus they concluded that there should be 2 2 2 2 some oxidant other than OH radical and H O . They assumed that it is O atom 2 2 (O + 2I(cid:3) + 2H+ ! I + H O). However, there has been no direct evidence on the 2 2 productionofOatominsolutionbycavitationbubbles. Atomicoxygen(Oatom)haseightelectrons.Twoofthemareinthe1sorbitals. Other two electrons are in the 2s orbitals. The rest of four electrons are in the 2p orbitals whenitisnothighlyexcited (Fig. 6).The orbitalsarecharacterizedbythe quantumnumbersn,l,m,andm,wherenistheprincipalquantumnumber,listhe l s orbital angular momentum, m is the magnetic quantum number, and m is the l s secondary spin quantum number [10]. Orbitals are designated s, p, d, f, g 8 K.Yasui Fig. 6 Electronic configurations of ground state, first excited state, and second excited state of atomicoxygen.Twoelectronsin1sstateareomitted correspondingtotheorbitalangularmomentuml = 0,1,2,3,4,respectively.Foran orbital with n = 2 and l = 1, it is called 2p orbital. For n = 1 and l = 0, it is 1s orbital. The number in front of the symbol for orbital angular momentum is the principalquantumnumber.Themagneticquantumnumber(m)cantakethevalues l of(cid:3)l,((cid:3)l + 1),..., (l(cid:3)1),l. Thusfor 2porbital(l = 1), m cantake thevalues of l (cid:3)1, 0, and1.Foreach m state, two electrons can occupy (up-spin (m = 1/2) and l s down-spin(m = (cid:3)1/2)). s When four electrons are in 2p orbitals, there are only three configurations as in Fig.6[11,12].AccordingtoHund’sfirstrule,thegroundstateistheconfiguration withthehighestmultiplicity.Onlyfortheconfi(cid:2)(cid:2)Xguratio(cid:2)(cid:2)natt(cid:3)heleftsideinFig.6,the totalspinangularmomentumisnonzero(S¼(cid:2) m (cid:2)¼1 .Thus,thiscorresponds s to the ground state as the multiplicity is the highest as 3 (For the otherXtwo configurations, themultiplicityis1).The totalorbitalangularmomentum(L¼ l i wherethesummationtakesforalltheelectronsofOatom)cantakethevaluesof0,1, and2becausetheallowedvaluesofthetotalangularmomentumforthesystemoftwo angularmomentaofj andj arej = j + j ,j + j -1,...,|j -j |accordingtoquantum 1 2 1 2 1 2 1 2 mechanics[13].Itshouldbenotedthatthestructureoftwoelectronsin2porbitalsisthe same as that offour electronsin 2p orbitals because the structure offourelectrons is equivalent to the closed-shell structure (six electrons in 2p orbitals as L = S = 0) minusthestructureoftwoelectronsin2porbitals[12].TheorbitalsforL = 0,1,2,3,.. arereferredtoasS,P,D,F,..[14].Whentherearetwoparallelspinelectronsasinthe leftsideofFig.6,L = 2isimpossibleduetoPauli’sexclusionprinciplebecausethe orbital angular momenta are also in parallel [15]. It is known that L = 0 is also impossible for this case due to Pauli’s exclusion principle [12]. Thus, the ground stateofOatomisforL = 1anddesignated3Pwherethetotalspinangularmomentum Siscodedintheformof2S + 1intheleftsuperscript. The first excited state of O atom is 1D, because with the same multiplicity of 1(S = 0)theconfigurationwiththehighesttotalorbitalangularmomentum(L)has thelowestenergy(Fig.6).Forthefirstexcitedstate,oneofthe2porbitalsisempty. Thus, it is more easy to undergo bond-forming addition reactions than the ground UnsolvedProblemsinAcousticCavitation 9 Fig.7 Threeregionsforacavitationbubble stateOatom.Forexample,thefollowingreactionwithwatermoleculesisknownto beveryfast: (cid:4) (cid:3) O 1D þ H O!H O : (1) 2 2 2 Therateconstantforthereaction(1)withH Ovaporisreportedas1:8(cid:4)0:8(cid:2)1010 2 L/(mols)[16].Iftherateconstantisthesameforthesamereactioninliquidwater, then the lifetime of O(1D) in liquid water is about 10(cid:3)12 s = 1 ps. The diffusion pffiffiffiffiffiffi lengthofOatominthislifetimeisonlyabout0.1nmwhichisestimatedby2 Dτ whereDisthediffusioncoefficientofOatominliquidwater(109m2/sisassumed) and τ is the lifetime of O atom. Thus, O(1D) atom could be present only in the gas–liquidinterfaceregionofabubble(Fig.7). Ontheotherhand,thegroundstateO(3P)isaselectiveoxidantbecauseitrather slowly reacts with moleculesthathavenounpairedelectronssuchasH Obecause 2 such reactions violate the principle of spin conservation. With molecules that have unpairedelectrons,O(3P)rapidlyreacts.However,detailedreactivityandsynthetic studies in solution are limited by lack of convenient and reliable methods for the generationanddetectionofO(3P)[17]. WithregardtoOHradical,thelifetimeinsolutionisdeterminedbythefollowing reactionwhentheconcentrationofothersolutesisnothigh: OH þ OH!H O : (2) 2 2 10 K.Yasui Therateconstantis5(cid:2)109L/(mols).ThusthelifetimeofOHradicalinsolutionis determinedbytheconcentrationofOHradicalsinthiscase.When[OH]is5(cid:2)10(cid:3)3 mol/L[4],thelifetimeofOHradicalis4(cid:2)10(cid:3)8s = 40ns.Whentheconcentration ofother solutesishigh, thelifetime ofOH radicalinsolution isdetermined bythe solute concentration. When it is 1 mol/L, the lifetime of OH radical in solution is 10(cid:3)9–10(cid:3)8s = 1ns–10nsbecausetherateconstantistypicallyintherangeof108 to109L/(mols).Inthelifetimeof40ns,thediffusionlengthofOHradicalisabout 10 nm. Thus OH radicals could be present only in the gas–liquid interface region (Fig.7). With regard to H O , the lifetime in solution strongly depends on the kind of 2 2 solutespresent.Withoutanysolutes,H O hasalifetimemuchlongerthan30min 2 2 determinedbytherateofthefollowingreaction[18]: H O !1=2O þ H O: (3) 2 2 2 2 InthepresenceofOHradical,thefollowingreactiontakesplace: OH þ H O !H O þ O (cid:3)þ Hþ (4) 2 2 2 2 The rate constant of the reaction is ð2:7(cid:4)0:3Þ(cid:2)107L/(mol s) [19]. When the concentrationofOHis5(cid:2)10(cid:3)3 mol/L,thenthelifetimeofH O is7.4μs.Asthe 2 2 lifetimeofOHisonly40nsatthisconcentration,thetime-averagedconcentrationof OHshouldbemuchlower.Ifitis10(cid:3)6mol/L,thenthelifetimeofH O isaslongas 2 2 about 40 ms. The diffusion length of H O in this lifetime is about 10 μm. Thus 2 2 H O could be present not only in the gas–liquid interface region but also in the 2 2 liquid region. If there are other kinds of radicals derived from solutes such as methanol by the reaction with OH radicals, however, the rate constant for the reaction of H O is as high as 108–109 L/(mol s). Then the lifetime is as short as 2 2 thatofOHradical. Physicalandchemicalpropertiesofthegas–liquidinterfaceregionofacavitation bubblearestillunderdebate.Suslicketal.[20]suggestedbasedontheexperimental resultsofthevaporpressuredependenceofsonochemicalreactionrateat20kHzthat the temperature of the gas–liquid interface region is as high as 1900 K. They also numericallycalculatedthetemporalandspatialevolutionoftheliquid-zonetemper- aturewithaheattransportmodel.Themodelpredictsaspatialandtemporalaverage liquid-zone temperature of 2730 K. Furthermore, it predicts the width and the duration for the high temperature in the gas–liquid interface region as 200 nm and 2μs,respectively.Theauthor[21,22]numericallycalculatedthetemperatureatthe gas–liquid interface region based on a simple model. The model predicts the temperatureatthegas–liquidinterfaceincreasesuptothesameorderofmagnitude with the maximum temperature inside a bubble (a few thousand Kelvin). The thicknessandthedurationforthehightemperatureregionatthegas–liquidinterface areestimatedasonly4–10nmand2–6ns,respectively.Furtherstudiesarerequired onthistopic.