Numerical and Experimental Studies on the Effect of Surface Roughness and Ultrasonic Frequency on Bubble Dynamics in Acoustic Cavitation

Abstract

With many emerging applications such as chemical reactions and ultrasound therapy, acoustic cavitation plays a vital role in having improved energy efficiency. For example, acoustic cavitation results in substantial enhancement in the rates of various chemical reactions. In this regard, an applied acoustic field within a medium generates acoustic streaming, where cavitation bubbles appear due to preexisting dissolved gas in the working fluid. Upon cavitation inception, bubbles can undergo subsequent growth and collapse. During the last decade, the studies on the effects of different parameters on acoustic cavitation such as applied ultrasound frequency and power have been conducted. The bubble growth and collapse mechanisms and their distribution within the medium have been classified. Yet, more research is necessary to understand the complex mechanism of multi-bubble behavior under an applied acoustic field. Various parameters affecting acoustic cavitation such as surface roughness of the acoustic generator should be investigated in more detail in this regard. In this study, single bubble lifetime, bubble size and multi-bubble dynamics were investigated by changing the applied ultrasonic field. The effect of surface roughness on bubble dynamics was presented. In the analysis, images from a high-speed camera and fast video recording techniques were used. Numerical simulations were also done to investigate the effect of acoustic field frequency on bubble dynamics. Bubble cluster behavior and required minimum bubble size to be affected by the acoustic field were obtained. Numerical results suggested that bubbles with sizes of 50 μm or more could be aligned according to the radiation potential map, whereas bubbles with sizes smaller than 10 μm were not affected by the acoustic field. Furthermore, it was empirically proven that surface roughness has a significant effect on acoustic cavitation phenomena.

Full text


Energies2020,13,1126;doi:10.3390/en13051126www.mdpi.com/journal/energies
Article
NumericalandExperimentalStudiesontheEffectof
SurfaceRoughnessandUltrasonicFrequencyon
BubbleDynamicsinAcousticCavitation
RanaAltay
1
,AbdolaliK.Sadaghiani
1,2
,M.IlkerSevgen
1
,AlperŞişman
2,3
andAliKoşar
1,2,4,
*
1
FacultyofEngineeringandNaturalSciences,SabanciUniversity,Tuzla,Istanbul34956,Turkey;
raltay@sabanciuniv.edu(R.A.);ilkersevgen@sabanciuniv.edu(M.I.S)
2
SabanciUniversityNanotechnologyandApplicationCenter(SUNUM),SabanciUniversity,Tuzla,Istanbul
34956,Turkey;a.sadaghiani@sabanciuniv.edu(A.K.S)
3
FacultyofElectricalandElectronicsEngineering,MarmaraUniversity,Kadikoy,Istanbul34722,Turkey;
alper.sisman@marmara.edu.tr
4
CenterofExcellenceforFunctionalSurfacesandInterfacesforNano‐Diagnostics(EFSUN),Sabanci
University,Tuzla,Istanbul34956,Turkey
*Correspondence:kosara@sabanciuniv.edu
Received:31January2020;Accepted:28February2020;Published:3March2020
Abstract:Withmanyemergingapplicationssuchaschemicalreactionsandultrasoundtherapy,
acousticcavitationplaysavitalroleinhavingimprovedenergyefficiency.Forexample,acoustic
cavitationresultsinsubstantialenhancementintheratesofvariouschemicalreactions.Inthis
regard,anappliedacousticfieldwithinamediumgeneratesacousticstreaming,wherecavitation
bubblesappearduetopreexistingdissolvedgasintheworkingfluid.Uponcavitationinception,
bubblescanundergosubsequentgrowthandcollapse.Duringthelastdecade,thestudiesonthe
effectsofdifferentparametersonacousticcavitationsuchasappliedultrasoundfrequencyand
powerhavebeenconducted.Thebubblegrowthandcollapsemechanismsandtheirdistribution
withinthemediumhavebeenclassified.Yet,moreresearchisnecessarytounderstandthecomplex
mechanismofmulti‐bubblebehaviorunderanappliedacousticfield.Variousparametersaffecting
acousticcavitationsuchassurfaceroughnessoftheacousticgeneratorshouldbeinvestigatedin
moredetailinthisregard.Inthisstudy,singlebubblelifetime,bubblesizeandmulti‐bubble
dynamicswereinvestigatedbychangingtheappliedultrasonicfield.Theeffectofsurface
roughnessonbubbledynamicswaspresented.Intheanalysis,imagesfromahigh‐speedcamera
andfastvideorecordingtechniqueswereused.Numericalsimulationswerealsodonetoinvestigate
theeffectofacousticfieldfrequencyonbubbledynamics.Bubbleclusterbehaviorandrequired
minimumbubblesizetobeaffectedbytheacousticfieldwereobtained.Numericalresults
suggestedthatbubbleswithsizesof50μmormorecouldbealignedaccordingtotheradiation
potentialmap,whereasbubbleswithsizessmallerthan10μmwerenotaffectedbytheacoustic
field.Furthermore,itwasempiricallyproventhatsurfaceroughnesshasasignificanteffecton
acousticcavitationphenomena.
Keywords:acousticcavitation;surfaceroughness;cavitationbubble;bubbledynamics;bubblesize;
bubblegrowth

1.Introduction
Acousticcavitationisaliquidtovaporphasechangephenomenonandtakesplacewithina
mediumduetotheeffectofultrasonicpressurefluctuations.Theseultrasonicpressurefluctuations
resultintheformationofbubblesfrompreexistingdissolvedgases,whichisfollowedbythe
subsequentgrowthandviolentcollapseofbubbles.Theoccurrenceofbubblecollapsesgeneratelocal

Energies2020,13,11262of15
highpressuresandatemperatureriseupto105K[1],whichleadtoseverephysicalimpact,shock
waveradiation[2,3],turbulence,microjetsandchemicalreactions[4]andcouldbeexploitedinmany
applicationssuchascancertreatment[5–7],ultrasoniccleaning[8–10],wastewatertreatment[11–
13],nanomaterialssynthesis[14,15],biomedicalapplications[16]andemulsification[17–19].
Althoughthegrowthandcollapseofbubblesinacousticcavitationarewidelyusedinmany
differentapplications,therearesomedisadvantagesofacousticcavitation.Theconsequencesof
bubblecollapseasshockwaves,temperaturechange,oraformationofaliquidjetmightleadto
cavitationerosion.Duetotheerosion,crevicesonsurfacesmightformorstressfatiguemightoccur.
Moreover,theformationofbubblesmightcauseadecreaseinthedeviceefficiency[20].To
understandtheeffectofacousticcavitationanditsdamageondifferentmaterials,somestudieswere
recentlyperformed.Forexample,Abedinietal.[21]investigatedcorrosionandmaterialalterations
ofCuZn38Pb3brassunderacousticcavitationduringdifferentsonicationdurations(maximum
durationof5h).Theyreportedthatthecorrosionrate,plasticdeformationandsurfaceroughness
werelargerforlongersonicationperiods.Also,thedamageduetothecavitationvariedaccordingto
theα‐β′phasesofbrassalloy.
Theaimofunderstandingtheunderlyingmechanismsmakesfundamentalstudiesattractive
startingfromthe1940s(Blake,[22]).In1949,Blakereportedbubblegrowthinanappliedacoustic
fieldandcoveredrectifieddiffusionandbubble‐bubblecoalescence[22].Later,Noltingkand
Neppiras[23]performedastudy,whereequationsofcavitationbubblegrowth,pressureandvelocity
distributionwerederivedforacousticcavitation.Ayearlaterin1951,theyreportedthatsome
parameterslimitedacousticcavitation[24],whichwerelistedaspressureamplitude,pressurewave
frequency,bubblecoreradius,andhydrostaticpressure.In1960,Leith[25]explainedthenegative
effectsofcavitationonmetalsandliquidcharacteristicsduetobubblecollapseandcavitationerosion.
Withtheadvancesinrelatedtechnology,thenumberofstudiesinthisfieldincreased.In1996,
Tianet.al.capturedtheoscillationsduetomicrobubblegenerationunderanacousticfield,usinga
Charge‐coupleddevice(CCD)camera[26].Ananalysisonthebubblesizebasedonthelevitationin
waterwasmade.Similarly,Mettin[27]implementedhigh‐speedimagingtechniquesfor
visualizationofdifferentbubbleshapes/structuressuchasconicalshape,clusteranddoublelayer,
whichformedatlowappliedfrequencies.Recently,Reuteretal.[28]studiedbubblesizeandits
distributioninvariousacousticstructures.Ahigh‐speedcamerawasusedfortheanalysisofbubbles
duringtheoscillationatalowappliedfrequency.Thereareotherdifferenttechniquesforbubble
dynamicsanalysisatanappliedultrasonicfrequencysuchaslightscattering[29]andstroboscopy
[30].
Manyrecenteffortshavefocusedonchangingthebubbledistributionbyapplyingdifferent
powersandfrequencies.Thedynamicresponsesofbubblesaccordingtothechangeofthese
parameterswereincludedintheliterature[8,31–36].Forexample,Brotchieetal.[31]obtainedbubble
distributionatdifferentappliedfrequenciesandpowersintheirexperimentalstudy.Theyobserved
thatbubblesizeandultrasoundfrequencyhadaninverserelationship,andthebubblesizewas
proportionaltotheacousticpower.InthestudyofSunartioet.al.[37],theeffectsofvaryingfrequency
andpoweronacousticbubblecoalescencewererevealedinthepresenceofsurface‐activesolutesby
calculatingthevolumechangeofthedispersionaftereachsonicationperiod.Theyreportedsurface
assimilationinthebubblesduetotheusageofsurface‐activesolutes,whichcausedadelayinbubble
coalescence.Furthermore,thealterationofpowerdidnothaveanyeffectonthedynamicsofbubble
coalescence.Yet,frequencyvariationcausedachangeinbubblecoalescence,whereshortrangesteric
revulsionwasdominant.Ashokkumaralsoreportedtheeffectofsurface‐activesolutespresentinthe
experimentalmedium,andbubblegrowthandcoalescencewerein‐depthdiscussedinthisstudy
[38].Toprovideadifferentperspective,Zhou[39]usedacousticcavitationinpoolboiling
experimentstoanalyzeitseffectonboilingheattransferenhancement.Itwasreportedthattheuse
ofacousticcavitationinpoolboilingexperimentsdecreasedthesuperheat,andemergingbubbles
increasedheatandmasstransfer,whichledtoenhancedboilingheattransfer.ThestudybyFanget
al.[13]focusedonwastewatertreatmentwithacousticcavitation.Acousticcavitationinthisstudy
servedforpropagationoftheplasmainwaterbytheformationofmicrobubbles.Cuietal.[40]used

Energies2020,13,11263of15
acousticcavitationtotreatcrudeoil.Accordingly,shorterbranchedchainandrelativelyshortalkanes
comparedtotheinitialversioncouldbeachieved.Meanwhile,asphaltenemoleculeswere
polymerized.
Whilemanystudiesdisplayedtheeffectofmajorparametersonacousticcavitationandbubble
dynamics,thesurfaceroughnesseffectonacousticcavitationbubbleshasnotbeenstudiedinthe
literaturetothebestknowledgeoftheauthors.Inthisstudy,bubbledynamicswasinvestigatedfor
differentsurfaceroughnessandappliedfrequencyvalues.Forvisualization,ahigh‐speedcamera
wasusedforrecordingvideos/images.Thus,growthandcollapseofcavitationbubblescouldbe
capturedfordifferentsurfaceroughnessandfrequencyvalues.Tovalidatetheobtainedresults,
numericalsimulationsofacousticstreamingandparticletrajectoryanalysisofairbubblesina
mediumwerealsoperformed.
2.MaterialsandMethods
2.1.ExperimentalSetup
TheschematicoftheexperimentalsetupisshowninFigure1.Acubicpoolmadeoftheglass
withdimensionsof15×15×15cm
3
wasusedforvisualizationofthecavitationexperiments.The
workingfluidwaschosenaswater.ALangevintypepiezoelectrictransducer,whichgenerates
mechanicalmovementsfromelectricalsignals,wasoperatedatfrequenciesof28kHzand40kHz.
Mountablediscsurfaceswithadiameterof40mmanddifferentsurfaceroughnessvalues(of100nm
and1μm)wereutilizedtoinvestigatetheeffectofsurfaceroughnessattheappliedfrequencyof40
kHz(showninFigure1b).Roughnessonthesurfacewasachievedwithasandpaper.Thetransducer
wasfixedatthetopofthepool.Ahigh‐speedcamera,whichallowsforfastrecordingofthevideos
andsnapshotsofthebubblesduringacousticcavitationphenomenawithexposuretimeof2μs,frame
rateof10,000,wasusedforvisualization.ThevisualizationwasachievedusingtheShadowgraph
ImagingTechnique.
Theshadowgraphimagesofacousticcavitationwerecapturedbyahigh‐speedcamera.Inthis
study,parallel‐lightdirectshadowgraphwasused.Accordingly,whenthelightbeampassesthrough
thebubble,thelightisfocused.Thestrongestlightrefractionisattheboundarybetweenthebubble
andsurroundingwater.Norefractionoccursoutsidethebubbleorexactlyatitscenter.Adark
circularshadowmarkstheperipheryofthebubble.Insideit,thereisabrighterilluminancering,
whichisthelightdisplacedfromthedarkcircularshadow.
Thecamerawasconnectedtotheworkstationtoanalyzebubbledynamics.Thedirectionofthe
ultrasoundapplication(fromthetransducer)wasfromtoptothebottomofthepool.Toensurethe
repeatabilityandreliabilityoftheexperiments,everyexperimentwasperformedforthreetimes.The
high‐speedcamerawaslocatedonthesideofthepoolsuchthatthesurfaceofthetransducerand500
μmaboveofthesurfacecouldberecordedforacousticcavitation.

(a) (b)
Figure1.
Descriptionofexperimentalsetupandmountablesurfaces:(a)Schematicrepresentationof
theexperimentalsetup;(b)Mountablesurfaceswithdifferentsurfaceroughnessvalues.

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2.2.AcousticCharacterizationandControlCircuit
Cavitationbubblesweregeneratedusingasandwich‐typeultrasonictransducer.Theelectronics
todrivethistypeoftransducermostlyusesadigitallycontrolledpush‐pulltransistorstage.To
preventanyshortcircuit,thetransistorexcitationtimingiscrucialforthistypeofdesign[41–45].In
thisstudy,anewdrivercircuit,whichusesasimplefunctiongenerator,wasdesigned.Thenew
designsimplifieselectronicsandreducessystemcomplexity.
Thesandwich‐typetransducersareusedinsidemanyindustrialdevicesandarewell
characterized[46,47].Thetransducerusuallyhasasingleoperatingband,whichhasafractional
bandwidthofaround5%.Theoperationfrequencybandwasinvestigatedusingtheexperimental
setupdepictedinFigure2a.Apulsegenerator(5072PR,OlympusCO.Waltham,MA,02453,USA)
excitedthetransducerusingawidebandpulse,andthereceivedechowasmeasuredbyaspectrum
analyzer(DSA875,Rigol,Beaverton,OR97008,USA).Themeasureresponseshowedanarrowband
characteristicwithanoperatingfrequencyof39.85kHz(Figure2b).Thesetupwasusedtodetermine
theexactoperatingfrequencysothatthe
transducercouldbedriveneffectively.

Figure2.Characterizationandmeasurementoftransducer:(a)Transducercharacterizationsetup;
(b)Themeasuredfrequencycharacteristicsofa40kHztransducer.
Thenarrowbandbehaviorofthetransducerincreasedthedependencyofefficiencyonthe
excitationfrequency(e.g.:0.3%ofthechangeinfrequencywouldresultin20%ofthechangeinthe
powertransmittedtothesystem).Hencethefrequencystabilityhadasignificanteffectonproviding
constantpower.
Thedesigneddrivercircuitrywasabletosetthedesiredfrequencyandpowerlevel.Thecircuit
wascontrolledbyadigitalsignalinordertoprovidefrequencystability.Unliketheusualdesign,a
singleswitchwasemployedinthedesign.Thehighvoltageswitchpumpedtheelectricalpowerto
thetransducerbyapredefinedfrequency.Theswitchwasametal‐oxidesemiconductor(MOS)
transistorconnectedtoahighvoltagedirectcurrent(HV‐DC)supply,whichwasprovidedfrom
rectifiedalternatingcurrent(AC)voltage(220VRMS).Inthedesign,onlyasingleswitchwasused.
Itchargedthepiezoelectrictransducerduringon‐time,andtheaccumulatedchargewasdischarged
inoff‐time.Themaincomponentwasinverselypositionedfastdiodesinthedischargingcircuitry.
Hence,onlyoneswitchwasusedtosimplifytheexcitationcircuitoftheMOStransistor.Asimple
functiongeneratorappliedthepulsewidthmodulated(PWM)signaltooperatethesystem.Theduty
cycleofthePWMsignaldefinedthepower(dutycyclemustbeunder40%),andthePWMfrequency
determinedthetransducer’soperationpoint.Theblockschematicexplainingthecircuitdesignis
giveninFigure3a.ThevoltageacrosstransducernodescanbeseeninFigure3b,andthefrequency
domainrepresentationofthevoltageshowsthatthetransducerisactuatedbyaprettynarrowband
signalaroundtherequiredfrequency(Figure3c).



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





(a)







(b)(c)
Figure3.Schematicandcharacterizationofutilizedelectroniccircuit:(a)Theblockschematicofthe
designedcircuit;(b)Measuredvoltagewhentransducerisactuatedby26.7kHz;(c)Thefrequency
domainrepresentationofthevoltagewaveformgivenin(b).
2.3.NumericalAnalysis
TheCOMSOL5.4softwarewasusedforsolvingthegoverningequations.Acousticandparticle
trackingmoduleswereusedtoinvestigatetheeffectofacousticfieldonairbubbles.Airbubbleswere
consideredassphericalparticleswithdiametersrangingfrom10μmto50μm.Acoustophoretic
radiation,gravityanddragforceswereimplementedinthenumericaldomain.Openboundary
conditionswereconsideredforsidewalls,whileplanewaveradiationwasdefinedasthetransducer
surface.Theconservationequationsforanacousticwavepropagationintoafluidaregivenas:
2
22
11
.0
P
Pct

 
 
 
 (1)
Here,P,ρ,c,andtarepressure,density,soundvelocityinmedium(water),andtime,
respectively.Fora(,) () it
P
rt Pr e


solution,where


,,rrxyzisthepositionvector,
2
f


isangularfrequency,and
f
isthefrequency.Substitutingthepressuredistributioninto
Equation(1),theacousticpressure()Pr isobtainedas:
2
2
10PP
c



 

 (2)
Theintensitydistributionisexpressedas:

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2
()
() 2
pr
Ir c


(3)
Aftermeshdependencyanalysis,thehomogeneouspressureequationwassolvedas:
()
(,)
itkr
Prt Ae



(4)
3.ResultsandDiscussion
3.1.SingleBubbleDynamicsinanAcousticField
Whenappropriateultrasonicradiationisapplied,“multi‐bubbles”appearinaliquidmedium.
Thegeneratedbubblescanbeformedduetoeithertheexistenceofthedissolvedgasnucleiorthe
cagedgasesinthesolidparticles.Anotherreasonfortheformationofbubblescanbeattributedto
theseparationoflargerbubblesintheliquidmedium.Theoretically,ifthebubbleovercomesthe
pressurethreshold,whichiscalledtheBlakethreshold,P
B
,(Equation(5)),nucleationtakesplace[1]:

03
0
83
922
B
BB
PP PRR




 




(5)
whereP
0,
R
B
andσaretheambientpressure,Blakeradiusandsurfacetension,respectively.Upon
nucleation,thebubblecanstarttogrowandgothroughstablecavitationforalargedrivingacoustic
pressure.Ontheotherhand,ifthedrivingacousticpressureislow,thebubblesdissolveinthe
medium.Formuchhigheracousticpressures,whichexceedthecavitationthreshold,thebubbles
becomeunstableortransient.Inanotherscenario,largerbubblescanbeaffectedbythebuoyancy
forceandmoveuptothesurfaceoftheliquidmedium,whichisreferredas“degassing”.
Thebubblegrowthprocessatanappliedultrasonicfrequencyismainlyseparatedintotwo
differentmechanisms:rectifieddiffusionandcoalescence.Thecoalescenceoccursduetothe
secondaryBjerknesforce[48]betweentwooscillatingbubblesinthesameoscillationphase.They
mergeandformabiggerbubble.Thegrowthofthebubblesviathecoalescencemechanismisfaster
thantherectifieddiffusion.Figure4representstherectifieddiffusion,inwhichthesinusoidal
acousticstreamingaffectsthebubbledynamicsandcausesperiodicalgrowthandwane.Duringthe
growth,theexpansiontakesplace,theinnerpressureofthebubbleislow,andthediffusionofgas
intothebubbleoccurs.Inversely,thediffusionofthegasoutofthebubbleappearsatthetimeof
compression.Afterthebubblereachesthecriticalmaximumsize,thebubblecollapseoccurswhich
leadstopressureshockwaves.

Figure4.

Rectifieddiffusionmechanismundertheeffectofsinusoidalacousticstreaming.

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Anexampleofasinglebubblelifetimeattheapplied40kHzacousticfieldfrequencyisshown
inFigure5a.Theexperimentisconductedwithasmoothtransducersurface.Byusingfastvideo
recording,therectifieddiffusionofthesinglebubblewasrecordedinevery150μs,asshownin
Figure5b.Thebubblegoesthroughtherectifieddiffusion,anditssizealtersaccordingtotheinside
pressure.Thepressuredifferencebetweentheliquidmediumandtheinnerbubbleallowsforthe
periodicgrowth,expansionandcompressionofthebubbleoverseveralcycles.After750μs,the
bubblereachesthemaximumsize,whichisfoundasapproximately35μm,whichisfollowedbythe
violentcollapseofthebubble.
 
(a) (b)
Figure5.

Sizevariationofasinglebubbleinanacousticfield:(a)Schematicrepresentationofthe
singlebubblelifetimeatanappliedfrequencyof40kHz;(b)Capturedimagesofrectifieddiffusionof
thesinglebubble
3.2.BubbleBehaviorinAcousticField
Acousticstreamingisofsinusoidalnature,whichcausespressurefluctuationsintheliquid
medium.Asaresultofanappliedacousticfield,theformationofmulti‐bubblecloudsoccurs.To
analyzethemulti‐bubblebehaviorunderacousticfield,thehigh‐speedcamerawasusedfor
visualization.Theshootingrangewassetto100μs.Thefrequencyofappliedultrasoundwaschosen
as40kHz,andthetransducersurfacewithsurfaceroughnessvalueof100nmwasused.Figure6
showsasnapshotofmulti‐bubblecloudswithin100μstimeintervals.Itcanbeobservedthatthe
compressionandrarefactionofthebubblecloudscanbeseenaccordingtothepressurenodesinthe
appliedultrasoundwave.

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
Figure6.Cont.

Figure6.Themulti‐bubblecloud’sbehaviorduring300μsattheappliedacousticfieldof40kHz:(a)
and(c)compressioncycle,(b)and(d)rarefactioncycle.
Duringthecompressioncycle,thecloudshrinks,whichisfollowedbytheirexpansion,where
theamplitudeoftheacousticpressureswitchesintothelowernode.Asaresult,similarbehaviorto
thesinglebubblecasecanbeobservedformulti‐bubblesatthesameappliedacousticfrequency.
Toprovidefurtherunderstandingabouttheeffectofacousticfieldonbubbledynamics,
numericalmodelingwasperformedusingtheCOMSOL®software(Burlington,MA01803USA)[49].
AccordingtotheexperimentalresultsshowninFigure7a,locallygroupedbubblecloudsintheliquid
arevisible.ThisbehaviorcanbealsorecognizedinsimulatedairparticletrajectoriesshowninFigure
7b.Accordingtothecomparisonbetweenexperimentalandnumericalresults,almostthesame
bubbledistributioncanbeachieved.


100


Energies2020,13,11269of15
(a) (b)
Figure7.
Bubblecloudformation(a)experimentalresults(b)numericalresultsfortheresponseof
airparticlestotheappliedacousticfield.
Anoscillatingflowfieldcanbedescribedasanacousticwavewithinfinitewavelength.Theflow
velocityisexpressedas

ˆ
() sin
ccf
ut u t

,where
ˆ
c
u
istheamplitudeofthevelocitywaveand
2
fr
f

istheangularfrequency.Resonancesize,Stokesnumber,
tr
Sfc
,anddensityratio,
pl


,aremajorparametersaffectingtheresponseofairparticlestotheacousticfield.
Theactingradiationforceonthebubblesinsidethemediumisduepressuregradientexpressed
as
PDu
xDt



.Inadditiontotheprimaryradiationforce,whichactsinthedirectionofacoustic
wavepropagation,asecondaryradiationforcemanipulatestheagentstoattractorrepeleachother.
Thetime‐dependentradiationforceonthebubblecanbecalculatedfromthedrivingpressurewave
andtime‐dependentvolumeofthebubble.Furthermore,thetranslationalmotionofthebubblein
responsetotheradiationforcecanbecalculatedbysolvingtheequationsofairparticletrajectory.
Foranairparticlewithmassof 𝑚

𝜌𝑉

,theparticletrajectoryequationisgivenas 𝑚



𝐹

𝑡
𝐹

𝑡.Theradiationforce(𝐹

𝑡andquasi‐staticdragforce(𝐹

𝑡areexpressedas:
𝐹

𝑡𝑉

𝑑𝑃

𝑑𝑥
(6)
𝐹

𝑡1
2𝜌

|𝑢

|𝑢

𝐴24
2𝑅|𝑢

𝑢

|
𝜐10.197 2𝑅|𝑢

𝑢

|
.
𝜐(7)
Here,𝑚

istheairparticlemass,𝑢

istheairparticlevelocity,𝑑𝑃

isthedrivingpressure
difference,𝑢isthevelocity,𝑢

𝑢

𝑢

istherelativevelocity,and𝜐istheviscosity.Toexamine
theeffectofradiationforce,themotionofbubbleswithdifferentdiameterswassimulatedatthe40
kHzultrasonicfrequency.TheobtainedresultsareshowninFigure8.Accordingly,thebubbleswith
diameterssmallerthan10μmarenotaffectedbytheacousticfield,whilebubbleswithdiameters
largerthan50μmcanbesortedaccordingtotheradiationpotentialmap.Theobtainedresults
indicatethattheresponseofairparticlestotheradiationforceisproportionaltotheirsize,whichis
alsodisplayedbythevisualimagesshowninFigure7a.

(a) (b)
Figure8.
Simulationresultsofbubbletrajectorieswiththebubbleshavingdifferentsizesatthe
appliedfrequencyof40kHz(a)Airbubblehaving50μmdiameter;(b)Airbubblehaving10μm
diameter.
3.3.EffectofSurfaceRoughnessandUltrasonicFrequency
Figure9showstheacousticcavitationinducedbubblesattheappliedultrasonicfrequencyof40
kHzwhendifferentsurfacesaremountedonthetransducer.Theimagesweretakenwiththehigh‐

Energies2020,13,112610of15
speedcameraand100μstimeslots.Figure9adisplaysthemulti‐bubbleformationwhenthesmooth
surface(with100nmsurfaceroughness)istested.Thebubblesappearandformacloud.Meantime,
thebubblesontheroughsurfaceexhibitmoredisorganizedbehavior.Asaresult,thecavitylength
diminutionisevidentwiththeincreaseintheroughness.
Whenasingleacousticcavitationbubblecollapsesintheliquidmedium,thetemperaturecan
belocallyincreasedupto10,000K[1].Thepooltemperaturesweremeasuredatfourdifferent
locations.Theaveragetemperatureoffourthermocoupleswererecordedforanalysispurposes.The
experimentswereconductedunderthe40kHzappliedultrasonicfield.

(a) (b)
Figure9.
Thecavitationbubblesat40kHz.(a)Multi‐bubblecloudformationonasmoothsurface
with100nmroughness;(b)Disorganizedbubbleswithdiminutionofcavitylengthonaroughsurface
with1μmroughness.
ThetemperaturevariationsofthepoolwithtimeareshowninFigure10.Accordingly,for
surfaceroughnessof100nm,thetemperatureincreasesfrom299K(roomtemperature)to340Kafter
35minutesofexperimentation.Thereasonforthetemperaturerisecanbetheenergyreleasedduring
thebubblecollapse.Ontheotherhand,forthesurfacewithsurfaceroughnessparameterRa=1μm,
thepooltemperatureisstabilizedwithinashortertime(almost25minutes).Here,Here,Raisthe
arithmeticalmeandeviationoftheassessedprofileandiscalculatedas 𝑅𝑎


∑|𝑦

|


,where,y
i
is
theverticaldistancefromthemeanlinetothei
th
datapoint.Moreover,thepooltemperatureis10K
colderthanthepreviouscase(smoothsurface),whichisduetolowerintensityofcavitationinside
thepoolforthecaseofroughsurface.

Figure10.
Thetemperatureriseduringtheacousticcavitationexperimentsattheappliedfrequency
of40kHz.

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Toobservetheeffectofappliedultrasonicfrequencyonacousticcavitation,28kHzand40kHz
areapplied.Foralltheexperiments,thesmoothsurfacetransducersurfaceistested.Atthe40kHz
appliedfrequency,morefrequentfluctuationscausemanybutsmallerbubblesthanthecaseof28
kHz.
Whilemoredetailedandextensivestudiesarerequiredforaccurateassessmentofenergy
efficiencyinenergyconversionprocessesinvolvingcavitation,thereportedresultsclearlyprovethat
thesurfaceroughnesshasasignificanteffectonacousticcavitationphenomena.Thisisevidentfrom
themaximumpooltemperature(Figure10)andbubblesize(Figure11).Althoughthemotivation
behindacousticcavitationstronglydependsontheapplications(sonoporation,ultrasoniccleaning,
andchemicalreactor),controlofacousticcavitationusingsurfaceroughnesscouldbeaneffective
passiveapproachforenergyefficiencyapplications.


(a)(b)

(c)(d)
Figure11.

ThebubbleswithdifferentshapeandquantityonthesurfacewithRa=1μmundertheeffect
ofdifferentappliedfrequencies(a)Bubblesoccurrenceat28kHz;(b)Bubblesoccurrenceat40kHz.
(c)Averagebubblediametersatdifferentacousticfieldfrequenciesandsurfaceroughnessparameters
(d)distributionofthenucleatedbubblesatdifferentacousticfieldfrequencyandsurfaceroughness
parameter.

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AsseeninFigure11a,thereareapproximately20bubbles,whereas50bubblesarevisibleonthe
samescaleinFigure11b.Theaveragesizeofgeneratedbubblesunderthe40kHzacousticfieldis
almosttwiceasmuchasthesizeofgeneratedbubblesunderthe28kHzacousticfield.Asthesizeof
bubblesincreases,thegeneratedenergyduetobubblecollapseremarkablydecreases.Furthermore,
ascanbeseeninFigure11c,surfaceroughnessreducesthebubblesize.Themainreasonisthe
propagationangleofsurfaceacousticwavepropagation.Assurfaceroughnessincreases,surface
wavepropagationoccurswithlowervelocity,andscatteringincreases,therebyweakeningthewave.
4.Conclusions
Thisstudywasperformedtoprovidemoreinformationabouttheeffectofsurfaceonacoustic
cavitationattwowidelyusedappliedultrasonicfrequenciesbelow50kHz.Theinvestigationofthe
effectofsurfacewithinthisrangeiscriticalformanyapplicationssuchasultrasoniccleaningand
drugdelivery.Theeffectofsurfaceroughnessonbubbledynamicsinacousticcavitationwas
experimentallyandnumericallyinvestigated.Surfaceswithroughnessvaluesof100nmand1μm
wereexaminedinthe28kHzand48kHzacousticfields.DI‐waterwasusedastheworkingfluid.A
high‐speedcamerawasusedtocapturebubbledynamicsinsidethepool.Singlebubblelifetimewas
investigatedbasedonvisualresults.Theaveragebubblesizesfordifferentconditionswereobtained
andtabulated.Itwasfoundthatsurfaceroughnessreducedthebubblesize.Thenumericalanalysis
indicatedthatthebubbleswithdiameterssmallerthan10μmwerenotaffectedbytheacousticfield,
whilebubbleswithadiameterof50μmcouldbesortedaccordingtotheradiationpotentialmap.
Theobtainedresultsshowedthattheresponseofairbubblestotheradiationforcewasproportional
totheirsize.Therecordedpooltemperaturesrevealedthatthepooltemperaturewasstabilized
withinashortertime(almost10minutesshorter)forthesurfacewithRa=1μm.Moreover,thepool
temperaturewas10Kcolderthanthepreviouscase(smoothsurface),whichwasduetolower
intensityofcavitationinsidethepoolforthecaseofroughsurface.Morestudiesarerequiredinthis
fieldtodeepentheunderstandingabouttheeffectofsurfaceonplanewavepropagationand
subsequentacousticcavitationwithinthemedium.
Nomenclature
ParameterDescription
cSoundvelocity(m/s)
fFrequency(1/s)
FRRadiationforce(N)
FQSQuasi‐staticdragforce(N)
kWavenumber(1/m)
PPressure(kPa)
P0Ambientpressure(kPa)
RBubbleradius(m)
StStokesnumber(‐)
tTime(s)
u(t)Velocity(m/s)
urRelativevelocity(m/s)
VVelocity(m/s)
Greekletters
ρ Density(kg/m3)
ω Angularfrequency(1/s)

Energies2020,13,112613of15
σ Surfacetension(N/m)
γ Densityration(‐)
ν Kinematicviscosity(m2/s)
Abbreviations
CCDCharge‐coupleddevice
MOStransistor Metal–oxide–semiconductortransistor
HV‐DCHigh‐voltagedirectcurrent
ACAlternatingcurrent
PWMsignalPulse‐widthmodulationsignal
AuthorContributions:Conceptualization,Methodology,Validation:R.A.andA.K.S.;Software,Setup
preparation:M.I.S;AcousticCircuitDesign:A.S;Supervision:A.K.Allauthorshavereadandagreedtothe
publishedversionofthemanuscript.
Funding:Thisresearchreceivednoexternalfunding
Acknowledgments:TheequipmentandcharacterizationsupportprovidedbytheSabanciUniversity
NanotechnologyResearchandApplicationsCenter(SUNUM)anditsstaffmembersareappreciated.
ConflictsofInterest:Theauthorsdeclarenoconflictofinterest
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