E ff ect of Surface Roughness on Hydrodynamic Characteristics of an Impinging Droplet - Singh et al. - 2021 - Unknown

《E ff ect of Surface Roughness on Hydrodynamic Characteristics of an Impinging Droplet - Singh et al. - 2021 - Unknown》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

pubs.acs.org/LangmuirArticleEffectofSurfaceRoughnessonHydrodynamicCharacteristicsofanImpingingDropletRajeevKumarSingh,*PeterD.Hodgson,NiladriSen,andSubratDasCiteThis:Langmuir2021,37,3038−3048ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Theinfluenceofsurfaceroughnessandimpactenergyonthehydrodynamicbehaviorofwaterdropletsimpingingupondryandrigidsurfacesofknownroughnesshasbeeninvestigatedexperimentally.Theinfluenceofthesetwoparametersonthedropletmaximumspreadingdiameter,sliplengthduringdropletrecoil,dynamiccontactangle,contactanglehysteresis,andapparentcontactangleofdropletsatresthasbeendetermined.Basedonthequantitativeassessment,acorrelationforthemaximumspreadingdiameterintermsofthenondimensionalparameter(We/Oh)andsurfaceroughnessratio(Ra/do)wasderived.Weproposetousesurfaceroughness“Ra”ratherthanusingthecontactangleforcorrelationascontactanglescannotbeknownapriori,whereassurfaceroughnesscanbedeterminedbeforehand.Thewettingstateofadropletdependsonthecombinedinfluenceofdropletimpactenergyandsurfaceroughness.Whileincreasingimpactenergyincreasesthespreading,highersurfaceroughnessresiststhedropletfromspreading.LowimpactenergyandasmoothersurfacetendtowardtheCassie−Baxterwettingstate,whereashighimpactenergyandroughsurfacespropelthedroplettowardtheWenzelstateofwetting.■INTRODUCTIONAsignificantamountofresearchworkhasbeendevotedtotheLiquiddropletsimpinginguponsurfacesareubiquitousaroundpredictionofmaximumspreadβmaxforavarietyofconditions,as18,1915,16,20,21usinnature,suchasraindropsfallingondifferentsurfacesorinisevidencedinthebooksandreviewarticles.Tableourdailylivesasmedicinalsprays,aerosols,andshowers.TheS1(seeTableS1intheSupportingInformation)summarizestransmission,impingement,andinteractionofdropletswithchronologicallyacomprehensivelistofresearchstudiessurfacesandthelifetimeofspeech/respiratorydropletscarryingcontainingmacroscopicmodelsforthepredictionofdroplettheSARS-Cov-2virusisconsideredoneofthemostcriticalspreadthathavebeenpublishedinthelast50years.1,2TheearlystudiesofJones,22Madejski,23andCollingsetal.24factorsforthespreadofCovid-19pandemic.Theresultantwettingfromthedroplet−surfaceinteractionsisfocusedonpredictingthemaximumspreaddiameterofmetallic3−5splatsforrapidsolidificationapplications.JonesintheirmodelDownloadedviaUNIVOFCAPETOWNonMay14,2021at15:46:34(UTC).acentralthemeinmanyapplicationssuchasspraycooling,6,789spraycoating,spraycombustion,inkjetprinting,3D-neglectedsurfacetensioneffectstoarriveatacorrelationofβmaxprinting,10,11ceramics,12andmetals.13∝Re1/8.MadejskiconsideredthelaminarfluidflowinthesplatThespreadingbehaviorofdropletsondrysurfacesisandneglectedsurfacewettabilitytoperformtheenergybalanceSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.governedbyabalancebetweentheinertial,viscous,andsurfacebetweenthekineticandpotentialenergyandthefrictionallossestensionforces.Thedroplet’sspreadingcharacteristicscanhaveinthesystem.Energywasconsideredlostthroughviscousmarkedlydifferentoutcomesduetosurfaceroughnessanddissipationandsurfacetensioneffects.InMadejski’smodel,surfacewettabilitythroughthecontactangleitmakeswiththewhenthespreadingisarrestedbythesurfacetensionforces,the14,15surface.Thedropletspreadsintoapancake-shapedlamellamaximumspreadingdiametercorrelatesasβ∝We1/2.Onthemaxaftertheimpingementontoadrysurface.Apartofthedroplet’sotherhand,whentheextentofspreadingisgovernedbythekineticenergyislosttoviscousdissipationduringspreading.viscousdissipationofenergy,themaximumspreadingscalesasSimultaneously,theotherportionofitisconvertedintosurfaceβ∝Re1/5.Collingsetal.neglectedtheviscousdissipationand16,17maxenergyforcreatingalargersurfaceareaoftheplanarlamella.includedthecorrectionforthesurfacewettabilityeffectthroughTheextentofthisspreadofthedropletischaracterizedbythe“spreadfactor”,whichistheratioofthespreadingdiametertothedroplet’sinitialdiameterbeforeimpact.ThemaximumReceived:November3,2020spread(βmax=dmax/do)andthicknessareconsideredtobetheRevised:February19,2021mostimportantfactorsfordropletimpingementhydro-Published:March2,202115,16dynamicsandareessentialintheevaluationofthespreadingbehaviorofdropletsinmanyinterfacialfluidflowsandheattransferapplications.©2021AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.langmuir.0c031933038Langmuir2021,37,3038−3048

1Langmuirpubs.acs.org/LangmuirArticle25theequilibriumcontactangle.ChandraandAvedisianthescalinganalysisorempiricalorsemiempiricalapproaches.consideredbothviscousenergydissipationandsurfacetensionThesecorrelationsscaleβmaxtoanon-dimensionalgroup,ReWe1/2,knownasthe“impactparameter”,whichisrepresentedwithcorrectionforsurfacewettabilityeffectsthroughthe215,17,37−40advancingcontactangleondropletsimpactingtheheatedas(ReOh)or(We/Oh).26surface.BennettandPoulikakosperformedacriticalassess-SincemostofthescalingmodelsweredevelopedforalimitedmentoftheearliertheoreticalmodelsbyJones,Madejski,rangeofWeberandReynoldsnumbers,theycannotbeappliedCollingsetal.,andChandraandAvedisian.Theymodifiedasageneralmodelforabroaderrangeoftheimpactregime.Madejski’smodeltoincorporatethesurfacewettabilityeffectSomeauthorshaveusedanapproximationfunctionthatthroughthecontactangleinthesurfaceenergyterm.Maoetprovidesasmoothcrossoverbetweentheviscousandcapillary2736al.appliedthestagnationpointflowandboundarylayerregimes.Eggersetal.basedthiscrossoverfunctiononthedevelopmentinthespreadinglamella,wheretheboundarylayerenergyconservationapproachratherthanthemomentum41thicknessesforlowviscosityandhighviscosityfluidswerebalance.Laanetal.utilizedEggers’concepttodevelopa28correlationapplicableforbothNewtonianandnon-Newtonianconsideredseparately.Healyetal.incorporatedacorrection14basedonthecontactangletothepreviouslydevelopedfluids.Leeetal.improvedfurtheronLaanetal.’smodelbyKurabayashi−Yang’smodelformulti-componentfueldroplets.incorporatingacorrectionfordroplets’spreadwithzeroimpact29velocity.AfewauthorshavealsoconsideredotheraspectsofPasandideh-Fardconsideredthedroplet’sshapeatthe14,40maximumspreadtothatofaflattenedcylindricaldiskanddropletspreadingsuchastheeffectofsurfaceroughness,4214,39consideredtheboundarylayerthicknesstoestimateviscoustexturedsurface,andwidelyvaryingviscosity.dissipation.TheyusedtheadvancingcontactangletoimproveMostofthemodelsorcorrelationslistedinTableS1(in30SupportingInformation)anddiscussedearliershowgooduponChandraandAvedisian’smodel.UkiweandKwokfurtherimprovedPasandideh-Fard’smodelbyconsideringtheagreementoverlimitedrangesintheirexperimentaldata.Thereflatteneddisc’slateralsidesforcalculationofsurfaceenergyatisageneralagreementinchoosingcharacteristicdimensionlessthemaximumspread.Theyarguedinfavorofusingannumbers,We,Re,orOh,forspreading.However,thereisno31universalacceptancefortheappropriatechoiceofthecharacter-equilibriumcontactangle.Later,Vadilloetal.revertedtothedynamiccontactangleintheirmodificationoverUkiwe’sisticcontactanglethatshouldbeemployedinthemodeltomodel.Wildeman32developedcorrelationsforthemaximumincorporatesurfacewettabilityeffects.Someauthorsarguein26,30spreadforthefreeslipaswellasnoslipconditionsusingafavoroftheequilibriumcontactangle,whileotherspropose25,29numericalmodelthatconsidereddissipationintheshearusingthedynamiccontactangleforcorrelations.boundarylayeratthesolidsurface.Forrealsurfaces,Young’sequilibriumcontactangledoesnotThesemacroscopicmodels,basedonphysicalarguments,exist.Ontheotherhand,thedynamiccontactanglecannotbeapplyeithertheenergyconservationormomentumconserva-knownapriorianddependsonthesurfacecharacteristicsandtionapproach.Theyestablishabalancebetweenthecapillaryexperimentalconditions.Surfaceroughnessisanindependentandviscousforcesafterimpacttotheinertialandsurfaceenergyparameterthatisnotaffectedbyexperimentalconditionsandforcesbeforeimpact.Whilethecalculationfortheinitialkineticcanbedeterminedbeforehand.Itchangesthewettingandsurfaceenergyhasbeenthesameforallthesemodels,theycharacteristicsofasurfaceandsignificantlyinfluencesthehavedifferedinevaluatingsurfaceenergyandviscousdissipationdynamiccontactangleduringthedroplet’sinteractionwiththeatthemaximumspread.Differencesaroseinthecomputationofsurface.Theuseofsurfaceroughnessasaparametertosurfaceenergyowingtoambiguityinthechoiceofthecontactincorporatethecorrelation’scontactangleeffecthasrarelybeen40angleconsideredorintheassumptionofthedropletshapeattheconsidered.Whileafewauthorshavementionedsurface14,27maximumspread.Variationintheviscousdissipationtermaroseroughness,thetreatmentismostlyqualitative.Quantitativefromthedifferentvelocityprofileassumptionsinthespreadingtreatmentofsurfaceroughnesshasmostlybeenignored.film.TheseearliermodelsareinaccurateastheydonotaccountInthepresentwork,ratherthanusingthedynamiccontactfortheedgeeffectsofthespreadinglamellaandtheenergylostangle,surfaceroughnesswasconsideredasaparametertototherim’sviscousboundarylayer.incorporatethesurfacecharacteristicsinthecorrelationdirectly.Intheviscousregime,utilizingtheenergyconservationQuantitativeassessmentoftheeffectofsurfaceroughnessontheapproach,mostoftheauthorshavefoundthatthemaximummaximumspreadofdropletsandotherdropletparametershasspread(β)isproportionalto(Re1/5).23,26,33Intheotherbeencarriedoutbyvaryingtheroughnessofsurfacespreparedmaxregime,mainlydominatedbytheinertialforce,thestrongfromthesameparentmaterial.LowtomoderateWeberinterplaybetweentheinertiaandcapillaryforceswithsomenumbers(We<15)wereemployedtoavoidsplashingandcorrectionsforviscousdissipationandsurfacewettabilityaffectsdisintegratingthedropletsontheroughsurfaces.themaximumspreadfactor.Scalinganalysisforbalancebetweenthekineticandsurfaceenergyinthisregimesuggeststhatβmax∝■MATERIALSANDMETHODSWe1/2forlargeWebernumbers.UsingthemassandmomentumSamplePreparationandSurfaceCharacterization.Five34balance,Clanetetal.developedanalternatemodeltosuggestdifferentsteelsamplesofsize(45mm×25mm×10mm)ofaveragethatβ∝We1/4.Theyproposedan“impactfactor”,roughness,Ra=0.2,0.4,0.8,1.1,and1.3μm,werepreparedbygrindingmax(WeRe−4/5),todistinguishbetweenviscousandcapillaryandpolishingoneofthebroadfacesandusedinthisstudy.Theseregimes.Formodelsbasedonthefilmthicknessofthespreadingsampleswerecutandpreparedfromthesameparentmaterial.Forlamella,analternate“impactfactor”,(P=WeRe−2/5),hasbeensmoothersurface,aluminaoxide-basedpolishwasused,whereasfortheroughersurfaces,asiliconacrbideabrasivewasusedforpolishing.Caredevised,whichreconcilesmostoftheexperimentaldataforthe33,35,36wastakentokeepthescratchesalignedalongthelengthofthesampleinertia-dominatedregime.duringpolishing.ThesampleswerecharacterizedforsurfaceroughnessSeveralotherauthorshavedevelopedcorrelationsfortheparametersusinganOlympusLEXTOLS5000industriallaserconfocalmaximumspreadofdropletswithWeberandReynoldsnumbersmicroscope.Table1showsthecharacteristicroughnessparametersof43ortheircombinationforawiderangeofimpactregimesusingthesamplesmeasuredaccordingtothestandardISO4287:1997.3039https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

2Langmuirpubs.acs.org/LangmuirArticleTable1.MeasuredRoughnessParametersoftheSamplessurfaceidentificationsampleidentificationno.(designatedroughnessparameter,S1S2S3S4S5Ra)(0.2μm)(0.4μm)(0.8μm)(1.1μm)(1.3μm)peaksurfaceroughness0.701.002.644.205.26(Rp)meansurface0.240.370.801.121.28roughness(Ra)rootmeansquare0.290.470.991.381.63surfaceroughness(Rms)meanwidthofsurface6.687.6810.5010.3817.11roughness(Rsm)roughnessratiothe2.002.072.082.312.91Figure2.Experimentalsetupfordropletimpingementstudy.ratiooftheactualsurfacetoprojectedsurfacearea(Φ)by∼3°sothatthedroplet’sreflectiononthesamplesurfacecanbe44capturedclearly.FourdifferentnozzleswereusedforcreatingTheroughnessprofileandthedegreeofunevennessonthedropletsofdifferentsizes.smoothestsurfaceareshowninFigure1.ThefigureclearlyshowsImageAcquisitionandAnalysis.Thesampleswereplacedonthemajorlyunidirectionalpolishingscratcheswithspatial/localvariationinholderwiththeirpolishedsurfacefacingtowardthenozzle.Beforeeachthesurfaceroughness,althoughtheaverageroughnessiswithintheexperiment,asnapshotofatransparentmicro-rulerfilmhavingarequiredrange.rectangulargridofresolution10−4m×10−4mwascapturedinthefocalExperimentalSetup.Figure2showsthearrangementofallplanetoconvertpixelresolutionintoactuallengths.Waterwasthensignificantcomponentsoftheexperimentalsetup.Thesetupconsistedforcedtotheconicaldispenserthroughamicroliterpump−syringeofanadjustablesampleholderforplacingthesample.Amicroliterattachmentfordropletgenerationatthenozzletipundertheinfluencepump(HarvardApparatusPhDUltra)fittedwithasyringewasofgravityandsurfacetension.Oncethedropletsattainedacertainsize,connectedtoaconicalliquiddispenserusingaPVCtubefordroplettheydetachedfromthenozzletipandfellonthesurface.Afewinitialgeneration.Attheotherendofthedispenser,flat-tippedstainless-steeldropletsweretrappedtoensurethatsubsequentdropletswerebubble-nozzlesofdifferentgaugescanbeattached.Thedistancebetweenthefree.Sharpimagesofthedropletsfallingandinteractingwiththesurfacenozzletipandthesamplesurfacewasadjustabletoimpartdifferentwerecapturedwithanimageresolutionof256×256pixelsat12,000impactvelocitiestothedroplets.fps.EachexperimentwasrepeatedthreetofourtimestoensureThesamplesurfacewashorizontallyalignedwithahigh-lumensrepeatabilityandeachcapturedroughly4000framestillthedropletsdiffusedlight-emittingdiodelightononesideandahigh-speeddigitalcametorest.Aftereveryrun,thesamplesurfacewaswipedcleanwithcamera(PhantomV7CineMagIII,VisionResearch)ontheother.Theethanolandacetonetoavoidsurfacecontamination.Theinitialimagesdiffusedlighthelpedinthedroplet’sbacklitilluminationwithasharpofdropletsfallingtowardthesurfacewereusedtocalculatetheirsize,focusandreducedthereflectionoflightfromthedroplet.Imagesphericity,andimpactvelocity.ThedistancefromthenozzletiptothemagnificationwasachievedbyusingaNikonED4FMicroNikkor-samplesurfacewasvariedtoimpartdifferentimpactvelocitiestothe200mm1:4Dlensmountedonthecamera.Thecameraaxiswastilteddroplets.UsingnozzlesofdifferentinnerdiametersenabledthecreationFigure1.CharacteristicsofthesteelsurfaceofroughnessRa=0.2μm.(a)3Dsurfacemap;(b)opticalmicrograph(mag.50×);(c)surfacetextureprofile;and(d)linearroughnessprofilealongtheevaluationlength.3040https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

3Langmuirpubs.acs.org/LangmuirArticleofdropletsofdifferentsizes.Thetotalexperimentaldesignconsistedofdimensionlesstime(t*=tvo/do)duringtheimpactandspreading.4(dropletsizes)×4(dropheights)×5(surfaceroughness).ThefigureshowsthatthecontactlinegetspinnedbythesecondorthirdTheproprietaryimage-sequencefileswereconvertedintotheAudiooscillation,butthedropletcontinuestooscillateoveraprolongedVisualInterleave(*.avi)formatandprocessedusinganopen-sourceduration.Definitionsofdifferentdropletparameterssuchasthe45imageanalysissoftwareFiji(ImageJ2)byconvertingthemintothemaximumspread,finalspread,sliplength,recoilheight,andfirstbinaryformat.Apixelanalysisapproachwasappliedtogenerateoscillationcyclethathavebeenusedforthequantitativeanalysisarequantitativeinformationondropletparameterslikeshapeandsize,alsomarkedonthefigure.Eachexperimentwasconductedatleastthreevelocity,spreadingdiameter,dynamiccontactanglevariation,recoiltimestoensuretherepeatabilityunderthesameconditions.The40,46height,andoscillationcharacteristicsinrealtime.Imagescalesweremethodemployedreproduceddatawithgoodrepeatabilitywithin±1%adjustedusingthecalibrationrulerrecordedpreviouslyduringforthespreadandwithin±5%forthecontactangle.experimentalruns.Thedropletreleaseheightwasvariedas5,10,15,and20×10−3mto■RESULTSANDDISCUSSIONvarythedropletimpactvelocity,vo.ThefallingdropletsarenotThedroplethydrodynamicbehavioronroughsurfaceswithaperfectlysphericalbutareovoidorslightlyflat-bottomedspheres.lowtomoderateimpactnumberispresentedhereunderthreeHowever,thesphericityofthedroplets,definedasφ=min(dh/dv,dv/d),wasdeterminedtobehigherthan0.9.Thedropdiameterwasmajorsections:(A)droplethydrodynamicbehavior,(B)droplethapproximatedasd=(d2d)1/3.15,47Theuseofnozzlesofdifferentspreadingcharacteristics,and(C)contactanglebehavior.Aohvboresresultedindropletsizesof2.1,2.6,2.9,and3.2×10−3m.Thequalitativedescriptionofdropletshapeevolutionisfollowedbydroplets’radiiaresmallerthanthecapillarylengthforwaterdroplets,aquantitativeanalysisofthetwomostsignificantparameters,−3themaximumdropletspreadanddynamiccontactangle.a==σρw/2g.48×10m,indicatingthatgravityeffectscanbeneglectedanddropletscanbeconsideredasspherical.Further,theinfluenceofsurfaceroughnessonthesetwoDropletimpactvelocitieswerecalculatedbytrackingthedropletparametersisalsoanalyzed.centroidfor10framesjustbeforeimpact.ThelinearfitslopetotheDropletHydrodynamicsatRoomTemperature.Figuredropletcentroid’sheightabovethesurfaceplottedagainsttimegives4showsthecontactanglevariationanddropletspreadbehaviorthedroplet’simpactvelocity.Areasonablyaccurateestimationofthe48impactvelocity,varyingwithin±5%ofthetheoreticalimpactvelocity,wasachievedbythemethodemployed.TheexperimentaldesignoffourdifferentdropsizesandfourdifferentfreefallheightsprovidedanimpactregimeoftheWebernumbervaryingas0.6≤We≤13andtheReynoldsnumbervaryingas370≤Re≤1740.Increasingthefallheightto25×10−3mledtooccasionalsplashingofthelargestsizeddroplets.Hence,allexperimentswererestrictedtoamaximumheightof20×10−3m,whichcorrespondstoamaximumWe=13.ContactAngle,DropletHeight,andDropletSpreadMeasurement.Thedropletcontactanglewiththesurfacewas49evaluatedusingaJavaplugin“DropSnake”thatcanbeusedwithFijisoftware.Thismethodaccuratelypositionsthetriplecontactpointonthesurface.ItutilizesedgedetectionbygrayscaleanalysisofthedropletimagestofitpiecewisecontinuouspolynomialB-splinestodetermine50thedropletboundary.ThepluginallowsareasonablyaccurateFigure4.Contactangleanddimensionlessdropletspreadvsestimationofthecontactanglefordropletsatequilibriumorweaknon-dimensionlesstimeinthefirstoscillationcycle(d=2.6×10−3m,oequilibriumconditionssuchasthoseindeformedconditions.TheleftWe=11,andRa=0.2μm).andrightcontactangleswereaveragedtotakecareofanyasymmetryinthedropletshapeduringdeformation.Otherdropletparameterssuchasduringthefirstcycleofoscillation.Thedropletshapeevolutions,thecontactspreadingdiameteratthebaselineandthedropletheightafterimpact,aresuperimposedatdifferentinstancesoftimetowerealsoextractedfromthesameimage.illustratetheshapesequenceduringthedropletimpactwithFigure3plotsthedimensionlessspread(β=d/do),dimensionlessdropheight(γ=h/do),andthecontactangleθagainsttherespecttothecontactangleandspreadfactor.Thedropletsundergodistinctphasesduringspreadingduetoinertial,surfacetension,andviscousforces.AtlowWeberandOhnesorgenumbers,theeffectofimpactvelocityisnegligible,andthedropletbehaviorcorrespondsto51theinviscidandcapillary-drivenspreadingregime.Theunbalancedcapillaryforceonroughsurfacesinfluencesthespreadingatthecontactline.Thisforcearisesfromthedifferencebetweentheequilibriumanddeformeddropletshapeandisresistedbyinertiaandfrictionalforces.Afterthedroplettouchesthesurface,theinertialandtheunbalancedYoung’sforcesatthecontactlinepullsitradiallyoutward,spreadingasadisk.Duringthisstage,thedroplet’sinitialenergyisconsumedtocreatealargersurfaceareaandispartlylostinovercomingtheresistancetospreading.Whilespreading,thecontactanglesubtendedbythemovingfrontiscalledtheadvancingcontactangle(θadv).Afterthedroplethasreacheditsmaximumspread,thecontactlinestopsmoving.SurfacetensionforcesthenpullthedropletbackforcingthefluidinthedropletcentertoriseFigure3.Contactangle,dimensionlessdropletheight,andspreadvsupward.Thisretractionofthedroplettowarditscenterisdimensionlesstime(d=2.6×10−3m,We=11,andR=0.2μm).termedtherecoilingstage.Duringthisstage,thesurfacetensionoa3041https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

4Langmuirpubs.acs.org/LangmuirArticleFigure5.Transientbehaviorofadropletonroughsurfacesat(a)We<2and(b)We=11(dropletsized=2.6×10−3m).oforcespropelthedroplettominimizeitssurfaceenergyandconstantβmax)beforeitstartsrecoilingback.Inthisphase,theattainanequilibriumstate.Duringthisretractionphase,thedropletbehaviorisgovernedbytheinterplayofinertial,surface,contactanglesubtendedbythedropletonthesurfaceiscalledviscous,andcapillaryforces,andthespreadinglawthatistherecedingcontactangle(θrec).Onreachingthemaximumapplicableinthekinematicphaseisnolongervalid.recoilheight,thedropletcollapsesagain.ThisprocesscontinuesAttheendofthespreadingphase,dropletsentertherecoilforawhilewiththedropletpinnedonthesurfaceandoscillatingphasewiththegrowinginfluenceofsurfacetensionandaboutitsequilibriumposition.Thespreadingandinertialwettability.Thesurfacetensionforcepullsthedropletbackoscillationsaredampedgraduallyasthedropletmovestowardtowarditsequilibriumposition,whilesurfaceroughnesstheequilibriumpositionatrest.preventsitfromrecoiling.Astheyrecoil,thedroplets’fluidDropletSpreadingCharacteristics.Dropletsfromonemassispulledinwardandupward,leadingtoaloweringofthenozzlearediscussedhereasarepresentativeanalysis.Figure5contactangle,(θrec).Thedifferencebetweenthemaximumdepictsthetemporalevolutionofthespreadingofwaterdropletsspreadβmaxandthefirstminimaβminafterthemaximumspreadofsize(d=2.6×10−3m)afterimpactingondrysurfacesofistermedasthesliplength,β=β−β.Fordropletswithoslipmaxminvariousroughnessvalues(Ra).Thebehaviorofotherdroplethigherimpactenergy,thesliplengthishighenoughtoovershootsizesissimilar.Fordropletswithasimilarimpactenergy,thetheequilibriumpositionwhileretracting.Thus,thedropletspreaddecreasesassurfaceroughnessincreases.spreadsoutagaintoregaintheequilibriumposition,causingittoDropletdeformationcanbedividedintofourdistinctphases:oscillateuntilitattainsitsequilibriumposition.Thisovershootis47kinematic,spreading,recoilorrelaxation,andequilibrium.InevidencedinFigure5bforspreadingonthesmoothestsurfacetheinitialkinematicphase,thelamellaisyettoemerge(Ra=0.2μm).underneathdroplets(β<1).ThespreadingbehaviordepictsaAtlowWebernumbers(We<2),dropletsexhibitspreadpower-lawrelationship,thatisβ∝(t*)a,wheretheexponent“a”withoutanysharpchangeindropletretractionduringitsvariesbetween0.28and0.50fordifferentexperimentalrecedingphase,whereasforhigherWebernumbers(We=11),conditions.Thispower-lawrelationshipisconsistentwiththatthedropletexhibitssharpretractionaftertheinitialimpact.Ata47reportedbyRiobooetal.,whoreportedanexponentvaryinglowWebernumber(We<2,Figure5a),thedroplet’sinertialbetween0.45and0.57fordropletsimpactingonsmoothenergyislow.Capillaryforcesaremoredominant,counteringsurfaces.Inthepresentstudy,theexponent’slowervaluemaybetheinfluenceofinertiaeffectively,andpulldropletsoutward.AtattributedtothesurfaceroughnessthatpreventsthedropletslowOhnesorgenumbers,theresistancetospreadingisgovernedfromspreading.Inertialforcedominatesoverthesurfaceforcebyinertialforces,whicharealreadylow.Hence,dropletsdonotandcapillaryforceinthisphase,andthespreadingbehaviorcanexhibitrecoil(orverynegligiblerecoil)attheendofthebeeasilydescribedusingtheimpactvelocityanddropletspreadingphase.Insteadofrecoiling,dropletscontinuetodiameter.Surfaceroughnesshasanegligibleinfluenceonthespreadfurtherastheyslowlyeaseintoanequilibriumposition.spreadingrate,indicatedbynearlycoincidingdatapointsintheThus,droplets’wettingeffectwithlowWeberandOhnesorgekinematicphaseforallsurfaceroughnessvalues.numbersisgovernedmorebythecapillaryforces.ThisdynamicInthesubsequentspreadingphase,lamellaeemergefromthewettabilityofroughsurfaces,atlowWebernumbers,iscrucialas38baseofthedroplets.Theinfluenceofsurfaceroughnessanditcontrolsthethinfilmformationonthesurface.Thedynamicimpactenergystartsbecomingsignificant,asindicatedbythewettingphenomenonwasabsentinothercaseswhereinertialseparationofcurvesfordifferentsurfaceroughnessvalues.Theandcapillaryforcesareofasimilarorderofmagnitude.Insuchinertiaofthedropletscontrolsthespreadingoflamellaeandthecases,theovershootintheinitialspreadingphasecausesthedroplet’sdeformation.Whilelamellaegrowoutward,thedroplet’sspreadtoretracttowarditsfinalequilibriumposition.droplet’sinertiaisprogressivelyweakenedbycapillary,retardingAftercompletingtherecoilorrelaxationphase,dropletsenterviscous,andfrictionalforces.Bythetimelamellaeachievetheirintotheequilibriumphasewherespreadingiscontrolledmore51maximumspread,βmax,thedroplet’skineticenergyiscompletelybytheviscousforcesthantheinertialforces.Dropletspreadingexhausted,andthecontactlinevelocitydropstozero.Theisoverdampedtowardthefinalspreadandremainsnearlydimensionlesstime,t*max,toreachthemaximumspreadisslightlyconstant,whileoscillationsinthedropletcontactanglegraduallyhigherfordropletswithhigherimpactenergy,thoughtheytakedamptowarditsequilibriumvalueatrest.Ideally,thefinallesstimetoreachthemaximumspreadinabsoluteterms.Thus,spreadforalldropletsonthesamesurfaceshouldbethesame.dropletswithhigherimpactenergyspreadfaster.ForabriefHowever,variationinthefinalspreadcanbeattributedtoperiod,thecontactlineremainspinnedatthisposition(nearlysurfaceheterogeneityduetoroughness.3042https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

5Langmuirpubs.acs.org/LangmuirArticleFigure6.Influenceof(We/Oh)onthemaximumspreadfactorfordropletsofsize(a)d=2.1×10−3m,(b)d=2.6×10−3m,(c)d=2.9×10−3m,oooand(d)d=3.2×10−3m.oMaximumSpreadingDiameter.Themaximumspreadingdiameterofdropletsisoneofthemostsignificantparametersforahostofindustrialapplicationssuchasforresolutionininkjetprinting,cooling,orcoatingefficiencyofsprays.Correlationformaximumspreadingintermsofthenondimensionalgroup(We/Oh)andsurfaceroughness(R*a=Ra/do)wasdeveloped.Likesomeofthecorrelationsbyother15,37,38,40authors,thenondimensionalgroupWe/Ohwasusedasitrepresentstheratioofspreadingtoresistingforcesandinvolvesallkinematicandmaterialproperties.Figure6indicatesthevariationinthemaximumspreadingfactorwithrespecttotheWe/Ohnumber.Themeasuredmaximumspreadfactordepictsanincreasingtrendwithapower-lawrelationshiptoWe/Ohandcanbecorrelatedasβmax=A(We/Oh)m,wheretheexponent“m”isapproximately0.10and“A”isthecoefficientrepresentingthesurfacecharacteristics.Figure7.EffectofsurfaceroughnessonthedropletmaximumspreadTheupperandlowerboundsofthedataarealsoplottedonthefactor.samegraphandhavethesameexponent.Variationinsurfaceroughnesscausesthecoefficient“A”tovarybetween−6andexponentvaluesuggeststhatsurfaceroughnesshasaweak+9%fromthemean.Increasingsurfaceroughnessresistsinfluenceonthespreadingbehaviorofthedroplet.dropletsfromspreading,whichresultsinlowervaluesofCombiningtheparameters(We/Oh)andthesurfacemaximumspread.Whencorrelatedintermsofimpactvelocity,1/5roughnessRa*,auniversalcorrelationforthemaximumthemaximumspreadfactorscalesasβmax∝(vo),whichisspreadinghasbeendevelopedthroughregressionanalysisand34similartothatreportedbyClanetetal.forwaterdropletsexpressedasimpactingonapartiallywettablesurface.Theeffectofthenondimensionalsurfaceroughness0.1iy−0.065β=0.39ijjWeyzzjjjjRazzzzparameter(R*a=Ra/do)onthemaximumspreadingfactorformaxjOhzjdzdropletsimpactinguponthesurfaceisdepictedinFigure7.k{ko{(1)Increasingsurfaceroughnesscausesalowerspreadindroplets.Comparedtoexperimentalresults,thepredictedmaximumForimpactsatsimilarWebernumbers,themaximumspreadisspreadingfromtheequationprovidedareasonablygoodfit,asloweronroughersurfaces.ThefiguresuggeststhatsurfaceshowninFigure8.Acomparisonoftheproposedcorrelationroughnesshasaninversepower-lawrelationshipwiththewiththatreportedintheliteratureisshowninFigure9.maximumspreadfactor.Fittingthepower-lawrelationshipβmaxAsisevidencedfromTable2,mostofthesecorrelationswere∝(R*)−n,theexponent“n”isapproximately0.065.Thelowdevelopedforthespreadingofwaterdropletsonsmootha3043https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

6Langmuirpubs.acs.org/LangmuirArticleFigure10ashowstheinfluenceofimpactenergyonthesliplengthofdropletsimpactingsurfaceswithdifferentroughnessvalues.Incontrast,Figure10bshowstheinfluenceofsurfaceroughnessonthesliplengthforvaryingWebernumbers.Fromthefigures,thefollowingobservationsaremade:•Onsurfacesofsimilarroughness,thesliplengthincreaseswithanincreaseinimpactenergy.Theinfluenceofimpactenergyismoreinthecaseofsmoothersurfaces.•Forsimilarimpactenergy,thesliplengthishigheronsmoothersurfacesofRa=0.2μmandRa=0.4μm.Onroughersurfaces(Ra=0.8,1.1,and1.3μm),alldropletshavesimilarslips,asdepictedbythetrendlines’clubbing.ThisindicatesthatcapillaryandfrictionalforcesaredominantenoughtonullifytheinfluenceofimpactenergyFigure8.Comparisonofallexperimentaldataofthemaximum(seeFigure10a).spreadingfactorwithpredictionusingtheproposedcorrelation.•Athigherimpactenergy(We∼10−12),theinfluenceofsurfaceroughnessisdominant.Thesliplengthfallssharplywithincreasingsurfaceroughness.Atlowerimpactenergy(We∼1−2),thecapillaryandfrictionalforcesaredominantenoughtonegatethelowinertialenergyforces.ThisleadstoanearlysimilarsliplengthforthedropletsatlowerWebernumbers,asdepictedbytheflattrendlineinFigure10b.DynamicContactAngleBehavior.Thetemporalevolutionofthedynamiccontactanglefor2.6×10−3mwaterdropletsafterimpactingthesurfacesatdifferentWebernumbersisshowninFigure11.Foraperfectsphericaldroplet,thecontactangleatimpactshouldideallystartfrom180°However,theimpactingdropletsarenotperfectlyspherical,andcapturinganimageatthesameinstanceofimpactisdifficult.Forallexperimentsinthisstudy,temporalcurvesofthecontactanglejustafterimpactstartfromavalue∼150°,droppingsharplytowardadynamicadvancingFigure9.Comparisonoftheproposedcorrelationofthemaximumcontactangleof∼120°asthedropletspreadingslowsdown.spreadingfactorwithpublishedcorrelationsintheliterature.Oncethedropletreachesitsmaximumspread,thebulkoffluidhasalreadybeenpushedoutwardtowardthecontactline.Atmaximumspread,thecontactanglecyclesthroughdynamic40surfaces,exceptfortheworkbyTangetal.,whichisforwateradvancingtotherecedingcontactangle,undergoingthecontactdropletsonsteelsurfacesofknownroughness.Whilethereisanglehysteresisperiod.Oncethecontactangledropsbelowthesignificantvariationbetweenthemaximumspreadingfactorrecedingcontactangle,thecontactlinestartsreceding,andthepredictedwithcorrelationsforasmoothsurfaceandthedynamiccontactangledecreasestowardaminimum.Afterthat,correlationdevelopedinthepresentwork,thepredictedresultsitstartsincreasingagaininthenextspreadingphase.Thiscycling40haveaclosermatchwiththatofTangetal.Hence,itcanbeofthecontactangle,betweenthemaximaandminima,continuesconcludedthatthecorrelationdevelopedinthisworkgivesawithbulkfluidoscillation,whichgraduallydampsovertime.goodestimateofmaximumspreadduringtheimpactofwaterEachsubsequentmaximaandminimaissmallerthanthedropletsonrealsurfacesatlowtomoderateWebernumbers.previous,graduallytaperingtowardtheequilibriumapparentSlipLength.Afterthedropletshaveachievedtheircontactangleatrest.maximumspread,thecontactlineslipsbackduringdropletInthefirstcycleofoscillation,dropletsexhibitapeculiar46,52,53recoil(seeFigure3forthedefinitionofthesliplength).Thestick−slipbehavior,wherethecontactlineacceleratesextentoftheslipβslipdependsontheimpactenergyandsurfacesharplywhileretracting,followedbyaquickincreaseintheroughness.contactangle.Thestick−slipbehaviorwasobservedinmostofTable2.CorrelationsoftheMaximumSpreadingFactorUsedinComparisonauthorscorrelationsremarks370.166Scheller&Bousfield(1995)βmax=0.61(We/Oh)waterdropletsonsmoothpolystyrenefilmandglass380.14Bayer&Megaridis(2006)βmax=0.72(We/Oh)waterdropletsonsmoothmirrorpolishedsteelsurface150.178Liangetal.(2019)βmax=0.505(We/Oh)waterdroplet,smoothstainless-steelsurface400.31Tangetal.(2017)βmax=0.11(We/Oh)waterdroplet,stainlesssteelsurfaceofroughness0.4−1.6μmÄÅÅÉÑÑ1/2Pasandideh-Fardetal.(1996)29ÅÅÅÅWe+12ÑÑÑÑwaterdropletsonasmoothandpolishedsteelsurface.θaistheadvancingcontactβmax=ÅÅÅÅ3(1−+cos)θ4(WeRe−0.5)ÑÑÑÑangleÇaÖ3044https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

7Langmuirpubs.acs.org/LangmuirArticleFigure10.Effectof(a)impactenergyand(b)surfaceroughnessonthesliplengthduringdropletspreading.Figure11.DynamicContactAngleevolutionfor2.6mmdropletonroughsurfacesat(a)We<2and(b)We=11.Figure12.Contactanglehysteresisfordropletmotiononroughsurfaceswithdifferentimpactenergies(d=2.6×10−3m),(a)R=0.4μmand(b)oaWe=8.thecaseswithroughsurfacesandforalltheWebernumbersμm)anddifferentroughnessvalues(forWe=8),respectively.studiedhere.Thisstick−slipbehaviorofthecontactlineisDatapointsinthepositivevelocityregionarefortheadvancingattributedtothepinninganddepinningofthecontactlineapparentcontactanglewhendropletsarespreading.Duringduringitsmotiononthesurfaceandcontactangleoscillation.initialspreading,thecontactlinevelocityishigherthantheThedynamiccontactanglevariationplaysanessentialroleintheimpactvelocity,steadilydeceleratinguptothecontactlinedroplet’spost-spreadingdynamicsandeventuallyinfluencesthearrest.Onthelinedepictingzerocontactlinevelocity,theupperdroplet’sfinalspreadatrest.endofdatapointscorrespondstotheadvancingapparentContactAngleHysteresis.Figure12plotsthedynamiccontactangleatthestartofthehysteresisperiod.Incontrast,theapparentcontactanglesduringthefirstoscillationcycleforlowerendofdatapointscorrespondstotherecedingapparentdropletsofdiameter2.6×10−3m.Thecontactlinevelocitywascontactangleattheendofthehysteresisperiod.Duringcontactnondimensionalizedasv*cl=vcl/vo.Figure12a,breferstotheanglehysteresis,thecontactlinevelocityiszeroanddropletscontactanglehysteresisatdifferentWebernumbers(forRa=0.4cyclethroughaseriesofcontactanglevalues,betweenthe3045https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

8Langmuirpubs.acs.org/LangmuirArticleFigure13.Effectof(a)impactenergyand(b)surfaceroughnessontheapparentcontactangleofdropletsatrest.apparentadvancingandrecedingcontactangles.OncetheFigure13a,bindicatesthattheinfluenceofsurfaceroughnesscontactlinestartsreceding(negativecontactlinevelocity),theontheapparentcontactangleatrestisamplifiedwhendropletscontactangledropsfurthertowardaminimum,beforeitcyclesimpactthesurfacewithhigherenergy.Theincreasingimpactupagaininthenextoscillationcycle.energycausesthedroplettospreadmore,whereasthehigherForthecasepresentedinFigure12,theadvancingapparentsurfaceroughnesspreventsthedropletfromreceding.Thiscontactanglestartsbetween130and140°,steadilydecreasingtoresultsinalargerfinalspread.Tomaintainthedroplets’volume∼120°atthestartofthecontactanglehysteresis.Attheendofwiththelargercontactfootprint,alowerapparentcontactanglethehysteresis,thecontactlinestartsrecedingoncetheapparentatrestissubtended.Thus,dropletsinteractingwithroughrecedingcontactangleisaround∼65°.ThedynamiccontactsurfacesandimpactingathigherWebernumbersformathinnerangledecreasesfurtheruntilaminimumisreached.Similarfilm,whichcanhavepotentialbenefitsinapplicationswhereabehaviorwasobservedinotherexperimentalrunsaswell.Thethinfilmisrequired.rateofchangeintherecedingcontactangletothecontactlinevelocitywashigherfordropletswithhigherimpactenergy,■CONCLUSIONSwhereasthespanofthecontactanglehysteresis,thatis,θadv−Theimpactenergyandsurfaceroughnesssignificantlyinfluenceθrec,washigheronroughersurfaces.Thespanisalsohigherforthedropletinteractionondry,rigid,androughsurfaces.dropletswithhigherimpactenergy(We=11).ThisvariationinHowever,surfaceroughnesshaslittleornoinfluenceduringthedropletretractiondynamicscanbeattributedmoretotheinitialspreadingbehavior.Itsdominancestartsincreasingasthedroplet’sapparentrecedingcontactangleduringtherecoildropletnearsitsmaximumspread,duringthecontactanglephase.hysteresisphase,andwhenthedropletretracts.RoughsurfacesApparentContactAngleatRest.Theapparentcontactincreasethedroplet’scontactlinepinning,whichleadstoanglesubtendedbydropletsrestingonthesurfaceisimportantrestricteddropletmotionafterinitialspreading.Forimpactataformanyapplicationssinceitinfluencesdroplets’spreadingandlowWebernumber,theimpactenergyisinsufficienttospreadthethicknessoftheliquidfilmformed.Theinfluenceofimpactthedropletonroughsurfaces.Instead,itistheunbalancedenergyandsurfaceroughnessondroplets’apparentcontactcapillaryforcethatpullsthedropletoutwardtowarditsfinalangleatrestwereanalyzed.equilibriumposition.ThisistrueforallthesurfaceroughnessFigure13adepictstheinfluenceofimpactenergyonthevaluesstudiedhere,andtheapparentcontactangleatrestapparentcontactangleatrestforthesmoothest(Ra=0.2μm)subtendedbythedropletis∼90±5°atlowWebernumbersandtheroughest(Ra=1.3μm)surfaceemployedinthisstudy.(We∼1−2).TheslightvariationinthecontactangletowardaFigure13bshowstheinfluenceofdimensionlesssurfacehighervalueisattributedtothemovingcontactline’spinningroughnessontheapparentcontactangleatrestforthelowesteffectwhileovercomingthelocalsurfaceroughnessvariationandthehighestWebernumbersstudied.Thereissomescatterinwhenthedropletispulledoutward.Ontheotherhand,whentheexperimentaldatawhicharoseduetolocalsurfaceroughnessdropletsimpactwithhigherenergy,thedroplet’sinitialspreadisinhomogeneities,especiallyatlowerWebernumbers.Itismorethanitsequilibriumspreadandthedroplettriestoretract.evidentfromFigure13athatimpactenergyhasalesserinfluenceDuringthedroplet’sretraction,thecontactlineispreventedontheapparentcontactangleatrestonthesmoothersurface.fromslippingbackonroughsurfaces.TheextentoftheslipisTheapparentcontactangleatrestis∼90±5°onthesmoothestloweronroughersurfacesduetolargesurfacefrictionalforcessurface(Ra=0.2μm).Ontheotherhand,theapparentcontactpreventingitsretraction.Thiseventuallyleadstoalargerangleatrestshowsadecreasingtrendwithincreasingimpactfootprintofdroplets.Thedroplet’svolumeismaintainedbyenergyfortheroughestsurface.Similarly,Figure13bshowsthatsubtendingalowercontactangle.Thelargerfootprint,lowertheapparentcontactangleatrestdoesnotchangeappreciablycontactangle,andpinnedcontactlinetendtostretchthewithachangeinsurfaceroughnesswhendropletsimpactatlowdropletsoverroughsurfaces.Thus,intherangeofsurfaceWebernumbers.However,athigherWebernumbers,theroughnessstudiedhere,thesurfaces’wettabilityimprovedwithapparentcontactangleatrestshowsadecreasingtrendastheincreasedroughnessforthedropletimpactingwithhigherdimensionlesssurfaceroughnessincreases.Theapparentenergy.contactangleatrestdropstovaluesaslowas∼70°fordropletsThisbehaviorofroughsurfacescanbeattributedtothe5455impactingtheroughestsurfacewithahighimpactenergy.Cassie−BaxterorWenzelstateofwetting,dependingonthe3046https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

9Langmuirpubs.acs.org/LangmuirArticlesurfacetexture,thatistheheightofpeaks,thewidth,andvalleys’projectadministration,funding,conceptualization,writingdepth.IntheCassie−Baxterregime,thedropletscontactthereviewandediting,andsupervision.PeterD.Hodgson:projectsurfaceonlyatpeakswithairpocketstrappedinthevalleys.Onadministration,conceptualization,writingfinalreviewandtheotherhand,intheWenzelregime,dropletsfollowtheediting,andsupervision.Themanuscriptwaswrittenthroughsurface’scontour,makingintimatecontactwithitatallpointsthecontributionsofallauthors.Allauthorshaveapprovedtheandfloodfillingthevalleys.Atlowimpactenergy,surfacefinalversionofthemanuscript.roughnesshadlittleornoinfluenceonthedroplets’finalcontactNotesangle.Thissignifiesthatdroplets’initialenergyfailstodisplaceTheauthorsdeclarenocompetingfinancialinterest.theairpocketstrappedinthevalleys,causingthedropletstofloatontheairpocketstrappedinthevalleysofsurface■roughnesstouchingthesurfaceonlyatthepeaks.ThisleadstoACKNOWLEDGMENTStheCassie−BaxterwettingregimewherethesurfacetendsTheauthorsaregratefultothemanagementofSteelAuthorityoftowardhydrophobicitywithincreasingsurfaceroughness.WithIndiaLtd.,theResearch&DevelopmentCentreforIronandincreasingimpactenergy,theinitialenergyisstrongenoughtoSteel,India,andDeakinUniversity,Australia,forthefinancialdisplacetheairtrappedinthevalleys.ThedropletthenhugsthesupporttopursuethisprojectundertheHigherDegreebycontourofthesurface,floodfillingthevalleysandleadingtotheResearchProgramandthepermissiontopublishthispaper.increasedinfluenceofsurfaceroughness.Thesurfaceroughnessthenresiststhecontactlinemotion,leadingtoahigher■ABBREVIATIONSadvancingcontactangleθadvandlowerrecedingcontactangleWeWebernumberθrec,thatisincreasedcontactanglehysteresis.ThewettingOhOhnesorgenumberbehaviorisintheWenzelstatewiththesurfaceshowinghigherReReynoldsnumberhydrophobicityduringthespreadingstage(asθadv>90°)andddiameterofthedroplet(m)higherhydrophilicityduringtherecedingstage(asθrec<90°).gaccelerationduetogravity(ms−2)Thus,onnon-idealroughsurfaces,bothCassie−Baxterandβspreadfactor(d/do)Wenzelstatesmaycoexist.Themoredominantstatedependsσsurfacetensionbetweenwaterandair(N/m)uponthelocalsurfaceroughnessvariationandthedroplets’−3ρdensityofwater(kgm)impactenergy.vvelocity(m/s)■hheightofthedropletalongthecentralaxis(m)ASSOCIATEDCONTENTθcontactangle(deg)*sıSupportingInformationttime(s)TheSupportingInformationisavailablefreeofchargeathttps://pubs.acs.org/doi/10.1021/acs.langmuir.0c03193.■SUBSCRIPTSCollectionofthemostcommonlyreferredcorrelationsforoatthetimeoftheimpactthemaximumspreadingdiameterasreportedinthemaxmaximumpublishedliteratureoverthelast50years(PDF)clcontactlineffinal■AUTHORINFORMATIONhalongthehorizontalaxisCorrespondingAuthorvalongtheverticalaxisRajeevKumarSingh−SchoolofEngineering,FacultyofScience,Engineering,andBuiltEnvironment,Deakin■REFERENCESUniversity,Geelong,Victoria3216,Australia;orcid.org/(1)Stadnytskyi,V.;Bax,C.E.;Bax,A.;Anfinrud,P.TheAirborne0000-0003-0000-8531;Phone:+91-8986880324;LifetimeofSmallSpeechDropletsandTheirPotentialImportanceinEmail:singhrajeev@sail.inSARS-CoV-2Transmission.Proc.Natl.Acad.Sci.U.S.A.2020,117,11875−11877.Authors(2)Dhand,R.;Li,J.CoughsandSneezes:TheirRoleinTransmissionPeterD.Hodgson−InstituteofFrontierMaterials,DeakinofRespiratoryViralInfections,IncludingSARS-CoV-2.Am.J.Respir.University,Geelong,Victoria3216,AustraliaCrit.CareMed.2020,202,651−659.NiladriSen−ResearchandDevelopmentCentreforIron&(3)Ciofalo,M.;Caronia,A.;DiLiberto,M.;Puleo,S.TheNukiyamaSteel,SteelAuthorityofIndiaLimited,Ranchi,JharkhandCurveinWaterSprayCooling:ItsDerivationfromTemperature−834002,IndiaTimeHistoriesandItsDependenceontheQuantitiesThatCharacterizeDropImpact.Int.J.HeatMassTransfer2007,50,SubratDas−SchoolofEngineering,FacultyofScience,4948−4966.Engineering,andBuiltEnvironment,DeakinUniversity,(4)Breitenbach,J.;Roisman,I.V.;Tropea,C.FromDropImpactGeelong,Victoria3216,AustraliaPhysicstoSprayCoolingModels:ACriticalReview.Exp.Fluids2018,Completecontactinformationisavailableat:59,55.https://pubs.acs.org/10.1021/acs.langmuir.0c03193(5)Sarmadian,A.;Dunne,J.F.;Long,C.A.;Jose,J.T.;Pirault,J.-P.;Rouaud,C.HeatFluxCorrelationModelsforSprayEvaporativeCoolingofVibratingSurfacesintheNucleateBoilingRegion.Int.J.AuthorContributionsHeatMassTransfer2020,160,120159.RajeevKumarSingh:conceptualization,methodology,inves-(6)Aziz,S.D.;Chandra,S.Impact,RecoilandSplashingofMoltentigation,dataextraction,analysis,writingtheoriginaldraft,andMetalDroplets.Int.J.HeatMassTransfer2000,43,2841−2857.writingreviewandediting.SubratDas:projectadministration,(7)Ye,Q.;Domnick,J.AnalysisofDropletImpingementofDifferentresources,conceptualization,methodology,formalanalysis,AtomizersUsedinSprayCoatingProcesses.J.Coat.Technol.Res.2017,writingreviewandediting,andsupervision.NiladriSen:14,467−476.3047https://dx.doi.org/10.1021/acs.langmuir.0c03193Langmuir2021,37,3038−3048

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