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lang-bubble formation in FFD-制备气泡
13904Langmuir04-13911BubbleFormationDynamicsinVariousFlow-FocusingMicrodevicesN.Dietrich,S.Poncin,N.Midoux,andHuaiZ.Li*LaboratoiredesSciencesduGe′nieChimique,Nancy-UniVersite′,CNRS1rueGrandVille,BP20451,54000NancyCedex,FranceReceiVedJune26,2008.ReVisedManuscriptReceiVedOctober2,2008Theaimofthisstudyistoinvestigatethreetypesofgas-liquidmicromixergeometries,includingacross-shapeandtwoconvergingshapechannelsforthebubbleformationindifferentliquids.Thebubbleshape,size,andformationmechanismwereinvestigatedundervariousexperimentalconditionssuchasthe?owratesoftwophases,physicalpropertiesoftheliquid,andmixergeometries.Amicroparticleimagevelocimetrytechniqueandahigh-speedcamerawereusedtocharacterizeandquantifygas-liquid?ows.Itwasrevealedthatthebubbleformation,inparticularthebubblesize,dependsonthegeometryofthemixingsectionbetweentwophases.Acorrelationgatheringnumerousexperimentaldatawaselaboratedfortheestimationofthebubblesize.Thein?uenceofdifferentparameterssuchasthe?owrateratiobetweentwophases,surfacetension,andliquidviscosityiswelltakenintoconsiderationonthebasisoftheunderstandingofthebubbleformationmechanismatthemicroscale.Thispapermarksanoriginalimprovementinthedomainwhereno?ow?eldcharacterizationsorcorrelationswereestablishedin?ow-focusingdevices.IntroductionMultiphase?owsinmicro?uidicdeviceshaverecentlyreceivedmuchattentionbecauseoftheforeseeableadvantagesthatuniquemicroscalepropertieshavetooffersuchasenhancementofheatandmasstransferef?ciency,reducedaxialdispersion,andsmallersamplevolumes.Toquantifythesebene?ts,agoodunderstandingofthecomplexmultiphase?owbehaviorinmicro?uidicdevicesmustbegained.Inparticular,theformationofbubbles?ndsverywideapplicationssuchasthegenerationofbiogasbubblesbyanaerobicsludgegranulesinabioreactor,1bubblenucleationinpolymerdevolatizationprocesses,2two-phasemicromixing,3?uorinations,4hydrogenations,5biochemicalreactionssuchasDNAanalysis,6microchannelheatexchange,7materialssyn-thesis,8,9ultrasonicimaging,10,11lipidencapsulation,12anddrugdiscovery.13Thetwo-phase?owpatternsinmicrochannelsaredeterminedbythe?owconditions,thechannelgeometry,andthepropertiesofboth?uidsinvolved.Generally,thegas-liquid?owin*Towhomcorrespondenceshouldbeaddressed.Phone:+33(0).Fax:+33(0).E-mail:Huai-Zhi.Li@ensic.inpl-nancy.fr.(1)Wu,J.;Lu,Z.Y.;Hu,J.C.;Feng,L.;Huang,J.D.;Gu,X.S.WaterSci.Technol.C16.(2)Frank,X.;Dietrich,N.;Wu,J.;Barraud,R.;Li,H.Z.Chem.Eng.Sci.0C7097.(3)Garstecki,P.;Fuerstman,M.J.;Stone,H.A.;Whitesides,G.M.LabChipC446.(4)Chambers,R.D.;Holling,D.;Spink,R.C.H.;Sandford,G.LabChipC137.(5)Kobayashi,J.;Mori,Y.;Okamoto,K.;Akiyama,R.;Ueno,M.;Kitamori,T.;Kobayashi,S.Science5C1308.(6)Burns,M.A.;Johnson,B.N.;Brahmasandra,S.N.;JamesK.H.;Webster,R.;Krishnan,M.;Sammarco,T.S.;Man,P.M.;Jones,D.;Heldsinger,D.;Mastrangelo,C.H.;Burke,D.T.ScienceC487.(7)Qu,W.;Mudawar,I.Int.J.HeatMassTransfer9C2565.(8)Yen,B.K.H.;Gunther,A.;Schmidt,M.A.;Jensen,K.F.Angew.Chem.,Int.Ed.7C5451.(9)Zhang,H.;Tumarkin,E.;Peerani,R.;Nie,Z.;Sullan,R.M.A.;Walker,G.C.;Kumacheva,E.J.Am.Chem.Soc.05C12210.(10)Hettiarachchi,K.;Talu,E.;Longo,M.L.;Dayton,P.A.;A.P.,Lee.LabChipC416.(11)Talu,E.;Hettiarachchi,K.;Powell,R.L.Langmuir),.(12)Talu,E.;Lozano,M.M.;Powell,R.L.Langmuir),.(13)Dittrich,P.S.;Manz,A.Nat.ReV.DrugDiscoVeryC218.microchannelscanbeclassi?edinto?vedifferentregimes,namely,thebubbly?ow,theslug?ow,theslugannular?ow,theannular?ow,andthespray?ow.14Thebubbly?owischaracterizedbytheformationofsinglesphericalbubbleswithbubblelengthssmallerthan,orequalto,thechannelwidth.Increasingthegas?owratecausesthecoalescenceofsmallbubbles,leadingtocylindricalbubbles(separatedfromthewallbyaverythin?lm);thisregimeisknownasslug?owandalsoastheplug,bubbletrain,orTaylorbubble.Thereafter,slugannular?owdevelops,inwhichwavesareformedfromtheannular?lmthatarenotlargeenoughto?lltheentirechanneldiameter.Asupplementaryincreaseinthegas?owrateleadstotheannular?owregime,characterizedbythepresenceofasubstantialliquid?lmatthewallandacentralgasstream.Whenthegas?owrateisfurtherincreased,thespray?owtakesplace,whichconsistsofverysmalldropletsofliquidinacontinuousgasphase.This?owregimemaphasbeendevelopedbyseveralauthors,15,16usuallyasafunctionofthesuper?cialvelocitiesofthegasandliquidphases.Finally,bubbly?owappearsathighliquid?owratesandlowgasvelocities,andslug?owoccursatintermediategasandliquidvelocities.Inthepresentstudy,experimentsaremainlyfocusedonthesegmentedgas-liquid?ows,i.e.,thebubblyandslugregimes,andthelaminar?owregimefortheliquidphase.Thepressuredropinsidethechannelsdependslinearlyonthe?owrateaccordingtoPoiseuille’slaw.ThemostpopulargeometriesforthegenerationofdispersedphasesareT-junctions3,17-22and?ow-focusingdevices.23,24,26,27Therearetwotypesofjunctiondeviceswhere?owfocusingcanoccur.The?rstislithographicallyprepareddevices,andthesecondisaT-junctionwhichcanbeputtogetherbyconnectingcapillaries.Boththesedevicesarecoveredbythiswork.Garstecki(14)Waelchli,S.;vonRohr,R.Int.J.MultiphaseFlowC806.(15)Cubaud,T.;Ho,C.-M.Phys.Fluids5C4585.(16)Haverkamp,V.;Hessel,V.;Lowe,H.;Menges,G.;Warnier,M.J.F.;Rebrov,E.V.;deCroon,M.H.J.M.;Schouten,J.C.;Liauw,M.A.Chem.Eng.Technol.5C1026.(17)vanderGraaf,S.;Nisisako,T.;Schroe,C.G.P.H.;vanderSman,R.G.M.;Boom,R.M.Langmuir4C4152.(18)Guillot,P.;Colin,A.Phys.ReV.E301.(19)Nisisako,T.;Torii,T.;Higuchi,T.LabChipC26.(20)Thorsen,T.;Roberts,W.R.;Arnold,F.H.;Quake,S.R.Phys.ReV.Lett.3C4166.10.1021/la802008kCCC:$40.75?2008AmericanChemicalSocietyPublishedonWeb11/14/2008BubbleFormationDynamicsinMicrodeVicesetal.27useda?ow-focusingdeviceofsmallori?cetogeneratemonodispersedbubbles.Theyfoundthatthebubbleformationwasgovernedbythepressuregradientandthebreakupcouldbecontrolledbythe?owrateofthecontinuousliquidphase.CubaudandHo28studiedtheformationofbubblesinsquaremicrochannelsthroughacross-shapedmixingsection.Theyreportedthatthebreakupmechanismintheirdevicescouldbeattributedtoacompetitionbetweenthepressuresinthegasandliquidphases.Recently,liquid?ow?eldsinmicro?uidicdeviceshavebeeninvestigatedbymeansofthemicroparticleimagevelocimetry(μ-PIV)technique.Forexample,single-phase?owsinmicrof-luidicT-junctionswerecharacterizedbyμ-PIVtechnique.29Earlier,Thulasidasetal.30usedaclassicalPIVtomeasuretheliquidvelocitydistributioninasegmentedgas-liquid?owwithincapillariesofroundandsquarecross-sections.Xiongetal.31describedtheformationofbubblesinasimpleco?owingmicrochannel.Theirμ-PIVmeasurementsshowthatthebubbleformationisduetothevelocitycomponentperpendiculartothegas?owcreatedbythesuddenchangeoftheliquidvelocitydistributionaroundthechannelfrontier.Friesetal.32studiedthetwocounter-rotatingvorticescreatedinslug?owbetweentwogasbubbles.μ-PIVmeasurementsrevealthattherecirculationmovementinmicrochannelsisverysensitivetothechannelgeometry.Theypresentthein?uenceofthesuper?cialvelocities,channeldiameter,andcurveradiusontherecirculationmotionanddemonstratethat,forsegmentedgas-liquid?ow,anincreaseofmasstransferoverthecompletechanneldiameterispossiblebyusingmeanderingchannels.Itisworthnotingthat,uptonow,therehavebeenveryfewμ-PIVstudiesdevotedtothe?ow?eldsaroundabubbleinformation.Velocity?eldsobtainedbyμ-PIVhavebeenreportedforthebubbleformationinaT-junction33andinaY-junction.34Thereisnoreportedworkin?ow-focusingmicrodevicestoourbestknowledge.Formanyindustrialapplications,itisessentialtobeabletoestablishtherelationshipbetweenthegeometricfeaturesandthe?owpatternsuchasthebubbleandsluglengths.Somecorrelationswereproposedtocharacterizetheformationofbubbles(lengthorvolume).Ganan-Calvo35andUtadaetal.25proposedcor-relationsforjet?Ganan-CalvoandGordillo26studiedacross-?ow-focusingmixerandproposedacorrelationbetweenthebubblelengthand?owrateratioswithoutprecisioninthephysicalpropertiesoftheliquid.Cubaudetal.24showedthatthelengthofthecon?nedbubblesfollowsalawbasedonthechannelsizeandtheliquidvolumefraction.Garsteckietal.3studiedacross-?owmicromixerandalsodevelopedasimplecorrelationbetween(21)Tice,J.D.;Song,H.;Lyon,A.D.;Ismagilov,R.F.Langmuir7C9133(22)Xu,.J.H.;Li,S.W.;Wang,Y.J.;Luo,G.S.Appl.Phys.Lett.506(23).Anna,S.L.;Bontoux,N.;Stone,H.A.Appl.Phys.Lett.C366(24).Cubaud,T.;Tatineni,M.;Zhong,X.;Ho,C.-M.Phys.ReV.E302(25).Utada,A.S.;Fernandez-Nieves,A.;Stone,H.A.;Weitz,D.A.Phys.ReV.Lett.502(26)Ganan-Calvo,A..M.;Gordillo.,J.M.Phys.ReV.Lett.501(27)Garstecki,P.;Stone,H.A.;Whitesides,G.M.Phys.ReV.Lett.4501(28).Cubaud,T.;Ho,C.-M.Phys.Fluids5C4585(29)Lindken,R.;Westerweel,J.;Wieneke,B.Exp.Fluids2006,11.,161C171(30)Thulasidas,T.C.;Abraham,M.A.;Cerro,R.L.Chem.Eng.Sci.7C2962(31)Xiong,.R.;Bai,M.;Chung,J.N.J.Micromech.Microeng.2C1011(32)Fries,.D.M.;Waelchli,S.;RudolfvonRohr,P.Chem.Eng.J.C45(33).vanSteijn,V.;Kreutzer,M.T.;Kleijn,C.R.Chem.Eng.Sci.5C7514(34)Dietrich,.N.,Poncin,S.,LiH.Z.Re′centsProgre`senGe′niedesProce′de′s,95th(35)ed.;GanaSFGP:?′?n-Calvo,Paris,A.2007M..Phys.ReV.Lett.C288.Langmuir,Vol.24,No.24,the?owrateratioandbubblelength.Pancholietal.36investigatedthebubbleformationinhighlyviscousliquidsanddeterminedthein?uenceofthedifferentoperatingparametersonthebubblesize.Itwasfoundthattheoreticalpredictionsofthe?owpro?lewereveryaccuratewhencomparedwiththeexperimentaldata.Boththetheoreticalandexperimentalresultsshowedthat?owrateratiosorviscosityhadasigni?cantin?uenceonthebubbleformationandsize:higher?owratesandhigherviscositiesproducedsmallerbubbles.However,toourbestknowledge,nocorrelationexistsfortheestimationofthebubblevolumeincludingwidephysicalpropertiesoftheliquid.Intheliterature,therearefewstudiesontheeffectofthemicromixergeometry.Haverkampetal.16studiedthe?owofgas-waterintwomixinggeometries:“T-type”and“smooth”mixers.TheyreportedthatthebreakupbyapressuregradientwasonlyobservedintheT-typemixer,whilethejetinstabilitywastheuniquemechanismforbubbleformationinthesmoothmixer.Fanetal.37investigatedtwotypesofmixergeometriesincludingthecrossandconvergingshapechannels.Thebubbleshapeandsizeandtheformationmechanismwereconsideredfordifferent?owrates.Theseauthorscomparedsatisfactorilythesimulatedresultswithexperimentaldataintheformofdimensionlessnumbers.Different?owregimeswithdifferentbubbleshapeswerefounddependingonthecapillarynumberofthe?ow.Thesimulateddatacon?rmedthatthebreakupwasinducedbythepressuredifferenceinbothphases.Thegeometryofthemixingsectionwasalsoobservedtohaveanimpactonthesizeofthegasandliquidslugs,butnoexperimentalquanti?cationofthebubblesizeandvelocity?ow?eldwasrealized.Thepresentworkisdevotedtotheformationofbubblesin?ow-focusingmicromixersofdifferentgeometries.Bymeansofaμ-PIVsystemandahigh-speeddigitalcamera,theroleofinertial,viscous,andinterfacialforceswasexperimentallyinvestigatedtogainnewinsightintothemechanismofbubbleformationatthemicroscale.ExperimentalSetupThedifferentgeometriesofthemicromixersusedinthisstudyareshowninFigure1.Themicrochannelswerefabricatedinpoly(methylmethacrylate)(PMMA).This?ow-focusinggeometryhasacentralchannelforthedispersedgas-phase?owandtwosidechannelsfortheinletofthecontinuousliquidphase.Twodifferentsizesofliquidinletandoutletchannels(600and1000μm)andofgasinletchannels(200and500μm)wereused.Thesectionofthegasinletiscirculartoavoidwettingproblems,andtheothersectionsaresquaretoenableabettervisualizationofthe?ow?eld.Twopressurizedtanksof10-3m3wereusedtomaintainaconstantpressureandtopushtheliquidandairstreamsintothemicrochannelwitharegular?owrateofeachphase.Agas?owmeterwasusedtodeterminethe?owratewithprecision.Imagesofbubbleswerecapturedbyahigh-speeddigitalcamera,CamRecord600(OptronisGmbH,Germany),equippedwithamicroscopicobjectiverangingfrom100×to600×.Thetypicalacquisitionratewas500framespersecondwithafullresolution().Underthesteadyformationconditions,thelengthofthebubblewasdeterminedthroughimageanalysissoftwareandthebubblevolume,Vb,wascalculatedfromthegas?owrate,Qg,andthebubbleformationfrequency,f,determinedbythehigh-speedcameraasfollows:Vb)Qgf(1)Theinstantaneousliquidvelocity?ow?eldsweremeasuredbyaμ-PIVsystem(DantecDynamics,Denmark).Thesystemconsists(36)Pancholi,K.;Stride,E.;Edirisinghe,M.Langmuir),).Fan,L.S.;Yu,Z.;Hemminger,O.Chem.Eng.Sci.5C7514.13906Langmuir,Vol.24,No.24,2008Dietrichetal.Figure1.Illustrationofthemicro?uidicchipusedtogeneratethemicrobubble.Fromthelefttotherightareshownthecrossshape(180°)andconvergenceshape(90°and60°).W)1
mm.Figure2.μ-PIVprinciple(50×50μmwindows).ofaFlowsenseDanteccamerawithapixelarrayanda7Hzfrequency.Theinversedmicroscope(LeicaDMILM)wasequippedwithdifferentobjectives(LeicaHCPLAN)rangingfrom5×to100×.Themicrodeviceunderinvestigationfacedthemicroscopeandwasilluminatedfromthebackbyamicrostrobeemittingalightat530×10-9m(themonochromaticcharacteravoidsthechromaticaberrationsintheimaginganalysis).Theliquidvelocity?eldsweremeasuredbytrackingandevaluatingthemotionofseedingparticlessuspendedinthe?uid.Theprincipleofμ-PIVisreportedinFigure2.Thecameratooktwosuccessiveimagesatthemaximumintensityofthemicrostroboscopeimpulse.Theacquiredimagesofthe?owwereanalyzedbydividingtheimagesintoafewthousandsmallareasof16×16pixelscalledinterrogationareas.Across-correlationwasthenappliedontheinterrogationareasinconsecutiveimageswitha50%windowoverlap.Foreachinterrogationarea,thedisplacementvectorwascalculatedfromthelocationofthecorrelationpeak.Thevelocity?eldswerethencalculatedfromthedisplacementvectorsandthetimechosenbetweentheimages.Themeasurementswererealizedonasliceofthemicromixerofavaluearound10μmduetothefocusofthemicroscope.However,thisvalueisnegligibleincomparisonwiththethicknessofthemicrochannel.Seedingparticlesshouldbeuniformlydispersedin?uidwithareasonableconcentration.Thedensityshouldbesimilartothatofthestudied?uid.Iftheseedingparticlesusedaretoosmall,theBrownianmotion38couldinduceerrorsinthemeasurements.Thisrandommotionsetsalowestlimitoftheseedingparticles’sizetoachieveμ-PIVmeasurements.StartingfromtheequationofEinstein-Sutherland,39itispossibletoestimatethein?uenceofthisBrownianmotionthroughthediffusioncoef?cient,D:m?s-1.Theliquidvelocityusedinthisstudybeingseveralhundredsofmicrometerspersecond,anerrorontheorderof1%isthenexpectedforthevelocity.LargerparticlesshouldbechosentoavoidinaccuracyproblemsduetotheBrownianmotion,butthebiggertheparticle,thehigheritssettlingvelocity.ThesedimentationvelocityofaparticleofdiameterdisestimatedintheStokesregime:d2g(Fp-Fl)Vp)18μ(4)D)kT6πμr(2)Tisthetemperature,μthe?uidviscosity,rtheparticleradius,andktheBoltzmannconstant.ThisequationshowsthattheBrownianmotiondependsinverselyontheradiusoftheparticle.Thestandarddeviationoftherandommovementofaparticleisgivenasfollows:Forseedingparticlesof3×10-6mdiameter,thevalueofthesedimentationvelocityisaround1.5×10-6m?s-1.Finally,toreachasuitablecompromisebetweentheBrownianmotionandsettlingvelocityforwhichtherelativeerrorisbelow1%,theoptimalsizeoftheseedingparticlehastobeintherange(0.5-3)×10-6m.Furthermore,thesizesofthegeometry,viewingwindows,andcameraobjectiveshelptore?nethevalueoftheparticlediameter.Inthisstudy,hydrophiliclatexmicrospheres(MerckEstapor,France)withadensityof1056kg?m-3andameancalibrateddiameterof0.88×10-6mwereusedasseedingparticles.Theseparticlesweresmallenoughtofollowthe?uidandlargeenoughtoavoidtheBrownianmotioneffects.Whenthe?owiscorrectlyinseminated,themeasurementerrorsofthemeasuredvelocitiesarelessthan5%.Inthiswork,theexperimentswereperformedusingairasthegasphaseandthreedifferentliquids(purewater,viscousNewtonianEmkaroxHV45,10and20wt%dilutesolutionsindemineralizedwater).ARheometric?uidspectrometer,RFSII(RheometricScienti?c),wasemployedtocharacterizetherheologicalpropertiesoftheliquids(Table1).ThesurfacetensionandthecontactangleoftheliquidonthePMMAsurfaceweremeasuredusingatensiometerbythependingdroptechniqueonaTrackerapparatus(I.T.Concept,France).Sodiumdodecylsulfate(SDS)surfactant(Amersco)wasalsousedtomodifythesurfacetension,whichallowsseparatecomparisonoftheeffectsofthesurfacetensionandviscousforce.Table1gathersallpropertiesofthevariousliquidsused.Allexperimentswerecarriedoutataconstanttemperatureof293K.(38)Brown,R.Philos.Mag.C173.(39)Einstein,A.Ann.Phys.-560[alsodemonstratedbyW.Sutherland(Philos.Mag.)]
.Σp)?xp≈√2Dδt(3)Thus,foracamerafrequencyof4s-1andaparticlediameterof200×10-9m,therandommovementisestimatedat3×10-6BubbleFormationDynamicsinMicrodeVicesTable1.PropertiesoftheDifferentLiquidsUsedinThisStudyat293Kθcontactσ(103?uidF(kg?m-3)μ(103Pa?s)(deg)N?m-1)waterwater+0.10%SDS(wt)water+0.15%SDS(wt)%HV45(wt)%HV45(wt)+0.05%SDS(wt)25%HV45(wt)1050304740ExperimentalResultsInthepresentwork,extensiveexperimentalinvestigationwasrealizedforthebubbleformationinthreedifferentmicromixergeometriesofvariousjunctionangles(180°,90°,and60°).Tounderstandthekeyparameterofthebubbleformationprocess,apreliminarystudywasdevotedtothein?uenceofeachfactor.Thegasandliquid?owratesrangefrom10-12to10-6m3?s-1,whichcorrespondtothebubblyandslug?owregimes-3andbubblediametersbetween50×10-6and5×10m.Thebubbleformationwasstudiedbybothμ-PIVand-9high-speedcameravisualization.Theshapeevolutionofa10m3bubbleintimeduringtheformationprocessuntiltoitsdetachmentisshowninFigure3.Thebubble1formationwasperfectlyperiodicwithafrequencyof34s-.Figure3showsthegrowthprocessduringoneperiod.Thebubbleshapewasobtainedthankstoahigh-speedcamera.Onecandistinguishtwostepsduringtheformationofthebubble:?rst,arapidexpansionstsecond,afastelongationofthebubbleuntilitsruptureunderadualactionofstretchingbythewallsandlateralliquid?ow.Itisclearlyseenthat,inthiscase,abubbleexpandssphericallyatthebeginningofthebubbleformatioand,thenevolvesfromsphericalshapetoaxisymmetricalteardropshape.Inthisstagethebubblegrowswithoutsigni?cantmovementintothestreamdirectionandtheliquidcirculateseasilyaroundthegrowingbubble.Subsequently,theeffectof?owinertiaonthebubblebecomesgraduallyimportantduringthegrowthofthebubble,theinterfacemoves,andthebubbleisstretchedtoformaneckthatiselongatedtoanobviousteardropshapeuntilrupture.Figure4representsthevelocity?eldsoftheliquidaroundabubbleinacrossshape?ow-focusingmicromixer.Att/tf)0.05(Figure4a),thebubblestartsitsprogressioninthemaincentralzoneanddoesnotseemtoperturbthe?owmuch.Att/tf)0.3(Figure4b),the?owrateofthecontinuousliquidisbypassingthebubbleasanobstacle.Whenthebubble?llsthecross-junction,theliquid?owpatterninthetwolateralchannelsbecomesreducedandcon?nedtothewallofthechannels.Att/tf)0.8(Figure4c),thevelocity?eldsvanishalmostinthechannel.Closetothegas-liquidinterfacetheliquid?owisacceleratedduetothemassconservation.Asaresult,relativelyhighvelocitiesupto4timestheaveragevelocityareobtainedinthegapbetweenthegas-liquidinterfaceandtheoppositewallofthechannel.Att/t)1(Figure4d),theformationcycleendswiththebreakupofftheneckofthebubbleandtheformedbubbleentersthemainchannel.Thevelocity?ow?eldisdirectedinbothoppositedirectionsduetothereleaseofthesurfaceenergywhenthebubblesnaps.Duetotheshorttimeofformationofthebubble,itisverydif?culttomeasurethevelocity?eldsjustbeforeandafterthebubblepinch-off.Theμ-PIVtechniqueisapowerfultooltoevaluatethemainforcesactingonthebubble.AsshowninFigure4c,d,theneckinterfaceundergoesthedeformationundershearstresseswhichcanbeestimatedfromtheliquid?owgradientattheinterfaceofthebubble.Forexample,inFigures3and4,theshearrateLangmuir,Vol.24,No.24,isabout500s-1.Bycomparisonwithotherforcesactingonthebubble,theshearstressisnotthekeyforce.Table2presentsthetypicalvaluesofthreemainforceswhichactonthebubbleduringtheformationandbreakup.Themainformationmechanismdependsonthecompetitionbetweentheseforces:thestaticpressureandsurfacetensionplayamajorrolewithrespecttotheshearstress.Themeasurementofthe?ow?eldaroundaformingbubbleina?ow-focusingmicro?uidicsystemcomfortstheproposedformationmechanismintheliteratureresults.3,24Moreover,asshowninFigures3and4,thebubbleshapeisnotsodeformed.ThiscanbeexplainedbythedominantvalueofthesurfacetensionevaluatedaccordingtotheLaplaceequationwithrespecttotheothertwoforces.Thisresultsalsoinaverysmalldeformationofthebubbleduringitsformation.Besidesthemeasurementoflocal?owpropertiesbymeansofμ-PIV,theglobalpropertiessuchasthebubblelengthandvolumewerequanti?edusingahigh-speeddigitalcameraanda?owmeter.Itisthereforepossibletodeterminethephysicalkeyfactorsinvolvedintheformationmechanism.The?owrateratioseemstoplayanimportantroleintheformationofmicrobubbles.Figure5aillustratestheevolutionofthedimensionlessratioL/Wofthebubblelengthtothechannelwidthwiththegas?owrate(whenliquid?owisconstant)andinversely.Theseresultsshowthatthedetachedbubblelengthisaffectedbybothgasandliquid?owrates.Thebubblevolumeincreasesgraduallywiththegas?owrateanddecreaseswiththeliquid?owrate.Thisslowevolutionmaybeexplainedbytheincreaseofshearstressandelongationwhentheliquid?owrateincreases,leadingtotheformationofsmallerbubbles.Thetransitionbetweenbubblyandslug?owwasaddedinFigure5basadashedline.Inourexperiments,wenotedthatthistransitionappearsforaReynoldsnumberofabout10,buttheuseofthisdimensionlessnumberwasnotrelevanttogeneralizeourresultsincontrarytothe?owrateratios.TheevolutionoftheL/WratioasafunctionoftheQg/Qlratioforvarioussizesofthegasinletandgas-liquidoutlet(Figure5b)mayberepresentedbythefollowingcorrelation:L(QW)??ggQ(5)l)RwhereboththepowerlawindexR)0.25andconstant??valuedependontheliquidphysicalpropertiesandthegeometryofthemicromixers.Thissimplecorrelationdescribesquitewellthein?uenceofboththe?owrateandthesizeofthemicromixer’schannels.Previousauthors26,27havepointedoutthattheexponentofthepowerlawthatrelatedL/WandQg/Qlwasabout1/3.Ourexperimentaldataindicateanexponentof1/4.Thisdifferenceisduetotheratiobetweenthewidthsofthegasandliquidchannels(Wg/Wl).AsreportedbyGarsteckietal.,27thepowerlawexponentincreaseswiththisratiofromR)0.4forW1toR)1forWg/W)lg/Wl)3.Ganan-CalvoandGordillo26foundanexponentofR)0.37forWg/Wlestablishalinearrelationshipbetween≈1.RandThenWitispossibletog/Wlfromtheseresultsasfollows:R)1Wg4W+1l9(6)Forourexperiments,whereWR)1/4,?tsperfectlyrelationshipg/W6establishedl≈0.5,thefromexponenttheliterature,found,makingthisequationvalidforagreaterrangeofmixers:Wg/W∈0.5To-improve3andRcorrelation∈0.25-1.l5,theliquidphysicalpropertiessuchasthesurfacetension,σ,theviscosity,μ,andthegeometryofthemixerarevariedtoinvestigatetheirrespectivein?uence.13908Langmuir,Vol.24,No.24,2008Dietrichetal.Figure3.Bubbleformationinthecross-?ow-focusingmicromixer.Vb)10-9m3.Thegasinletchannelis200μm,theliquidinletandoutletchannelsare1000μm,theliquidispurewater,andtheliquidandgas?owratesare10-8m3?s-1
.Figure4.Velocity?eldmeasurementbytheμ-PIVsystemfora10-9m3bubbleformationinacross-?ow-focusingmixer.Thefocusplaneoftheμ-PIVmeasurementissituatedinthemiddleofthechannel.Thegasinletphaseis200μm,theliquidinletandoutletchannelsare1000μm,andtheliquidispurewater.Key:(a)t/tf)0.05;(b)t/tf)0.3;(c)t/tf)0.8;(d)t/tf)1.Table2.ThreeMainForcesActingonaFormingBubbleinaFlow-FocusingMicromixerforaBubbleRadiusatDetachmentof300×10-6mthreemainforcesactingonthebubbleshearstresssurfacetensionpressuredistributionτ)μγB?Pσ)2σ/R?P)(1/2)FV2valuesforFigures3and4τ)0.5Pa?Pσ)483Pa?P)1.25PaFigure6showstheevolutionoftheL/WratioasafunctionoftheQg/Ql?owrateratio.ThesimilartendencyisobservedforallthegeometriesinFigure6withthesamepowerlawindexR)0.25.TheeffectofthemixingsectiongeometryonthebubblelengthwasstudiedforthreetypesofmixersasshowninFigure6a:across-shapedmixerforwhichtheliquidinletchannelwasperpendiculartotheoutletchannelandconvergingmixerswithrespectiveanglesof45°and30°betweenbothliquidinletchannelsandthecentralgas-liquidoutletchannel.Thewidthofthechannelsinthesegeometrieswas200μmforthegasinletand1000μmfortheliquidinlet.Experimentswerecarriedoutforeachgeometryusingdifferentoperatingconditions.Foragivengeometry,theincreaseoftheratioofthegas?owratetotheliquid?owrateyieldstheaugmentationofthebubblelength.However,thebubblesizeincreaseswithadecreaseoftheangleθ(Figure
6a).BubbleFormationDynamicsinMicrodeVicesLangmuir,Vol.24,No.24,Figure5.(a)In?uenceofgasandliquid?owratesonthebubblelengthtochannelwidthratio(L/W):(×)vsQgatconstantQl;(4)vsQlatconstantQg.Theinletchannelsizeis200μmandtheoutletchannelsize1000μm.(b)EffectofinletandoutletchannelsizesontheevolutionofL/Wasafunctionofthe?owrateratiosinwater.Re∈0.005-
950.Figure6.In?uenceoftheliquidphysicalpropertiesandmicromixergeometry(inletof200μmandoutletof1000μm):(a)in?uenceofthejunctionangleofthemixer,θ(b)in?uenc(c)in?uenceoftheviscosity.<parisonoftheMicromixerGeometry
CorrelationsTheeffectofthesurfacetensionwasinvestigatedbytheadditionoftheSDSsurfactantinwaterinonemicromixergeometry(180°).Asexpected,thebubblelengthincreaseswiththesurfacetension(Figure6b).Finallytheeffectoftheliquidviscositywasinvestigatedinthe180°anglemicromixerwiththreeliquidsofthesamesurfacetension(Figure6c).Onceagain,thebubblelengthincreaseslogicallywiththeliquidviscosityduetotheincreaseoftheshearstressesactingonthebubble.Thefactor??ineq5seemstobelinkedtothesethreeparameters.Adimensionalanalysiswasappliedtoobtainadimensionlesscorrelationofbubblelengthunderalloperatingconditionsandmixergeometriesinvestigatedinthisstudy.Forthispurpose,150datapointswereusedtodeterminesuchacorrelation.Table3resumesthecorrelationsobtainedforeachmixergeometry.Thedimensionlessnumbersbasedontheviscosityandsurfacetensionwereintroducedusingthephysicalpropertiesμrefandσrefofwaterasareference.Theexperimentaldataarequitewelldescribedbythesecorrelationswithanaveragerelativeerrorbelow3%andamaximumerroroflessthan13%.Twoconclusionscanthenbedrawnfromthistable.First,thein?uenceofthesurfacetensionismoreimportantthanthatoftheviscositywithahigherpowerindex.ThisisinagreementwiththemagnitudeofvariousforcesgatheredpreviouslyinTable2:theshearstressismuchsmallerthanthesurface
tension.13910Langmuir,Vol.24,No.24,2008Figure7.Flow?eldofa10-9m3bubbleintwodifferent
micromixers.Figure8.Paritydiagrambetweencorrelateddataandexperimentalresults.Second,theeffectofthesurfacetensionincreaseswiththedecreaseoftheangleθthroughasigni?cantincreaseoftheelongationratio.Thisisopposedtothetendencyoftheviscosityeffect.Infact,thepowerindexofthesurfacetensiondecreasesandthatoftheviscosityincreaseswiththeangleθ.Clearly,theuseofboththeμ-PIVtechniqueandthehigh-speedcamerabringssomenewinformationintotheunderstandingofthebubbleformationatthemicroscale.Figure7showsthe?ow?eldsofliquidaroundaformingbubbleinacross-?ow-focusingmixer(Figure7a)andinaconvergence(θ)60°)?ow-focusingmixer(Figure7b).Thedetailed?ow?eldobtainedjustbeforethebubblepinch-offisusefultoevaluatetheshearstressinthesemixersforthecomparisonwiththepressuredistributionandsurfacetension.Obviously,theshearrateishigherinthe180°anglegeometry(500s-1)thaninthe60°geometry(350s-1).Theeffectoftheshearstressisthereforemoreimportantwhenθincreases,whichisinagreementwithcorrelationsreportedinTable3.Theanglebetweentheinletwallandthebubbleatitsformation(θformation)andthedimensionlessratiooftheelongationLb/Rb(RbistheequivalentradiusofthebubbleandLbthelengthofthestretchedbubble)arealsoreportedinFigure7.ThebubbleismoreelongatedintheY-sectionthanintheT-section.AnarroweranglesuchastheY-sectionobligatestheelongationofaformingbubblesothattheeffectofthesurfacetensionincreasesduetothedeformation.Thiscon?rmsthetendencyeffectofthesurfacetensionproposedinthecorrelationsofTable3.Thus,μ-PIVmeasurementscanprovidequantitativeinforma-tionforvalidatingthecorrelationsestablishedforthevariousmixers.Totakeintoaccountthein?uenceofthemixerangleonthebehaviorinducedbytheeffectoftheliquidviscosityandtension,aθ/θmaxratiowasaddedinthecorrelationsofTable3,whereθmaxisthemaximalangle(i.e.,180°).ThefollowingDietrichetal.dimensionlesscorrelationwasobtainedonthebasisofabout150experimentaldata:L1/8σμ1/10Qg1/4W)8.3(θgθmax)-(σref)(μref)(Q)(7)lFigure8showsthegoodagreementobtainedbetweenexperimentalL/Wvaluesandthoseestimatedfromthiscorrelation.Theaveragerelativeerrorisabout6.5%withamaximumerrorof18.7%.Thiscorrelationgivesagoodestimationforthebubbleformationinaliquidofviscosityrangingfrom1to30mPa?sandsurfacetensionrangingfrom40to72.5mN/mandwithdifferentgeometriesandsizesofmicromixers(angleof180°,90°,and60°andWg)200,500,and1000μm).Itcouldbeausefultoolformicromixerdesigntakingintoaccounttheliquidphysicalpropertiesaswellasthegeometryofthemicromixer.Furthermore,asimilarcalculationwaselaboratedforthebubblevolume:Vb1/4)300θW3(8)g(θc)-1/6(QgQl)Withanaverageerrorofabout12%,theparitydiagramisnotreportedhereasitisveryclosetoFigure8.Inthisequation,theviscosityratiowasretiredduetoitsweakin?uence(powerlawexponentof1/50),whichcon?rmstheconclusionofGarsteckietal.27thatbubble-formingsystemsarelargelyindependentoftheviscosityratiosandcapillarynumber.Also,inthiscorrelation,thesurfacetensionisreplacedbythecontactangle,θcontact,oftheliquidonthematerialtosimplifytheuseofthecorrelation.AsshowninTable2,theeffectofshearstressissmallerascomparedtothesurfacetensionandpressuredistribution,whichisingoodagreementwiththiscorrelationrevealinganinter-tiocapillaryregime.ConclusionThesegmented?owofatrainofbubbles?ndsverywideapplicationsofmultiphase?owinmicro?uidicdevices.Inthiswork,experimentswerecarriedouttostudythegas-liquid?owsinmicrochannels.Thebubbleshape,size,andformationmechanismwereinvestigatedunderdifferent?owconditions.Themechanismofbubbleformationina?ow-focusingmicromixerwaspreviouslyproposedaspinchedoffbythepressuredifferenceinbothphases.3,24Thecurrentworkcon?rmsthisgeneralmechanismofbubbleformationbythemeanofμ-PIVmeasurements.Theliquid?ow?eldsofthecontinuousphaseduringtheformationofbubblesprovideimportantquantitativedetailsthatwereneverreportedintheliteratureforthiskindofmicromixer.Moreover,thebubblesizewasshowndependentontheliquidphysicalpropertiessuchastheviscosityandsurfacetensionaswellasthegeometriesofthemixingsection.Accordingtothemicromixer’sgeometry,theviscosityandthesurfacetensionhavedifferentin?uences.Finally,somecorrelationswereproposedtopredictthebubblevolumeandlengthforallgas-liquidsystemsandmicromixergeometriesinvestigated.Thepredictedvaluesareingoodagreementwiththeexperimental
results.BubbleFormationDynamicsinMicrodeVicesGlossaryNotationVbbubblevolume,m3Wchannelwidth,mQ?owrate,m3s-1Llength,mRbbubbleradius,mrradius,mkBoltzmannconstant,J/KDdiffusioncoef?cient,m2/sTtemperature,KVvelocity,m/sGreekLettersγBshearrate,s-1Σstandarddeviation,mR,??powerlawcoef?cientsLangmuir,Vol.24,No.24,μviscosityoftheliquid,Pa?sθangle,degFdensity,kg?m-3σsurfacetension,N?m-1SubscriptsggaslliquidpparticlerefreferencepropertiesmaxmaximalAcknowledgment.The?nancialassistanceprovidedbytheFrenchMiniste`redel’EnseignementSupe′rieuretdelaRechercheisgratefullyacknowledged.LA802008K
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