接触角和倾斜角的测定

Understandingofslidingandcontactangleresults

intiltedplateexperiments

E.Pierce,F.J.Carmona,A.Amirfazli∗

DepartmentofMechanicalEngineering,UniversityofAlberta,Edmonton,ABT6G2G8,CanadaReceived30June2007;receivedinrevisedform10September2007;accepted18September2007

Availableonline25September2007

Abstract

Tiltedplateexperimentalmethodologyisstudiedinordertoaddressmisinterpretationsandomissionsthatexistintheliterature.Theeffectofmethodologyonsubsequentslidinganglemeasurementsisquantitativelyassessedintwoparts.Thefirstpartisacomparisonofdropplacementtechniquesintheconventionaltiltedplatemethod(dropsplacedonalevelsurface,theninclined).Thesecondpartisacomparisonbetweentheconventionaltiltedplatemethodandamodifiedmethod,inwhichthedropisplacedonasurfacethatisalreadyinclined.Thefirstpartofthestudyinvolvedwaterdropsplacedonalkylketenedimmer(AKD)surfacesusinganeedlefromaboveaswellasbelowthesurface(throughahole).Fordropsplacedfrombelow,threedifferentdroplocations(withrespecttotheholeinthesurface)areincludedinthestudy.Itwasfoundthatthedropplacementtechniquehadastatisticallysignificantimpactonslidinganglemeasurements,andthemostconsistentandunbiasedmeasurementsresultedwhenthedropwasplacedfrombelow,withtheholeleading(downhillfrom)thedrop.ThesecondpartofthestudyinvolvedwaterdropsonbothAKD(highcontactanglehysteresissystem)andfluorinatedsilicon(lowcontactanglehysteresis)surfaces.Foreithersystem,itwasshownthatslidingangleswerelowerwhendropswereplacedonsurfacesthatwerealreadyinclined.Sincethemaximumandminimumcontactangleswereidenticalbetweenthetwoexperimentalmethods,thedifferenceinadhesionwasduetovariationincontactlineshape.Theresultsofthisstudyshowthaterrorsof50–60%wouldresultfromusingconventionaltiltedplatemeasurementstopredictdropletmobilityonfixed,inclinedsurfaces,suchasthosefoundincondensers.Theimportantdistinctionbetweenrepellency(measuredbytheadvancingcontactangle)anddropmobilityisalsodiscussed.Further,itwasobservedthattheadvancingandrecedingcontactanglesdonotalwayscorrespondtothemaximumandminimumcontactanglesobservedinatiltedplateexperiment.©2007ElsevierB.V.Allrightsreserved.

Keywords:Tiltedplate;Slidingangle;Repellency;Contactangle;Hysteresis;Wetting;Dropmobility;Inclinedsurface

1.Introduction

Inatypicalwettingexperimentusingthetiltedplatemethod,adropisplacedontoasurface,whichistheninclineduntilthedropbeginstoslide.Theslidingangleisameasureofthemobilityofadroponthesurface,whichisofconcerntoavarietyofappli-cationsfromtextilestomicrofluidics.Thetiltedplatemethodisalsosometimesusedtodeterminetheadvancingandreced-ingcontactangles.However,thismaynotbethemostsuitablemethod,aswillbediscussed.Unfortunately,studiesthatusethetiltedplatemethodareseldomaccompaniedbymethodologicaldetailsmuchbeyondprovidinganapparatusmodelnumber.Itwillbeseenthatanumberofimportantsubjectivitiesarethereby

∗

Correspondingauthor.

E-mailaddress:a.amirfazli@ualberta.ca(A.Amirfazli).

withheld:fromthedropplacementtechniquetotheprecisedef-initionofslidingangle(thelatterbeingespeciallyimportantforverificationoftheoreticalresults).Theseissuesnotonlyprecludesurfaceperformancecomparisonsbetweendifferentresearchersbutcanobscurethephysicalmeaningoftheresults.

Anexampleofamisinterpretationarisingintheliteratureistherelationshipbetweendropmobilityandrepellency.Repel-lencyisameasureofasurface’sresistanceto“wettingout.”Repellencycanbedefinedbythethermodynamicquantityoftheequilibriumcontactangle,butduetotheimpracticalityofequilibriumcontactanglemeasurements,itistypicallyrep-resentedbytheadvancingcontactangleofadrop,whichis

¨measuredonalevelsurface.OnerandMcCarthy[1]havepru-dentlydrawnattentiontorecentliteraturethatindiscriminately

associatesadvancingcontactanglewithmobility.However,theygoontostresstheimportanceofcontactanglehysteresistomobility,citingtheoriginalequation,derivedbyFurmidge[2],

0927-7757/$–seefrontmatter©2007ElsevierB.V.Allrightsreserved.doi:10.1016/j.colsurfa.2007.09.032

74E.Pierceetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects323(2008)73–82

thatdefinedslidingangleasafunctionoftheadvancingandrecedingcontactangles(θAandθR):sin(α)=γ

Rk

mg(cosθR−cosθA)(1)

whereαistheslidingangle,γissurfacetension,misthemassofthedrop,andRandkarealengthscaleandshapeconstantforthecontourofthedrop,respectively(Risgenerallytakenasthedropradiusandkisafittingparameterbasedonimentaldata).AlthoughOner¨theexper-andMcCarthymadeitclearthat

contactanglehysteresiscanbeaqualitativeindicationofdropmobility,ithasbeenarguedbyKrasovitskiandMarmur[3]thatadvancingandrecedingcontactangles,asmeasuredonalevelsurface,shouldtheoreticallynotbeusedinnumericalpredic-tionsofslidingangles(ameasureofdropmobility).Instead,theauthorsdefinethemaximumandminimumcontactangles(θmaxandθmin),whicharethoseattheleadingandtrailingedgesofadropprofileonasurfaceinclinedtotheslidingangle(Fig.1a).Theyreportthattheoreticalevidencesuggeststhattherelation-shipbetweenθmaxandθAaswellasθminandθRvariesbetweendifferentsurface/liquidcombinations.AlthoughthisconclusiondisagreeswiththeempiricaldataofElSherbiniandJacobi[4],whichexhibitθmaxandθminapproximatelyequaltoθAandθRforallsurface/liquidcombinations,theresultsofthisstudysup-portit.Thecontactanglesofwaterdropsonbothalkylketene

Fig.1.(a)Illustrationofthemaximum(θmax)andminimumcontactangles(θmin)aswellasthebodygravityforce(mg),andsurfacetensionforce(γ)foradropinclinedtotheslidingangle(α);thecomponentsoftheseforces,γxandmgx,actparalleltothesurfaceandperpendiculartotheaxisofinclination.(b)Topviewofthecomponentofthesurfacetensionforcedistributionthatisparalleltothesurface(γϕ)foradroponanincline;dashedlineshowscontactangletransitionthrough90◦.Adhesion(reaction)forcesareequalandoppositetothecomponentof(γϕ)thatisperpendiculartotheaxisofinclination(γx).

dimmer(AKD)andfluorinatedsiliconsurfacesweremeasuredbothattheslidingangleaswellasonalevelsurfaceaswaterwasaddedandwithdrawnfromthedrop.Therecedingcon-tactangle(θR)ofawaterdroponAKDsurfacewasatleast73◦lessthantheminimumcontactangle(θmin),butforflu-orinatedsiliconsurfaces,theywerenotmeasurablydifferent.Therefore,therelationshipsbetweentheadvancing/recedingandmaximum/minimumcontactanglesareuniqueconsequencesofsurface/liquidcombinations,soEq.(1)mustberedefinedasfollows:sin(α)=γ

Rk

mg(cosθmin−cosθmax)(2)

AsinEq.(1),Randkarelengthscaleandshapeconstantsforthecontourofthedrop.Theseparametersareneces-sarybecausetheslidingdropproblemcannotbeadequatelyrepresentedbyatwodimensionalprofileimageofthedrop(providingθmaxandθmin).Dropadhesionistheresultofadistributedforceactingparalleltothesurfaceandperpen-diculartothecontactline(Fig.1b).Themagnitudeoftheforcedistributionisdeterminedbythecontactangleateachpoint,butitsdirectionresultsfromtheshapeofthecontactline(representedbythefittingparameterk).Therefore,theshapeofthecontactlinedefinesthecomponentoftheforcedistributionthatisactiveinadhesion,i.e.opposesthecom-ponentofgravitationalforceactingalongthesurfaceplane.Itwillbeseenthatthecontactlineshapehasasignificantinfluenceonmobility.Assuch,dropmobilityisnotapri-marythermodynamicproperty,asitisthemanifestationoftheinteractionbetweenanexternalforceanddropadhesionforce.

Precisionisanissueofgreatconcernwithtiltedplateexper-iments.Toobtainstatisticallysignificantresults,itisoftennecessarytorepeatexperimentsmanytimes.Furthermore,ithasbeenobservedthatsmalldifferencesinexperimentaltech-niquesamongstresearcherscandramaticallyaffecttheslidingangle.Inordertoincreasemeasurementconfidenceaswellasfacilitatethecomparisonofdatabetweenresearchers,detailedtiltedplateexperimentprotocolmustbediscussed.Thisstudyexaminesseveralpointsregardingtiltedplateexperimentproto-colwithrespecttotheiraffectonthemagnitudeandprecisionoftheresults.Inparticular,itwillbeshownthatdifferingplacementmethodsofawaterdroponAKDcansignificantlyaffectthemagnitudeandprecisionofslidinganglemeasure-ments.

Tiltedplatemethodologymustbeconsiderednotonlyintermsofexperimentalprecision,butalsointermsofitsapplicabilitytothephysicalprobleminquestion.Certainly,notallfluidsheddingapplicationsemulateaconventionaltiltedplateexperiment,whereindropsareplacedonlevelsurfacesthataresubsequentlyinclined.Forexample,con-siderawindshield,whichisalreadyinclinedwhendropslandonit.Canwepredictmobilitybehaviorforallapplicationsbasedontheresultsofconventionaltiltedplateexperi-ments?

Toillustratetheimportanceofthisquestion,theproblemofdropgrowthandsheddingonfixed,inclinedsurfaces,such

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Fig.2.Illustrationof45◦mirrorblockusedtoobtaintopviewofdropswithcamera.

asinacondenser,isinvestigated.Itwillbeshownthatthecontactlineshape,andsubsequentslidinganglemeasure-ments,canchangedependingonwhetherthedropisplacedusingtheconventionalmethod,onalevelsurfacethatissub-sequentlyinclined,oronasurfacethatisalreadyinclined.CallaghanandAmirfazli[5]havereportedadiscrepancyinslidinganglesbetweenthetwomethodsandlinkedthisbehav-iortoamarkeddifferenceintheminimumcontactangle,ratherthancontactlineshape.However,itwasunclearwhethertheresultsofthestudyhadbeenaffectedbytheadditionofkineticenergywhenthedropwasplacedbyhandonthesurface.Inthecurrentstudy,dropplacement/growthhasbeenautomatedandslowedinordertoreducekineticenergyinput.2.Apparatus

ProfileimagesofdropsweretakenusingaCCDcamera(A302f,BaslerAG)at0×480pixels;dropswerebacklitwithadiffused10Whalogenlamp.Thecamerawasmountedtoacustomstagethatwasinclinedbyalinearmotor(P01-23×80/150×210,LinMot)atanangularspeedof1.2◦/sandaccelerationof1.0◦/s2.Vibrationfromthelinearmotorwasisolatedfromthestageusingrubbergrommets.Thereweretwostepperservo(HT11-012,AppliedMotionProducts)con-trolledsyringes(#1725GasTight,Hamilton)with26Gneedles,whichcouldplaceadropfromeitheraboveorbelowthesurface(throughaholedrilledinthesample).Theinclinationangleofthestagewasmeasuredusingatwo-axisinclinometer(TSD-90,Instruments&ControlInc.),whichwascalibratedtobeaccu-ratewithin±0.01◦from0to60◦.Eachexperimentwasentirelysoftwarecontrolledandautomatedtoensureconsistency.

Topviewsofthedropsarereflectionsinamirrorpositionedabovethedrop,at45◦tothecameraviewplane.Lightingwasprovidedbyanincidentringlightthatwasmountedonthecameralens.Fig.2isadiagramofthisarrangement.

Evaporationofthedropwasmeasuredanddeemedtohaveaninsignificanteffectontheresultsofthestudy.However,differentstudydurations,surfacematerials,andtestliquidsmaywarrantmoreattentiontothisproblem.Onepossiblesolutionisaclearenclosurethatisfilledwithairsaturatedwiththetestliquidvapor[6].

3.Methodology3.1.Samplepreparation

Thisstudyinvolvedtwotypesofhydrophobicsurfaces,whichlieoneitherendoftheroughnessspectrum:texturedalkylketenedimmer(AKD)andfluorinated(smooth)siliconwafer.TheAKDsurfacesweresuperhydrophobicandwereproducedasperthedirectionsofMohammadietal.[7].AKDpellets(Aquapel3,HerculesInc.)weremeltedandheatedto90◦C,thenimme-diatelyallowedtocooldowntoapproximately35◦C,whenthemoltenpelletsbegantonucleate.TheAKDwasthenpouredintoastainlesssteelmoldwithaluminumheatsinks,which,afterafewminutes,wasopenedandplacedinadrynitrogenenvironmentfor72h.Duringthistime,theopenfaceoftheAKDsurfaceformedarandommicrostructure(texture)withanRMSroughnessof2±1␮m(AFMwasusedtofindtheRMSroughnessvalue,notethatthemaximumroughnesswasoneorderofmagnitudelarger).Theresulting2mmthicksurfacewasthensectionedintoapproximately15mmsquaresamplesusingahotknifeandstoredwithadesiccant.Ifneeded,aholewasdrilledthroughthesamplebyhand,usingabeveled-tipsyringeneedle.

Fluorinatedsiliconsampleswereproducedfrompolishedwafers(TypeP/BoronOrient100,UniversityofAlbertaNanofab)thatweredicedintoapproximately15mm2samples,soakedovernightinchromic–sulfuricacid,andthenthoroughlyrinsedwithdistilledwater.A6%Teflonsolution(TeflonAF1600,DuPontCo.)wasdilutedinasolvent(FC-75,DuPontCo.)atavolumetricratioof1:3.Approximately100␮lofthissolutionwasappliedtoeachsampleandleveledinaspincoater(Model6700,SpecialtyCoatingSystemsInc.).Thecoatedsam-pleswereallowedtodryovernightundervacuum.Ifneeded,aholewasdrilledthroughthesampleusinga0.46mmdia-monddrill(MCDU18,UKAMIndustrialSuperhardTools).Theroughnessofsurfacesproducedinthiswayisgenerallyintheorderof1nm.

3.2.AdvancingandrecedingcontactanglemeasurementTheadvancingandrecedingcontactangleswereobtainedbyaddingandwithdrawingwaterfromadroponalevelsurface.Althoughitiscommonpracticetomanipulatethedropvolumewithaneedlethatisimmersedintothedropfromabove,itispreferredtoinjectliquidfrombelow,throughahole,inordertoavoidpossibleinfluenceoftheneedleontheobservedcontactangles,especiallyforsmalldrops.Thesamplesweredrilledandplacedonthestagesothattheneedleranthroughthehole,withitstipjustbelowthesurfaceofthesample.Waterwasaddedandwithdrawnfromthedropveryslowly(0.2␮l/s)toavoiddynamiceffects,andanimageofthedropprofilewastakenevery4s.Inthreeseparateexperiments,waterwasaddedtothedropsuntiltheyreachedmaximumvolumesof30,50,and70␮l,thenwaterbegantobewithdrawn.Thesevolumescorrespondtocontactlinediametersofapproximately4,5,and6mmforwateronfluorinatedsiliconsurfaceand2,3,and4mmonAKDsurface.

76E.Pierceetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects323(2008)73–82

Fig.3.Four-dropplacementmethodsforconventionaltiltedplateexperiments.Toplaceadropwiththeholetrailingorleadingit,thesurfaceisinclined3◦forwardorbackward,respectively,whilethedropisformedonthesurface.Beforetheexperiment,inwhichthesurfaceistiltedslowlyforward,thesurfaceisalwaysbroughtbacktolevel.

3.3.Dropplacementinconventionaltiltedplateexperiments

DropsofwaterwereplacedonAKDsurfaceusingfourprac-ticalmethodsinordertoascertaintheireffectontheslidingangleorexperimentalprecision.ThefourplacementmethodsareillustratedinFig.3:fromabove(noholeonsurface);frombelow,holeleadingthedrop;frombelow,holetrailingthedrop;andfrombelow,randompositionofdropwithrespecttothehole.Inordertoplacethedropsothattheholewasleadingortrailingthedrop,thestagewastilted3◦backwardsorforwards,respectively,thenthedropwasformed;thesurfacewassubse-quentlyleveledbeforethestartoftheexperiment(seeFig.3).Intherandomplacementmethod,thesurfacewasleveled,andthenthedropwasformedfrombelow;thepositionofthedropwithrespecttotheholewasnotcontrolled.Inplacingthedropfromabove,a10␮ldropwastransferredfromtheneedletiptoalevelsurface,thenwaterwasaddedtothedropatarateof1␮l/swiththeneedletippositionedjustabovethesurfaceofthedrop,withoutevertouchingit.Theneedletipcouldnotbeimmersedinthedropbecausethecontactanglewouldhaverecededslightlywhentheneedlewasretracted.Forrepeatableslidingbehavior,thedropmustbeplacedinanadvancingcontactangleregimeeachtime.Whenanaxisymmetricdropisadvancing,itisinsuredthatthecontactlinelengthisidenticalforagivendropvolume.Afterplacingthedroponthesurfaceusinganyoftheabovefourtechniques,thesurfacewasinclinedinincrementsofapproximately2◦.Ateachincrement,animageofthedropprofilewassavedbeforeandaftera5spause.Thepurposeofthispausewastoobservewhetherthedropwouldmovewith-outthekineticinputoftheincliningstage.Thebeforeandafterimagescouldlaterbecomparedtodeterminewhethertheentiredrophadslippeddownthesurface,asindicatedbyadiscerniblemovementofboththeleadingandtrailingedgeswithoutanychangeinthecontactangles.Achangeincontactanglewouldindicatethatonlyaportionofthecontactlinehadslipped,anotherwiseindiscernibleeventinaprofileviewofthedrop.For

eachdropplacementmethod,thisprocedurewasrepeatedeighttimes,eachtimeusingafreshAKDsurfacesample.Thevolumeofthedropwasalways30␮l.

Thedefinitionoftheslidingangleisnottrivial.Adropseldomslidescompletelyoffasurfaceatagiveninclinationangle,butinsteadtendstoslideataspeedthatisrelatedtotheangleofinclination(i.e.higherinclination,higherslidingspeed).Therefore,thelengthofthepausedeterminestheslidingspeed(andcorrespondinginclinationangle)necessaryforadis-cerniblemovementbetweenthebeforeandafterimages.A5spausewasasubjectivechoicethatwasjudgedtodetectmove-mentslightenoughtobeconsideredincipientmotionwhilenotbeingexcessivelytime-consuming.

3.4.Handhelddropplacementoninclinedsurfaces

TheexperimentsofCallaghanandAmirfazli[5]wererepeatedwithAKDandfluorinatedsiliconsurfaces.Dropsofwaterwereplacedonthesurfacesusingahandhelddigitalpipette(NichipetEX,FisherScientific).Theslidinganglesoftwoexperimentalmethodswerecompared:placingadroponalevelsurface,thenincliningit,andplacingadroponasur-facethatisalreadyinclined.Inthelattermethod,thesurfacewasinclinedatsomeangle,anda20␮ldropwasplacedonthesurface.Ifthisdropdidnotslide,thenthevolumeofthedropwasincreasedinincrementsof10␮luntilitdid.Becausedropplacementwasnotautomated,thepointofslidinghadtobedeterminedwiththenakedeye,ratherthanasacomparisonbetweenconsecutiveimages.Forthisreason,theslidinganglemeasurementsforhandhelddropplacementwereslightlyhigherinmagnitudeandlowerinprecisionthanthosefortheautomateddropplacementmethod.Althoughdirectnumericalcomparisonbetweentheseslidinganglemeasurementsandthoseintherestofthisstudyisnotrecommended,theirtrendsremaincompara-ble.Allexperimentswererepeatedbetweenthreeandfourtimesforeachdatapoint,whichwassufficienttoestablishaconsistenttrend.

3.5.Automateddropplacementoninclinedsurfaces

Inordertoavoidkineticenergyinput(e.g.dropping,slightpushing,orvibration)fromthehandheldpipette,anautomatedmethodofdropplacementwasconceived.Onalevelsurface,a“seed”dropwasgrownfromaboveatarateof1␮l/s,andtheneedletipofaservooperatedsyringewasimmersedintoitscenter.Thevolumeoftheseeddropwaschosentobe10–30␮llessthanthevolumeatwhichthedropwasexpectedtoslide(e.g.a40–60␮lseedifthedropwasexpectedtoslideat70␮l).Thesurfacewastheninclinedtosomeangle;whereuponthedropwasgrownin10␮lincrements,at0.2␮l/s,untilthedropwasobservedtoslidewhilewaterwasnotbeingaddedtothedrop.Again,theslidinganglewasdefinedbyadiscerniblemovementwithina5spause,whichbeganaftereach10␮ladditionofwaterwascompleted.

Carewastakentoensurethattheneedletipwasneverlocatedneartheedgeofthedropbecausethedropwouldthenclingtotheneedle,resultinginamuchhigherslidingangle.Withthe

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Fig.4.(a)Typicaladvancingandrecedingcontactangledataforwaterdroponfluorinatedsiliconsurface.(b)TypicaladvancingandrecedingcontactangledataforwaterdroponAKDsurface.Waterwasaddedandwithdrawnfromthedropwhilethesurfaceremainedlevel.

needletipinthecentreofthedrop,adhesionforcesbetweentheneedleandthedropwereobservedtobemuchlowerbutwerestillanticipatedtohavesomeeffectontheslidingangle.There-fore,aconventionalmethod(dropplacedonalevelsurface,theninclined)benchmarkwastakenwiththeneedlelikewiseimmersedinthedrop.Thus,theeffectofplacingadroponaninclinedsurface(ratherthantheconventionalmethod)couldbeinvestigatedwithoutconcernforanyadhesionbetweenthenee-dleandthedrop.Again,experimentswererepeatedbetweenthreeandfourtimesforeachdatapoint.4.Resultsanddiscussion

4.1.AdvancingandrecedingcontactanglemeasurementAsexpected,theadvancingandrecedingcontactanglesofwateronbothAKDandfluorinatedsiliconsurfaceswereunaffectedbythemaximumdropvolumeused(i.e.30,50,or70␮l).The50␮lcontactanglecurvesforAKDandsil-icon(Fig.4)arerepresentativeofthesemeasurements.Theadvancingandrecedingcontactanglesforsiliconare128±0.2◦and115±0.2◦,respectively.TheadvancingcontactangleforAKDis165±2◦,buttherecedingangleistoosmalltobemeasuredaccuratelywithADSA;byobservation,it

Fig.5.WaterdropswereplacedonlevelAKDsurfacesamplesusingfourdif-ferentmethodsandtheninclined.Thegraphshowsthemeanslidinganglesforeachplacementmethod,withonestandarddeviationerror.At-test(5%alphalevel)concludedthatonlythe“holeleadsdrop”resultswerestatisticallydistinctfromtheothers.

appearedtobelessthat10◦(pinningofcontactlinewasobserved).

4.2.Dropplacementinconventionaltiltedplateexperiments

TheslidingangleswithonestandarddeviationerrorforeachofthefourwaterdropplacementmethodsonAKDsurfacesarepresentedinFig.5.Thesemeasurementswerealltakenusingtheconventionaltiltedplatetechnique:dropsplacedonalevelsurface,theninclined.At-testwitha5%alphalevelconfirmedthattheonlyplacementmethodthatgivesstatisticallydistinctresultsfromthoseoftheothertechniquesisthe“holeleadingdrop”method.Althoughthestatisticaldifferencesbetweenthesemethodsaresmall,itisimportanttounderstandtheircauseandpossiblerelevancetodropmobilitystudies.

Fig.6.TopviewofwaterdroponAKDin“leadinghole”positionbefore(a)andafter(b)inclining:contactlinedoesnotpinontheholeatincipientsliding.Theendoftheneedleandholecanbeclearlyseenin(b),butappearonlyasadarkspotneartheedgeofthedropin(a).Thegravityvectorpointsintothepagein(a).

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Fig.7.(a)Whentheneedletipisinthecenterofthedrop,surfacetensionforcesaroundtheperipheryoftheneedleopposeeachother,leavingasmallresultantreactionforce.(b)Whentheneedletipnearstheedgeofthedrop,thedirectionsofthesurfacetensionforceschange,andtheresultantreactionforceincreases.Notethatthedropisinclinedin(b)butnotin(a).

Dropsplacedwiththeholeleadingdroptechniqueresultedinlowerslidinganglesthanotherplacementmethodsfrombelow.Thereasonisthatthetrailingedgeofthedropdidnottendtopinontheholebeforesliding.Asthedropwasinclined,itsleadingedgewouldmoveforwarduntilthecontactlinedidnotlieonthehole(Fig.6).Thecontactlinewouldremaininthispositionuntilthesurfacewasinclinedtotheslidingangle,whenthedropbegantoslide.

Theleadingholemethodalsoresultedinameanslidinganglemeasurementthatwas24%(8◦)lowerthanthatofplacementfromabove.Dropsplacedfromabovehadwateraddedtothemfromaneedlethatwaspositionedjustabovetheirsurface.Aswaterwasadded,thedropswouldvisiblyvibrateandasaresult,oftendisplayedlessthananadvancingcontactangleafterplace-ment.Thissituationwouldresultinaslightlylargerwettedarea(andcontactlinelength)foragivendropvolume,andsubse-quently,higherslidingangles.Therandomvibrationcausedbyplacingdropsfromabovealsoledtosomewhatinconsistentslid-inganglemeasurements.Amongthosedropsplacedfrombelow,measurementprecisionwasaffectedbythepinningofdropsonholes,whichhadvaryingedgeconditions.Fortheserea-sons,thestandarddeviationofmeasurementsusingtheleadingholemethodwas50–60%(3–5◦)lessthantheotherplacementtechniques.

Dropsplacedwiththeholeleadingwereobservedtointeractleastwiththeholewhilealsoavoidingthedetrimentaleffectsofvibrationcausedbyplacementfromabove.Therefore,holeleadingdropplacementisrecommendedwheneverpossibleintiltedplateexperimentsusinghydrophobicsurfaces.4.3.Effectofneedleimmersedindroponslidinganglemeasurements

Inresearchingsomephysicalproblems,itmaybeusefultoaddorwithdrawliquidfromadropwhileitisrestingonaninclinedsurface.Onesuchapplicationcouldbefluidtrans-ferthroughaninclinedmembrane,whichsubsequentlyslidesoffasdroplets(e.g.fuelcell);amorecommonexamplemightbethecondensationofdropsoninclinedsurfaces.Section3.4describedatechniqueusedinthisstudythatinvolvedinject-

ingwaterthroughaneedlethatwasimmersedintoadroponaninclinedsurface.Theneedletipwasplacedasnearaspossibletothecenterofthedrop,wheretheresultantreactionforcebetweentheneedleandtheslidingdropwasobservedtobeminimized(Fig.7).

Fig.8showsthatthedifferencebetweenslidinganglemea-surementswithandwithoutneedleimmersionisalwayslessthan

Fig.8.ForwateronAKD(a)andfluorinatedsiliconsurfaces(b),effectofneedleimmersedindropislessthanthatofthecombineduncertaintyofthemeasurements(onestandarddeviation).ForAKD,theobservedeffectismorepronouncedatlowerdropvolumes.Forfluorinatedsilicon,needleimmersiondoesnotaffecttheslidinganglesofdropslargerthan40␮l.

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Fig.9.DropsabouttoslideonAKDsurface(a)aremoreelongatedthanthoseonfluorinatedsilicon(b).Thedissimilardirectionsofthesurfacetensionforcesin(a)leadtoahigherresultantreactionforcebetweenthedropandtheneedle.Notethatthecameraisinclinedwiththeexperimentalstage,sothesurfaceappearstobehorizontalintheseimages.

theircombineduncertaintyofonestandarddeviation.Theeffectofneedleimmersionappearstobegreatestatlowerdropvolumes(lessthan70␮lforAKDand40␮lforfluorinatedsilicon),likelybecausetheresultantreactionforcebetweentheneedletipanddropisinsignificantcomparedtotheadhesionforcerequiredtoretainlargedropsonthesurface.DropsonAKDsurfacestendedtoadheretotheneedletipmorethanthoseonfluorinatedsiliconsurfacesbecauseofdifferencesindropprofileshape.InFig.9,itcanbeseenthattheelongatedshapeofadropthatisabouttoslideonanAKDsurfaceincursahigherresultantreactionforcethanthemoresymmetricshapeofadroponfluorinatedsilicon.Fortiltedplateexperimentswithlargerdrops,especiallythosewithlittledropelongation(suchaswithlowcontactanglehysteresissurface/liquidsystems),immersionoftheneedletipinthedropapexhasanegligibleeffectonslidinganglemeasure-ments.Withproperattentiontoneedleplacement,thistechniqueisavalidmethodforstudyingdropgrowthoninclinedsurfacesoflowcontactanglehysteresis.

4.4.Dropplacementonfixed,inclinedsurfaces

TheresultsoftheCallaghanandAmirfazli[5]experimentswithwateronAKDandfluorinatedsiliconarepresentedinFig.10.Fig.10aillustratestheoriginalobservation:thatdropsplacedoninclinedAKDsurfaceshavelowerslidinganglesthanthoseplacedonlevelsurfaces,theninclined.Onfluorinatedsilicon,Fig.10b,thereisnostatisticallysignificantdifference(basedont-test,5%alphalevel)betweenthetwomethods,butthereappearstobeasimilartrendaswithAKDsurfaces.AsmentionedinthediscussionbyCallaghanandAmirfazli,itisunclearifthistrendissimplyduetokineticenergyinput(e.g.handvibration,etc.)whenthedropisplacedwithahandheldpipette.

Automateddropplacementdata(Fig.11)showsasimilar,butstrongerdistinctionbetweentheslidinganglesofdropsplacedoninclinedsurfacesanddropsplacedonlevelsurfaces,theninclined.Sincedropgrowthusingtheautomatedplacementtech-niquewasveryslowandfreeofoperatorinducedvibrations,thesefindingsrevealthatthebehaviorobservedbyCallaghanandAmirfazli[5]wasnotsimplyduetoinadvertentkineticenergyinput.Therearetwofactorstoconsiderwhencomparing

handheldwithautomatedmethoddata.Recallthatslidinganglesfoundwiththeautomatedmethodshouldbeslightlylowerthanwiththehandheldmethodbecauseofanecessarychangeinthewaytheslidinganglewasdetermined.However,thiseffectisnegatedbyretentionforcesbetweentheneedletipandthedrop(onlypresentwithautomatedmethod),especiallyforAKDsurfacesandlowerdropvolumes.

Fig.10.(a)ResultsforhandhelddropplacementonAKDsurfaceshowasignif-icantdifferencebetweenthetwomethodsatlowervolumes,butthedifferencediminishesathighervolumes.(b)Forhandhelddropplacementonfluorinatedsilicon,at-test(5%alphalevel)revealsnostatisticallysignificantdifferencebetweenthetwomethods,butthereappearstobeasimilartrendaswithAKDsurfaces.

80E.Pierceetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects323(2008)73–82

Table1a

Summaryofcontactangledatafortiltedplateexperimentswith30␮ldrops

AKDθmax(◦±S.D.)

Tiltedplatemethod

Dropplacedoninclinedsurface

Conventional(level

161±5163±5

θmin(◦±S.D.)86±383±6

θmax−θmin(◦±S.D.)75±880±±11

Fluorinatedsiliconθmax(◦±S.D.)126±3124±4

θmin(◦±S.D.)113±4112±3

θmax−θmin(◦±S.D.)13±712±7

surface,theninclined)

Thisdataclearlyillustratesthatconventionaltiltedplateexperiments(dropplacedonlevelsurface,theninclined)can-notbeassumedtoadequatelyrepresentthephysicalproblemofdropsgrowingandsheddingfromaninclinedsurface,suchasinacondenser.Forbothahigh(AKD)andalow(fluorinatedsilicon)contactanglehysteresissurface/liquidcombination,theerrorofthisassumptionwouldbeashighas50–60%.Inunderstandingdropmobilityonafixed,inclinedsurface,theconventionaltiltedplatemethodwouldnotbeappropriate.Thereasonforthisdeviationliesintheshapeofdropspro-ducedbyeithermethod.Despitetheobserveddifferenceinslidingangles,themaximumandminimumcontactanglesforwateronbothsurfaceswerenotaffectedbydropplacement

Fig.11.(a)AutomateddropplacementresultsshowthatwaterdropsplacedoninclinedAKDsurfaceshavesignificantlylowerslidingangles,especiallyatlowerdropvolumes.(b)Automatedresultsforwateronfluorinatedsiliconsurfaceshowasignificantdifferencebetweenthetwomethodsaswell.

method(Table1a).However,topviewsofdropsatthepointofslidingoninclinedAKDexhibitadistinctdifferenceincon-tactlineshape.Beingahighcontactanglehysteresissystem,awaterdropthathasbeenplacedonalevelAKDsurface,theninclined,tendstopin,leadingtoamoreelongatedcontactlinewithawidetrailingedge,showninFig.12a.Recallthatdropadhesionistheresultofthecomponentofthesurfacetensionforcedistribution(Fig.1b)thatisperpendiculartotheaxisofinclination.TheshapeinFig.12aismoreeffectiveinadheringtothesurfacethanthenearteardropshapethatformswhenadropisgrownontheinclinedsurface(Fig.12b).Althoughitwasonlypossibletoobservethemaximumandminimumcon-tactanglesofthedrop,itisintuitivethatchangesincontactlineshapewouldbeaccompaniedbychangesinintermediatecontactangles.Itisimportanttonotethattheobserveddiffer-encesindropadhesionarethecombinedresultofchangesinthecontactlineshapeandsubsequentintermediatecontactangledistribution.Calculationsofk-value(thefittingparameterusedinapplicationofEqs.(1)or(2)),whichismeanttocapturethecombinedeffectofcontactlineshapeandcontactangledis-tribution(alongthecontactline)confirmsthis.UsingEq.(2)andresultsfromTable1a,andFigs.10aand11a,thekvalueswerefoundasapproximately1.8and1.15,forconventionalandpre-inclinedsurfaces,respectively(thekvaluesarerepresenta-tiveofbothmanualandautomateddropplacementprocedures).Interestingly,ifEq.(1)wasusedtocalculatethek-value,anunreasonablenegativevalueforkwouldhaveresulted(notethatinthiscasedatafromTable1bshouldbeused).ThisisanotherindicationthatEq.(2)istheappropriateequationtouseforinter-pretationofdata,ratherthanEq.(1)asdiscussedearlier;thisisregardlessoftheprotocolusedfortheexperimentation.

Althoughtherelativedifferenceinslidinganglesforfluo-rinatedsiliconsurfaceswassimilartothatonAKDsurfaces(50–60%),thetopviewsofdropsonfluorinatedsilicondonotshowsuchanobviousdifferenceinshape(Fig.13).Therefore,averysmallchangeinadhesionforceforfluorinatedsiliconpro-ducedthesamerelativedifferenceinslidingangleasamuchlargerchangeforAKD.Theexplanationliesintherespectivemagnitudesoftheseslidingangles,astheadhesionforceisnotproportionaltotheslidingangle,butitscosine(seeFig.1a).Toillustrate,consider◦thecaseofa30␮ldrop:theslidinganglesforAKDwere22fordropsplacedonaninclinedsurfaceand45◦fortheconventionalmethod(51%difference),andforfluori-natedsilicon,theywere6◦and14◦(57%difference).However,thecorrespondingdifferenceinadhesionforcesis25%forAKDandonly4%forfluorinatedsilicon.Althoughtheshiftincontact

E.Pierceetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects323(2008)73–8281

Fig.12.Topviewof30␮ldropsoninclinedAKDsurface:(a)placedonlevel,theninclinedto48◦,(b)placedon22◦incline.Bothdropsshownareattheirrespectiveslidingangles.Thebrightrectangularareasarereflectionsfromtheneedle.Table1b

Summaryofcontactangledatafordropexpansion/contractiononlevelsurfaceAKDθA(◦±S.D.)165±2

θR(◦)<10

CAhysteresis(◦)>155

FluorinatedsiliconθA(◦±S.D.)128±0.2

θR(◦±S.D.)115±0.2

CAhysteresis(◦±S.D.)13±0.4

lineshapeforfluorinatedsiliconislesspronouncedthaninthecaseofAKD,itmustbeassumedthatitexists.Thisisconfirmedbythedifferentk-valuefoundforeachsystem.Thekvaluesforfluorinatedsiliconsurfacewerefoundtobeapproximately5and3forconventionalandpre-inclinedsurfaceexperiments,respectively.

ComparingthedatainTables1aand1b,thereisnosignificantdifferencebetweentheadvancing/recedingandmax-imum/minimumcontactanglesforfluorinatedsiliconsurfaces.ThisresultisinaccordancewiththefindingsofElSherbiniandJacobi[4]:thatθAandθRareequaltoθmaxandθmin.However,therecedingcontactangleofwaterontheAKDsurfacesisatleast73◦lessthantheminimumangle.ThisbehaviordoesnotagreewiththetheoreticalstudybyKrasovitzandMarmur[3],whichpredictedthatarecedingcontactanglelessthanthemini-mumangleisonlyexpectedfromahydrophilicsurface,definedbytheauthorsashavinganaveragecontactangle((θA+θR)/2)of

30◦.ItalsoobviouslydoesnotagreewithElSherbiniandJacobi[4],possiblybecausetheirconclusionswerebasedoncaseswhereθAwaslessthan112◦andgreaterthan49◦.Insystemsofhigherrepellency,especiallythosewithtexturedsurfaces,theremaybewettingmechanismswhicharenotrepresentedinthedatasetfrom[4].Consideringtheprominenceofultra-hydrophobicsurfaceresearchintherecentliterature,itwouldbeprudenttorecognizethepossibilityofothersurfacesthatbehavelikeAKD,anddrawnoindiscriminateparallelsbetweentheadvancing/recedingandmaximum/minimumcontactangles.Theresultsofthisstudyalsoillustratethedangerofassociat-ingrepellencywithdropmobility.FromtheadvancingcontactangledatainTable1b,itisclearthatAKDsurfacesaremorewaterrepellentthanfluorinatedsiliconsurfaces.However,thetiltedplatedatainthisstudyshowsthattheslidinganglesofwaterdropsonAKDsurfacesareatleastdoublethoseforfluori-natedsiliconsurfaces.Thisapparentparadoxisexplainedbythe

Fig.13.Topviewof30␮ldrops(outlineishighlightedingreyforgraphicalclarity)oninclinedfluorinatedsiliconsurface:(a)placedonlevel,theninclinedto16◦,(b)placedon7◦incline.Bothdropsshownareattheirrespectiveslidingangles.Thebrightrectangularareasarereflectionsfromtheneedle.

82E.Pierceetal./ColloidsandSurfacesA:Physicochem.Eng.Aspects323(2008)73–82

differenceininclinedcontactangles(θmax−θmin)presentedinTable1a.ThedifferencebetweenθmaxandθminismuchgreaterforAKDthanforfluorinatedsilicon,resultinginahigherslidingangle,aspredictedbyEq.(2).5.Conclusions

Themethodologyoftiltedplateexperimentshasbeeninvesti-gatedwithrespecttoslidinganglemeasurements.Anoveldropplacementtechniquethatemulatesthecondensationofaliq-uidonaninclinedsurfacehasalsobeenintroduced,leadingtotheconfirmationandexplanationofresultsfromCallaghanandAmirfazli[5].Thedetaileddiscussioninthisinvestigationhasalsoservedtobridgeagapinthedocumentationofslidinganglemeasurementprotocol.

Associationsbetweentheadvancing/recedingandmaxi-mum/minimumcontactanglesmustbeapproachedwithcaution.Inthisstudy,itwasfoundthattherecedingcontactanglewasmuchless(74◦difference)thantheminimumcontactangleforwaterdropsonAKD.Thisresultagreeswithneitherthethe-oreticalpredictionsfromKrasovitskiandMarmur[3]northeempiricalpredictionsofElSherbiniandJacobi[4].ThoseofthelatterwerebasedondataforsystemswithθAbetween49◦and112◦.ItwassuggestedthatspecialcircumstancesmayariseforsuperhydrophobicsystemslikeAKDandwater(θA=165◦).Conversely,observationsofwateronfluorinatedsiliconsurface(θA=128◦)agreedwiththepredictionsofElSherbiniandJacobi,exhibitingalmostidenticalmaximum/minimumandadvanc-ing/recedingangles.

Inplacingdropsforconventionaltiltedplateexperiments(placedonlevelsurface,theninclined),therearetwomajorproblems:dropspreadingduetovibrationwhenplacedfromaboveandpinningontheneedleholewhenplacedfrombelow.ExperimentswithwaterdropsonAKDsurfaceshowedthattheseproblemshadastatisticallysignificantaffect(t-test,5%alphalevel)onthemagnitudeofslidinganglemeasurements.Theywereminimizedwiththe“holeleadingdrop”placement,whichresultedinmeasurementsthatweremorethantwiceaspreciseasthoseoftheotherplacementstested.Thisdropplacementtechniqueisrecommendedwheneverpossible.

Thegrowthandsheddingofdropsonaninclinedsurface,suchasinacondenser,wasemulatedonAKDandfluorinatedsiliconsurfaces.Itwasshownthatdropsplacedoninclinedsurfaces

havelowerslidinganglesthanthoseplacedconventionally(onalevelsurface,theninclined).However,themaximumandmin-imumcontactanglesforbothsurfaceswereunchangedbetweenthetwoexperimentalmethods,sothechangeinadhesionhadtobearesultofdifferentcontactlineshapes.ThisdifferencewasvisuallyverifiedwithtopviewsofthedropsonAKD.However,thecontactlineshapevariationforfluorinatedsiliconwastoosmalltobevisuallydistinguishable.

Canwepredictmobilitybehaviorforanapplicationsuchasacondenserbasedontheresultsofconventionaltiltedplateexper-imentsortheadvancingcontactangle(repellency)?Inthecaseofbothahighandlowcontactanglehysteresissystem,ithasbeenshownthattheconventionalmeasurementwouldhavebeeninerrorby50–60%.Furthermore,itwasshownthatadvanc-ing/recedingcontactanglemeasurements(onalevelsurface)cannotbereliedupontopredictdropmobility.Therepellencyofthetestsurfaceswascompletelymisleadingintermsoftheirrela-tivedropmobility,andtheadvancing/recedingcontactanglesdidnotconsistentlycorrespondtothemaximum/minimumcontactangles(onatiltedsurface).Theseresultsclearlyunderlinetheimportanceoftiltedplateexperimentdesignandinterpretation.Acknowledgements

TheauthorsacknowledgefundingfromtheNaturalScienceandEngineeringResearchCouncilofCanada(NSERC),theCanadianFoundationforInnovation(CFI),andtheCanadaResearchChairProgram.HerculesInc.isalsothankedforgenerouslysupplyinganAKDpelletsample.F.J.Carmonaacknowledgesfundsgivenbythe“IPlandeInciaci´onalaI+D+IbyVicerrectoradodeInvestigaci´on,DesarrolloeInno-vaci´on,UEx2005.”References

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