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1、JournaloftheEuropeanCeramicSociety31(2011)2543-2550Inkjetprintingceramics:FromdropstosolidB.DerbySchoolofMaterials,UniversityofManchester,OxfordRoad,ManchesterM139P1.,UKAvailableonline16February2011AbstractInkjetprintingisapowerfulInicrofabricationtoolthathasbeenappliedtothemanufactureofceramiccompo
2、nents.Tosuccessfullyfabricateceramicobjectsanumberofconditionsmustbesatisfiedconcerningfluidpropertiesanddropplacementaccuracy.Ithasbeenproposedthatfluidsareprintablewithinthebounds1Z2forstabledropgeneration.19Reisextendedthisthroughnumericalsimulationandproposedthefollowingrange,10Z1,forstabledropf
3、ormation.20IfZ10,dropletsareaccompaniedbyunwantedsatellitedrops.Jangetal.studiedtheDODprintabilityofanumberoffluidmixturesofethanol,waterandethyleneglycol.ThroughthistheyexploredarangeofvaluesofOhanddeterminedthattherangeofprintabilitywasFig. 1. Fromm,sparameterZ(Z=1/Oh)influencestheprintabilityoffl
4、uids.DashedlinesidentifythelimitsforprintabilityproposedbyReisetal.20Experi-mentalpointsareplottedforanumberofceramicsuspensions/inks:greysymbolsindicatesuccessfulinkjetprinting,blacksymbolsindicatethatnodropswereformed,andwhitesymbolsindicatethepresenceofsatellitedropsalongwiththemainprinteddrop.4Z
5、Z1(whereZ=lOh)canbeusedasaguidetothedevelopmentoffluidsforinkjetprinting.ThesuitabilityofafluidforinkjetprintingcanberoughlyassessedbyitsOhnesorgenumber.Howeverthereareotherlim-itsoffluidbehaviourthatimposeadditionallimitstopracticaldropgeneration.Inordertogenerateasmallradiusdrop,thesur-facetension
6、andassociated1.aplacepressuremustbeovercomebeforeadropcanbeejectedfromaprinter.DuineveldproposedthatthiscanbedescribedbyaminimumvalueoftheWebernumber,We4,belowwhichthereisinsufficientfluidflowtoovercomesurfacetension.24Afinalboundtoprintabilityisgivenbytheonsetofsplashingthatoccursifadrophitsthesubs
7、tratewithvelocityaboveacriticalthreshold.FromtheworkofStoweandHadfield,25thisoccurswhenWel2Rel450.Theselimit-ingboundsdefinearegionoftheparameterspaceofWeandRe,withinwhichDODinkjetprintingispossible.5,6Fig.2showsFig. 2. Inkjetprintingispracticalforalimitedrangeoffluidsandprintingcon-ditions.Thisisil
8、lustratedhereinaparameterspacedefinedbyaxesofReynoldsandWebernumbers.BasedonadiagramoriginallypublishedinRef.5.thisparameterspaceandtheregionsuitableforDODinkjetprinting.Dropvelocityincreasesdiagonally,asindicatedandhaslowerandupperboundsthataredefinedbytheappropriatelimitsofdropejectionandsplashing
9、,orthogonaltovelocityistheOhnesorgenumber;whichdefinesthelimitsofthefluidprop-erties,thusFig.2canbeconsideredrepresentingaguidetothelimitsofbothfluidcharacteristicsanddropdynamicsconsistentwiththepracticaluseofpiezoelectricDODinkjetprinting.3. Dropimpact,spreadingandcoalescenceAsdiscussedearlier,ani
10、mportantaspectofinkjetprintinginmanufacturingtechnologyistheprocessbywhichadjacentdropsinteracttoformasolid.Inallcasestheliquiddropwillinteractwithasolidsubstrate.Followingdepositiontherewillbeaperiodwhenthedrop,sshapeiscontrolledbyfluidpro-cessespriortosolidification.Thusanimportantconsiderationist
11、heappropriatetimeconstantsthatapplytothemechanismsofsurfacespreadingandsolidication.Hereweareconfiningourdiscussiontosolidificationthroughevaporation.Giventhatdropletsolidificationtimescalesarenormallyintheregimeofaround1sanddropletdepositionratesare1kHz,weneedtoconsidertheinteractionbetweenmanyliqu
12、iddropletsonthesurfaceofthesubstrate.Itispossibletouseinterlacingandsequentialprintingpassestodepositisolateddrops,allowthemtosolidifyandthenfillinthegapstoproduceaprintedplane.However,thismethodologyproducesanirregulardepositwithpoorsurfaceroughnessforeachprintedlaye9withaconse-quentriskofdefectsfr
13、ompoorpenetrationoftheliquid.Ifprintingoccurswithappropriatedropspacingtoallowover-lapbeforesolidication,theinteractionbetweenadjacentliquiddropsandtheconsequentinfluenceofsurfacetensionwilltendtoproducesmoothsurfacesandeliminatepossibledefectsbetweensolidifieddrops.Whenaliquiddropimpactsaplanarsubs
14、trateitwilldeformandspreadtocoverthesubstrate,ultimatelyachievinganequi-Iibriumsessiledropconfiguration.YarinhasrecentlyreviewedtheimpactofdropsoverasizeandvelocityrangethatintersectsthoserelevanttoDODprinting.26Thetypicalrangeofdropsize(radiusfrom5to50mm)andvelocity(1v10ms-l)issuchthattheinitialdef
15、ormationofthedropwillbecontrolledbydynamicimpactandviscousdissipationprocesses.6,18,26However,thisinitialstageofdropdeformationisexpectedtohavefinishedafterafewmsandsubsequentspreadingtoequilibriumwillbedrivenbycapillaryforces.27Aschematicrepresenta-tionofthetimescalesassociatedwithdropdeformationaf
16、terimpactispresentedinFig.3.Thedynamicprocessesofdropimpactoccuroveratimescaleofms.26Firstthedropdeformsonimpactwithitskineticenergyconvertedintonewsurfaceareaasthedropdeforms,someenergyisabsorbedthroughviscousdissipation.Iftheimpactconditionsaresuchthatsplashingdoesnotoccur(asisnormalwiththeconditi
17、onsofinkjetprinting),thedropmayrecoilafterexpansionandoscillatebrieflydissipatingenergy.Meanwhiletheprocessofcapillaryspreadingwilloccur,thishasatimescaleofmsfordropdimensionsconsistentwithinkjetprintingandthefinalequilibriumdropshapeisnormallycontrolledbythisprocess.2546Fig.3.Schematicillustrationo
18、fthetimescalesappropriatetotheprocessesofdropdeformationandspreadingonasubstrateafterimpact.Axesofdiameterandtimearetoarbitrarynon-linearscales.ReproducedwithpermissionfromRef.6.Onceequilibriumhasbeenreached,thedropcanbemodelledasasphericalcapbecausetheBondnumberissufficientlylowthatwemayignorethein
19、fluenceofgravity.Inwhichcasetheequilibriumcontactdiameterofthedrop,deqm,canbecalculatedwith(2a)deqm=d,where=2taneqm3+tan2eqm-1/3(2b)wheredisthediameterofthedropinflightandeqmistheequilibriumcontactangle.Foranisolateddropofpuresolvent,wewouldexpectthedropdiametertodecreaseandthecontactlinetoretractat
20、aconstantrecedingcontactangleduringevap-oration.However,forthecaseofparticlesinsuspension,thebehaviourofaliquiddropisdifferent.Solventevaporationdoesnotoccuruniformlyfromthesessiledrop.Atlowcontactangles,thefluidclosetothecontactlineisadjacenttoalargedrysurfaceandthisenhancesthetransportofthesolvent
21、vapourpromotingfasterevaporation.Thisleadstoaringofparticlescomingoutofsuspensionandthepresenceofthisdrieddepositpinsthecontactlineandpreventsitretracting.Thiscontactlinepinningresultsintherecedingcontactangledecreasingassolventisremoved.Itcanalsoresultinaflowofparticlestothecontactline,leadingtosus
22、pensionsegregationandaringdeposit;thisisaphenomenonknownasthecoffeestaineffect.28Wewillreturntothecoffeestainphenomenonlaterinthisarticle.Oneeffectofcontactlinepinningduringdryingisthatthefootprintorequi-libriumdiameterofthespreaddropofceramicinkwilldefinethediameterofthedrieddepositonthesurfaceaftersolventevaporation.Inordertoprinttwo-dimensionalpatternsitisnecessarytoallowadjacentdropletstointeractandcoalesce.Itisadvanta-geousforthesedropstointeractwhileinaliquidstatebecausesurfacetensionforceswillresultinasmo