Keywords:
Inkjetprinting;Shaping;Drying;Suspensions
1.Introduction
Inkjetprintinghasmajorcommercialapplicationsingraph-icsoutputandotherconventionalprintingoperations.However,therehasbeendevelopinginterestinusinginkjetprintingtomanufacturecomponentswithapplicationsfor:
displays,1plas-ticelectronics,2rapidprototyping,3tissueengineering,4andceramiccomponentmanufacture.5Asignificantandfundamen-taldifferencebetweenthesenewapplicationsandthemorewidespreadapplicationofprintingtextorimagesisthebehaiouroftheprintedinkdropletsontheprintedsubstrate.Mostimagesareconstructedbythedepositionofdiscretedropletsand,inordertooptimiseresolutionandcontrast,thesedropletsareiso-latedanddonotcontacteachother.Incontrast,manyofthenewapplicationsforinkjetprintingenvisagethemanufactureofcontinuous1-,2-,or3-dimensionalstructures（1-,2-,or3-D）.Suchstructuresrequireacontinuousdistributionofmaterialandthisnecessitatescontactandadhesionbetweenindividualdropsafterprinting.Inkjetprintingconstructsobjectsbytheprecisionplacementofpicolitrevolumesofliquidandthustheinitialinterac-tionbetweenprintedmaterialandasubstrateisaliquid/solidinteraction.Ultimately,theprinteddepositundergoesasolid-ificationprocessthatcanoccurthroughsolventevaporation,
temperatureinducedsolidification/gelationorchemicalreac-tion.Considerationsoftherelativetimescalesofdropspreadingandsolidificationindicatethattherewillbeasignificantperiodoftimeafterprintingwhenaliquidispresentonasurface6andthusthemorphologicalstabilityofcoallescingliquidfilmsmustbeexamined,asmusttheeffectsofthesolidificationprocess.
Therehasbeenaconsiderablenumberofpublicationsontheuseofinkjetprintinginthemanufactureofceramics.7–17Thesepriorstudieshaveusedallinkjetdropgenerationtechnologies（continuous,thermaldrop-on-demandandpiezoelectricdrop-on-demand）tosuccessfullyproduceceramicobjectsusingbothsolventevaporationandphase-changesolidification.Industrialinkjetprintingtechnologynowusespiezoelectricdrop-on-demand（DOD）generationtechnologyandthisisthechosenmethodformostapplicationsinprintingfunctionalmaterials.Thephysicaloperationofthesedifferentprintingtechnologies
andthereasonsforthechoiceofpiezoelectricDODprintinghavebeendiscussedindetailelsewhere6,18;henceherewewill
confineourconsiderationstothistechnology.Wewillalsoonlyconsidertheprintingofceramicinksthatsolidifythroughsol-ventevaporation.Despiteearlierworkdemonstratingthatitispossibletosuccessfullyprintcmscaleobjectsusingawaxbasedphasechangeceramicink,11–13ceramicinkscontainrelativelylowvolumefractionsofsolidandthusthereisconsiderableshrinkageandpotentialfordistortionduringdewaxingandsintering.14
Inordertofabricateceramicobjectsusinginkjetprinting,itisnecessarytosatisfyanumberofrequirements.Firstthereis
aneedtoproducestableceramicsuspensionswithdefinedfluidpropertiessuchthattheycanbepassedthroughadropletgener-atorandformregulardrops.Second,thesesuspensionsneedtobedeliveredontoasubstrateorontoapreviouslyprintedlayerofsolidifiedceramicink,withdropsinsufficientproximitytoeachothertoallowthemtointeractandformdesired2-Dfeatures.Next,theprintedceramicinkmustundergophasetransitiontoasoliddeposit.Finally,toproduce3-Dstructuresthedeposi-tionanddrying/solidificationprocessesneedtoberepeatedonalayerofpre-depositedanddriedmaterial.Herewewillconsidereachoftheserequirementsandtheiroptimizationforthedirectprintingofceramics.
2.Ceramicinks
ManufacturersofDODinkjetprintingequipmentnormallystatearangeofviscosityandsurfacetensionwithinwhichinksmaybesuccessfullyprinted.However,thisinformationisnor-mallyprovidedforthebenefitofformulatinggraphicsinksandmaynotbedirectlyapplicabletothedevelopmentofceramicinks.Thisisbecauseinkscontainingasignificantvolumefrac-tionofceramicparticlesinsuspensionhavemuchhigherdensityvaluesthantypicalgraphicsinks,whichtypicallyhavedensitiesintherange800–1000kgm−3andthebehaviourofafluidduringprintingdependsstronglyonitsinertialbehaviour.
Thefluidrheologicalrequirementsforaprintableinkaredeterminedbythephysicsandfluidmechanicsofthedropgen-erationprocess.6,18ThebehaviouroffluidsduringinkjetprintingcanberepresentedbytheReynolds,WeberandOhnesorgenum-bers（Re,We,Oh）:
Re= vρa , （1a）
η
We= v2ρa （1b）
γ
√ η
Oh= We = （1c）
Re （γρa）1/2
whereρ,ηandγarethedensity,dynamicviscosityandsurfacetensionofthefluidrespectively,visthevelocityandaisacharacteristiclength.FrommidentifiedtheOhnesorgenumber,Oh,astheappro-priategroupingofphysicalconstantstocharacterisedropgenerationinaninkjetprinter.19Ohisindependentoffluidvelocityandiscommonlyusedinanalysesdescribingthebehaviourofliquiddrops.However,inFromm’spublication,hedefinedtheparameterZ=1/Ohandfromasimplemodeloffluidflowinadropgeneratorofsimplifiedgeometry,hepro-posedthatZ>2forstabledropgeneration.19Reisextendedthisthroughnumericalsimulationandproposedthefollowingrange,10>Z>1,forstabledropformation.20IfZ<1,viscousdissipa-tionpreventsdropejectionfromtheprinterandifZ>10,dropletsareaccompaniedbyunwantedsatellitedrops.Jangetal.studiedtheDODprintabilityofanumberoffluidmixturesofethanol,waterandethyleneglycol.ThroughthistheyexploredarangeofvaluesofOhanddeterminedthattherangeofprintabilitywas
Fig.1.Fromm’sparameterZ（Z=1/Oh）influencestheprintabilityoffluids.DashedlinesidentifythelimitsforprintabilityproposedbyReisetal.20Experi-mentalpointsareplottedforanumberofceramicsuspensions/inks:
greysymbolsindicatesuccessfulinkjetprinting,blacksymbolsindicatethatnodropswereformed,andwhitesymbolsindicatethepresenceofsatellitedropsalongwiththemainprinteddrop.
4Thereisnowasubstantialbodyofliteraturedescribingtheinkjetprintingofanumberofceramicsuspensionsandotherfluidsfornon-graphicsapplications;unfortunatelynotallpublicationsreportsufficientinformationontherheologi-calpropertiesoftheceramicsuspensionstotestthisproposedcriterionforprintabilityinallcases.Fig.1presentssuchdatathateitherreportedthevalueofOh（orZ）orreportedsufficientdatathatitiseasilycalculated.TheverticaldashedlinesonthefigureatOh=1andOh=10representthelimitsforstableinkjetprintingcalculatedbyReis.20Theexperimentaldataispresentedfromeightfluidsystemswithagreysymbolindicat-ingthesuccessfulprintingofindividualdrops,ablacksymbolindicatesthatfluidswiththesepropertiescouldnotbeprinted,andfinallyawhitesymbolshowsthecaseswhereafluiddropwassuccessfullyejectedbutaccompaniedbyoneormoresatel-litedrops.Itisusefultoseparatethesedataintotwosets:
fluidsystems1–6weredeliveredusingpiezoelectricDODprinters,whilefluidsystems7and8weredeliveredusingathermalDODprinter.ThedataobtainedfromexperimentsusingpiezoelectricDODprintingshowsreasonablygoodagreementwithReis’smodel,howeverthatobtainedintheonestudyusingathermalDODprintershowsverypooragreement,17atleastwiththeupperboundforthepredictionoftheonsetofsatellitedropfor-mation.ÖzkolconsideredthatonereasonforthediscrepancybetweenReis’spredictionandtheirresultscouldbethediffer-enceinactuationbetweenpiezoelectricandthermalDODinkjetdropletgenerators.17
Thehypothesisthatchangesinactuationexplainthedif-ferentbehaviourobservedbetweenthermalandpiezoelectricDODinkjetprintingissupportedbyanexperimentalstudyofdropandsatelliteformationinapiezoelectricDODprinterbyDongetal.22Theyfoundthatthedropformationmechanismandtheconditionsunderwhichagivenfluidformedsatellitesisalsocontrolledbytheshapeandamplitudeofthedriving
pulseappliedtothepiezoelectricactuator.Thedrivingpulse
inDODprintingisalsoknowntocontrolboththesizeoftheejecteddropanditsvelocity.12,22,23Reisdemonstratedthatfor
theformationofdropsusinghighlyloadedceramicsuspensions,acousticphenomenaareimportantandthat
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