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英文原文MIXINGEFFECTSOFCONSTITUTINGELEMENTSOFMIXINGSCREWSINSINGLEANDTWINSCREWEXTRUDERSDJVANZUILICHEM,EKUIPER,WSTOLP,TJAGERDEPARTMENTOFFOODTECHNOLOGYANDNUTRITIONALSCIENCES,WAGENINGENAGRICULTURALUNIERSITY,FOODANDBIOPROCESSENGINEERINGGROUP,POBOX8129,BOMENWEG2,6700EVWAGENINGEN,NETHERLANDSRECEIVED21APRIL1998；ACCEPTED29MARCH1999ABSTRACTINEXTRUSION,MIXINGOFSOLIDSANDMELTSHASALWAYSBEENPROBLEMATIC,LEADINGTODIVERSEMODELSDESCRIBINGTHEMELTINGPROCESSITISFOUNDTHATFORFOODSBASEDONCEREALS,ONLYAFEWAREVALID,DUETOTHESIMULTANEOUSPRESENCEOFWATERANDHIGHVISCOUSNONNEWTONIANMATERIALMIXINGTRIALSARESUMMARISEDFORSINGLEANDTWINSCREWEXTRUDERS,WITHPARTICULATESOLIDSOFDIFFERENTPARTICLESIZESLIKE,MAIZEGRITS,WHEATFLOUR,SUCROSECRYSTALSANDGLUCOSESYRUPSPECIALMIXINGHEADSFORSINGLESCREWEXTRUDERSLIKE,PINEAPPLEHEADS,ANDSLOTTEDFLIGHTSECTIONSFORCOUNTERROTATINGTWINSCREWEXTRUDERSAREINVESTIGATEDTHEEFFECTSOFSCREWGEOMETRYONMIXINGHASBEENMEASUREDUSINGCOROTATINGTWINSCREWEXTRUDERMODULARELEMENTSLIKESINGLELEADELEMENTS,MIXINGPADDLESANDREVERSEDPITCHELEMENTSINATRANSLUCENTMODELEXTRUDERBYMEANSOFASTUDYOFFLOWPHENOMENAANDRESIDENCETIMEDISTRIBUTIONRTDMEASUREMENTSMIXINGEFFECTSAREREPORTEDANDTHEIRINFLUENCESONVISCOUSDISSIPATION,RESIDENCETIME,CURVESPREADANDSTAGNANCYAREEXPLAINED1999ELSEVIERSCIENCESAALLRIGHTSRESERVEDKEYWORDSSINGLESCREWEXTRUDERS；TWINSCREWEXTRUDERS；MIXING1INTRODUCTIONPARTOFTHEDEFINITIONOFFOODEXTRUSIONCOOKINGISTHATTHEFOODMATERIALONITSWAYTHROUGHTHEOPENCHANNELOFASINGLESCREWEXTRUDERSSE,ISSHEARED,MIXEDANDCOMPRESSEDINTHECASEOFATWINSCREWEXTRUDERTSEWITHCLOSELYINTERMESHINGSCREWS,THEFOODISTRANSPORTEDINSOCALLEDCSHAPEDCHAMBERS,WHICHAREENCLOSEDBYTHENEIGHBOURINGINTERMESHINGSCREWANDTHEBARRELWALLSEEFIG1THEFOODPOWDERISTAKENUPATTHEFEEDPORTINTHECSHAPEDCHAMBEROFONESCREW,ISCONVEYED,INTERNALLYMIXED,FORCEDTHROUGHTHEGAPSANDCLEARANCESOFTHISSCREWOREVENTUALLYTRANSFERREDTOTHENEIGHBOURINGSCREWANDFINALLYTHISCSHAPEDCHAMBERDELIVERSITSCONTENTATWXTHEDIE13,23THEDIFFERENCESINTHEWAYOFOPERATIONBETWEENSSE’SANDTSE’SAREOBVIOUSANDEACHOFTHEMWILLASKFORITSOWNDESIGNOFMODULARSCREWPARTSTHATWILLENHANCEANDIMPROVETHEMIXINGEFFECTSOFTHESCREWSWX14,17MIXINGOPERATIONSINCOOKINGEXTRUDERSCANBEDISTINGUISHEDINTHREEDIFFERENTTYPESTHEFIRSTONEISCOARSEMIXINGORLONGITUDINALRAXIALMIXINGTHESECONDONEISDISPERSIVEMIXINGORCOMMINUTIONOFTHEDISPERSEPHASETHETHIRDONEISDISTRIBUTIVEMIXINGORRADIALMIXINGTHEOPERATIVEMECHANISMTOREALISECOARSEMIXINGISTHEROTATIONALMOVEMENTOFTHESCREWS,CAUSINGRESIDENCETIMEDISTRIBUTIONRTDINCASEOFPLUGFLOWHOWEVER,THEREWILLBENOCOARSEMIXINGTHESEDIFFERENTMECHANISMSARERESPONSIBLEFORTHEMIXINGEFFECTSFORDISPERSIVEMIXINGTHEFUNCTIONOFTHECOMMINUTIONISTOBREAKAGGLOMERATESOFTHEDISPERSEPHASEINTOSMALLERONESTHEOPERATIVEMECHANISMISTHEEXISTENCEOFELONGATIONALFORCESANDRORSHEARSTRESSESDISTRIBUTIVEMIXINGISCAUSEDBYTHEACTIONOFASCREWELEMENT,DISTRIBUTINGTHECONCENTRATIONOFTHEDISPERSEPHASEOVERTHETOTALVOLUMEOFTHECHAMBERORCHANNELOFTHEEXTRUDERCROSSSECTIONINSUCHAWAYTHATTHECONCENTRATIONOFTHEDISPERSEPHASEINEACHVOLUMETRICELEMENTEQUALSTHEAVERAGEDCONCENTRATIONTHISREQUIREMENTISSTRICTERWHENTHEELEMENTARYVOLUMETOBECONSIDEREDISSMALLERALTHOUGHTOTALLYDIFFERENT,THETHREEMECHANISMSDESCRIBEDARENOTINDEPENDENTOFEACHOTHERTHEANISMSDESCRIBEDARENOTINDEPENDENTOFEACHOTHERTHETHREETYPESOFMIXINGSHOULDTHEREFOREBECAREFULLYDISTINGUISHEDITISPOSSIBLETODESIGNSCREWSWITHMIXINGELEMENTSONDIFFERENTLOCATIONS,PROVOKINGACERTAINCOMBINATIONOFTHETHREEMIXINGTYPESATACERTAINAXIALLOCATIONTHEPOSSIBILITIESOFTHESECOMBINATIONSARESTRONGLYDEPENDENTOFEXTRUDERGEOMETRY,PROPERTIESOFFOODMATERIALSANDPROPERTIESUNDEREXTRUSIONCONDITIONSALTHOUGHALOTOFKNOWLEDGEISGATHEREDCONCERNINGTHEUSEOFWELLKNOWNMIXINGELEMENTSFROMTHEPLASTICATINGINDUSTRY,INCORPORATIONOFTHISKNOWLEDGEINTODESIGNSOFSSE’SANDTSE’SARENOTALWAYSSUCCESSFULFORFOODPRODUCTSANDOTHERBIOPOLYMERSTHEREARESEVERALREASONSFORTHISPHENOMENONTHEFIRSTDISTURBINGFACTORWHENCOMPARINGPLASTICPOLYMERSWITHBIOPOLYMERSISTHEDIFFERENCEINFEEDTOTHEEXTRUDER,EG,THEPRESENCEOFMULTIPLESOLIDS,WATERANDEVENTUALLYVEGETABLEOILINTHECASEOFBIOPOLYMERSSECONDLY,BIOPOLYMERSDONOTHAVEAWELLDEFINEDMELTINDEXLIKEMANYCHEMICALPOLYMERSANDINGENERALTHEIRVISCOSITYBEHAVIOURDIFFERSFROMTHATOFCHEMICALPOLYMERSWX1THIRDLY,THEREAREANUMBEROFDEGRADATIONREACTIONSOFIRREVERSIBLENATUREOCCURRINGSIMULTANEOUSLYWHENABIOPOLYMERISSUBJECTEDTOATEMPERATUREANDSTRESSFIELDINANEXTRUDER,CHANGINGTHEPHYSICALANDCHEMICALPROPERTIESWXDRASTICALLYFROMLOCATIONTOLOCATION15INTHISFIELDNUMEROUSPAPERSHAVEBEENPUBLISHEDBYWELLKNOWNAUTHORSFROMRESEARCHINSTITUTIONSLIKECAFTRRUTGERSUNIVERSITY,IFRNORWICH,INRA,CEMEFFRANCETHEAIMOFTHISARTICLEISSUMMARISINGTHEPOSSIBILITIESANDSOLUTIONSFORMIXINGPROBLEMSFORSINGLESCREWANDCOUNTERROTATINGTWINSCREWEXTRUDERSANDGIVINGBETTERINSIGHTINTHEFUNCTIONSOFSCREWELEMENTSINCOROTATINGTWINSCREWEXTRUDERS2MIXINGMECHANISMS21LONGITUDINALORAXIALMIXINGWHENFOODPARTICLESDURINGTHEIRLIFETIMEINANEXTRUDERARESUBJECTEDTOAXIALMIXING,THISCANBESEENANDMEASUREDBYACHANGINGRTDEXTREMESINTHISCASEAREPLUGFLOW,WHEREALLPARTICLESHAVETHESAMERESIDENCETIME,ORAWIDERTDWHICHISCAUSEDBYAXIALMIXINGSOMEPARTICLESWILLSTAYINTHEEXTRUDERCOOKERFORAPROCESSTIMESHORTERTHANTHEAVERAGE,WHILSTOTHERSWILLDWELLFORMUCHLONGERTHANTHEAVERAGEWHENDIFFERENTFLOWSYSTEMSARECOMPILEDSEEFIG2FIG3SHOWSTHETHEORETICALRTDFORAMATERIALWITHACOEFFICIENTNS1INTHEPOWERLAWEQUATIONFORTHESHEARDEPENDENCYOFTHEVISCOSITYINANSSETHISFIGUREALSOSHOWSTHERTDDATA,MEASUREDWHENPROCESSINGCORNGRITSINABATTENFELDSSEATTWOMOISTUREY1CONTENTSVS0142,020KGKGANDSCREWREVOLUWY1WXTIONSRANGINGFROMNS133,166,20REVS22THERTDDATAAREREPRESENTEDASAN‘CUMULATIVEEXITAGE’ORFFUNCTION,WHICHSHOWSTHEFRACTIONFOFTHEINFLOW,WXWHICHHASLEFTTHEEXTRUDERAFTERTSECONDS3,4,16THEEFUNCTION,THEDERIVATIVEOFTHEFFUNCTION,SHOWSTHESOCALLED‘EXITAGE’DISTRIBUTIONOFFOODPARTICLES,FEDINTOTHEEXTRUDERATANINFINITESMALLTIMEANDISRELATEDTOTHEFFUNCTIONWITHTFTSETDT1H0THEAVERAGERESIDENCETIMETOFTHEFOODMATERIALINTHECOOKINGEXTRUDERISCALCULATEDWITHTSTETDT2HWHENTHEFFUNCTIONINFIG3ISOBSERVED,ITFOLLOWSTHATMOSTOFTHECORNGRITSHAVEANEXITAGEBETWEENTANDT,0WHEREAST3R4TTHESEMEASUREMENTSSHOWTHATFORA0SINGLESCREWEXTRUDERTHEREISASTRONGINFLUENCEOFTHEMOISTURECONTENTANDTHENUMBEROFREVOLUTIONSOFTHESCREWONTHESHAPEOFTHEFFUNCTIONANDTHEBREAKTHROUGHWXPOINT3THEOPERATINGPRINCIPLEOFTWINSCREWEXTRUDERSCANBEDESCRIBEDWITHTHEEXISTENCEOFTWOPARALLELSERIESOFCONTINUOUSLYSTIRREDTANKREACTORSCSTR,WHEREEACHWXCSHAPEDCHAMBERREPRESENTSSUCHACSTR13INFIG4,ASCHEMATICISGIVENOFTHISPRINCIPLEANDTHELEAKAGEGAPSANDFLOWSBETWEENTHECHAMBERSANDBETWEENTHESERIESCSTR’SAREINDICATEDTHELEAKAGEFLOWSTHROUGHTHECALENDAR,SIDE,FLIGHTANDTETRAHEDRONGAPSQ,Q,Q,CSFQ,RESANDFORCEDCONVEYINGOFTHECHAMBERSRESULTSINATWXNETTPOSITIVEMASSFLOWFROMFEEDPORTTOTHEDIE13,17THISAPPROACHWASTHEBASISOFASERIESOFPUBLICATIONSOFTHEWAGENINGENRESEARCHGROUPONTHERTDOFEXTRUSIONWXCOOKING,WHICHISDESCRIBEDBELOW8–12,24–26,28THERTD’SOFTSE’SAREMOREASYMMETRICCOMPAREDTOACASCADEOFCSTR’STHEDIFFERENTPARALLELSERIESOFCSHAPEDCHAMBERSINATSE,CANBESUMMEDUPTOANRTDMODELOFCSTR’SINSERIESTHESECSTR’STRAVELFROMFEEDPORTTODIE,DURINGWHICHTHECHAMBERVOLUMECHANGESANDTHESECHAMBERSLOOSEMATERIALINTHEOPPOSITEDIRECTIONWXSEEFIG4JAGERETAL11PRESENTEDAWAYBYWHICHTHERTDCOULDBECALCULATEDTHEAVERAGERESIDENCETIMEANDTHECURVEWIDTHSARECALCULATEDFROMTHEUNCORRECTEDECURVEUSINGTODD’SMETHODOFRECORDINGTHEPASSINGBYOF16,84AND92OFTRACERMATERIALTHEYARECORRECTEDWITHASYSTEMATICALERRORASCALCULATEDBYAMONTECARLOWXPROCEDURE18THEUNCORRECTEDAVERAGERESIDENCETIMEISCALCULATEDUSINGEQUATIONSFORTHEZERO,FIRSTANDSECONDTIMEMOMENTM,M,MOFTHEMEASUREDEXTINCTION012CTASMSTICTDT3HITSMRM410ANDM21UNS52MMYM021NUGIVESTHENUMBEROFMIXERSOFASERIESOFCSTR’SAHIGHERNUMBEROFNUSTANDSFORAFLOWTHATRESEMBLESAMOREPLUGFLOWNATURERTDMODELSCANBEDIVIDEDINCURVEFITMODELS,WHICHDESCRIBETHECURVESHAPEANDINMODELSTHATDESCRIBETHEAXIALMIXINGINTHEEXTRUDERREACTORINAPREDICTIVEANDRORDESCRIPTIVEWAYANEXAMPLEOFADESCRIPTIVEMODELISTHEPLUGFLOWMODELWITHWXAXIALDISPERSION16THEAXIALDISPERSIONISDESCRIBEDWITHACONSTANTEFFECTIVELONGITUDINALDISPERSIONCOEFFICIENTIDE2Y1WXMS21THEPECLETNUMBERPE,THERATIOOFTHEAVERAGEAXIALCONVECTIVETRANSPORTANDTHETRANSPORTBYDISPERSIONISEQUALTOLPES6IDEINWHICHLISTHEEXTRUDERLENGTHANDISTHEAVERAGEAXIALVELOCITYTHEAXIALDISPERSIONMODELANDAMODELOFAWXCASCADEOFCSTR’SDOGIVECOMPARABLERTD’S16JAGERWXWXHASSHOWNIN199111AND199212THATBOTHMODELSFOREXTRUDERSCANBECOMBINEDANDTHATPEANDNARERELATEDASPE2UNS7UYPE2PEY1Q10ITISPOSSIBLETOUSETHISRTDMODELFORDIFFERENTTWINSCREWEXTRUDERDESIGNS,TOEVALUATETHEIRWORKINGBEHAVIOURTHISCANBEREALISEDBYINTRODUCINGASOCALLEDCHAMBERMIXINGCOEFFICIENT,
