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河南理工大学万方科技学院本科毕业论文1附录外文资料与中文翻译外文资料COMPARINGMIXINGPERFORMANCEOFUNIAXIALANDBIAXIALBINBLENDERSAMITMEHROTRAANDFERNANDOJMUZZIODEPARTMENTOFCHEMICALANDBIOCHEMICALENGINEERING,RUTGERSUNIVERSITY,PISCATAWAY,NJ,08855,UNITEDSTATESRECEIVED17FEBRUARY2009REVISED30MAY2009ACCEPTED14JUNE2009AVAILABLEONLINE27JUNE2009ABSTRACTTHEDYNAMICSINVOLVEDINPOWDERMIXINGREMAINSATOPICOFINTERESTFORMANYRESEARCHERSHOWEVERTHETHEORYSTILLREMAINSUNDERDEVELOPEDMOSTOFTHEMIXERSARESTILLDESIGNEDANDSCALEDUPONEMPIRICALBASISINMANYINDUSTRIES,INCLUDINGPHARMACEUTICAL,THEMAJORITYOFBLENDINGISPERFORMEDUSING“TUMBLINGMIXERS”TUMBLINGMIXERSAREHOLLOWCONTAINERSWHICHAREPARTIALLYLOADEDWITHMATERIALSANDROTATEDFORSOMENUMBEROFREVOLUTIONSSOMECOMMONEXAMPLESINCLUDEHORIZONTALDRUMMIXERS,VBLENDERS,DOUBLECONEBLENDERSANDBINBLENDERSINALLTHESEMIXERSWHILEHOMOGENIZATIONINTHEDIRECTIONOFROTATIONISFAST,MEDIATEDBYACONVECTIVEMIXINGPROCESS,MIXINGINTHEHORIZONTALAXIALDIRECTION,DRIVENBYADISPERSIVEPROCESS,ISOFTENMUCHSLOWERINTHISPAPER,WEEXPERIMENTALLYINVESTIGATEANEWTUMBLINGMIXERTHATROTATESWITHRESPECTTOTWOAXESAHORIZONTALAXISTUMBLINGMOTION,ANDACENTRALSYMMETRYAXISSPINNINGMOTIONADETAILEDSTUDYISCONDUCTEDONMIXINGPERFORMANCEOFPOWDERSANDTHEEFFECTOFCRITICALFUNDAMENTALPARAMETERSINCLUDINGBLENDERGEOMETRY,SPEED,FILLLEVEL,PRESENCEOFBAFFLES,LOADINGPATTERN,ANDAXISOFROTATIONINTHISWORKACETAMINOPHENISUSEDASTHEACTIVEPHARMACEUTICALINGREDIENTANDTHEFORMULATIONCONTAINSCOMMONLYUSEDEXCIPIENTSSUCHASAVICELANDLACTOSETHEMIXINGEFFICIENCYISCHARACTERIZEDBYEXTRACTINGSAMPLESAFTERPREDETERMINEDNUMBEROFREVOLUTIONS,ANDANALYZINGTHEMUSINGNEARINFRAREDSPECTROSCOPYTODETERMINECOMPOSITIONAL河南理工大学万方科技学院本科毕业论文2DISTRIBUTIONRESULTSSHOWTHEIMPORTANCEOFPROCESSVARIABLESINCLUDINGTHEAXISOFROTATIONONHOMOGENEITYOFPOWDERBLENDSGRAPHICALABSTRACTTHEDYNAMICSINVOLVEDINPOWDERMIXINGREMAINSATOPICOFINTERESTFORMANYRESEARCHERSHOWEVERTHETHEORYSTILLREMAINSUNDERDEVELOPEDMOSTOFTHEMIXERSARESTILLDESIGNEDANDSCALEDUPONEMPIRICALBASISINMANYINDUSTRIES,INCLUDINGPHARMACEUTICAL,THEMAJORITYOFBLENDINGISPERFORMEDUSING“TUMBLINGMIXERS”INALLTHESEMIXERSWHILEHOMOGENIZATIONINTHEDIRECTIONOFROTATIONISFAST,MEDIATEDBYACONVECTIVEMIXINGPROCESS,MIXINGINTHEHORIZONTALAXIALDIRECTION,DRIVENBYADISPERSIVEPROCESS,ISOFTENMUCHSLOWERINTHISPAPER,WEEXPERIMENTALLYINVESTIGATEANEWTUMBLINGMIXERTHATROTATESWITHRESPECTTOTWOAXESAHORIZONTALAXISTUMBLINGMOTION,ANDACENTRALSYMMETRYAXISSPINNINGMOTIONKEYWORDSPOWDERMIXINGCOHESIONBLENDERMIXERRELATIVESTANDARDDEVIATIONNIRACETAMINOPHENARTICLEOUTLINE1INTRODUCTION2MATERIALSANDMETHODS21NEARINFRAREDSPECTROSCOPY22BINBLENDERSUSEDINTHISSTUDYUNIAXIALBLENDERBLENDER1,BIAXIALBLENDERBLENDER223EXPERIMENTALMETHOD3RESULTS4CONCLUSIONREFERENCES河南理工大学万方科技学院本科毕业论文31INTRODUCTIONPARTICLEBLENDINGISAREQUIREDSTEPINAVARIETYOFAPPLICATIONSSPANNINGTHECERAMIC,FOOD,GLASS,METALLURGICAL,POLYMERS,ANDPHARMACEUTICALSINDUSTRIESDESPITETHELONGHISTORYOFDRYSOLIDSMIXINGORPERHAPSBECAUSEOFIT,COMPARATIVELYLITTLEISKNOWNOFTHEMECHANISMSINVOLVED1,2AND3ACOMMONTYPEOFBATCHINDUSTRIALMIXERISTHETUMBLINGBLENDER,WHEREGRAINSFLOWBYACOMBINATIONOFGRAVITYANDVESSELROTATIONALTHOUGHTHETUMBLINGBLENDERISAVERYCOMMONDEVICE,MIXINGANDSEGREGATIONMECHANISMSINTHESEDEVICESARENOTFULLYUNDERSTOODANDTHEDESIGNOFBLENDINGEQUIPMENTISLARGELYBASEDONEMPIRICALMETHODSTUMBLERSARETHEMOSTCOMMONBATCHMIXERSININDUSTRY,ANDALSOFINDUSEINMYRIADOFAPPLICATIONASDRYERS,KILNS,COATERS,MILLSANDGRANULATORS4,5,6,7AND8WHILEFREEFLOWINGMATERIALSINROTATINGDRUMSHAVEBEENEXTENSIVELYSTUDIED9AND10,COHESIVEGRANULARFLOWSINTHESESYSTEMSARESTILLNOTCOMPLETELYUNDERSTOODLITTLEISKNOWNABOUTTHEEFFECTOFFUNDAMENTALPARAMETERSSUCHASBLENDERGEOMETRY,SPEED,FILLLEVEL,PRESENCEOFBAFFLES,LOADINGPATTERNANDAXISOFROTATIONONMIXINGPERFORMANCEOFCOHESIVEPOWDERSORTHESCALINGREQUIREMENTSOFTHEDEVICESHOWEVER,CONVENTIONALTUMBLERS,ROTATINGAROUNDAHORIZONTALAXIS,ALLSHAREANIMPORTANTCHARACTERISTICWHILEHOMOGENIZATIONINTHEDIRECTIONOFROTATIONISFAST,MEDIATEDBYACONVECTIVEMIXINGPROCESS,MIXINGINTHEHORIZONTALAXIALDIRECTION,DRIVENBYADISPERSIVEPROCESS,ISOFTENMUCHSLOWERINTHISPAPER,WEEXPERIMENTALLYINVESTIGATEANEWTUMBLINGMIXERTHATROTATESWITHRESPECTTOTWOAXESAHORIZONTALAXISTUMBLINGMOTION,ANDACENTRALSYMMETRYAXISSPINNINGMOTIONWEEXAMINETHEEFFECTSOFFILLLEVEL,MIXINGTIME,LOADINGPATTERNANDAXISOFROTATIONONTHEMIXINGPERFORMANCEOFAFREEFLOWINGMATRIXOFFASTFLOLACTOSEANDAVICEL102,CONTAININGAMODERATELYCOHESIVEAPI,MICRONIZEDACETAMINOPHENWEUSEEXTENSIVESAMPLINGTOCHARACTERIZEMIXINGBYTRACKINGTHEEVOLUTIONOFACETAMINOPHENHOMOGENEITYUSINGANEARINFRAREDSPECTROSCOPYDETECTIONMETHODAFTERMATERIALSANDMETHODSAREDESCRIBEDINSECTION2,RESULTSAREPRESENTEDINSECTION3,FOLLOWEDBYCONCLUSIONSANDRECOMMENDATIONS,WHICHAREPRESENTEDINSECTION4河南理工大学万方科技学院本科毕业论文42MATERIALSANDMETHODSTHEMATERIALSUSEDINTHESTUDYARELISTEDINTABLE1,ALONGWITHTHEIRSIZEANDMORPHOLOGYACETAMINOPHENISBLENDEDWITHCOMMONLYUSEDEXCIPIENTSANDISUSEDASATRACERTOEVALUATETHEDEGREEOFHOMOGENEITYACHIEVEDASAFUNCTIONOFNUMBEROFREVOLUTIONSACETAMINOPHENISONEOFTHEDRUGSMOSTWIDELYUSEDINMIXINGSTUDIES,ANDAVICELANDLACTOSEARECOMMONLYUSEDPHARMACEUTICALEXCIPIENTSINTHEINTERESTOFBREVITYTHEIRSEMIMAGESARENOTINCLUDEDINTHISPAPER,BUTCANBEFOUNDIN“HANDBOOKOFPHARMACEUTICALEXCIPIENTS”21NEARINFRAREDSPECTROSCOPYACETAMINOPHENHOMOGENEITYWASQUANTIFIEDUSINGNEARINFRAREDSPECTROSCOPYACALIBRATIONCURVEWASCONSTRUCTEDFORAPOWDERMIXTURECONTAININGINAVERAGE35AVICELPH102,62LACTOSEAND3ACETAMINOPHENNEARINFRAREDNIRSPECTROSCOPYCANBEAUSEFULTOOLTOCHARACTERIZEACETAMINOPHENSAMPLESAREPREPAREDBYKEEPINGTHERATIOOFAVICELTOLACTOSERANDOMIZEDINORDERTOMINIMIZEEFFECTSOFIMPERFECTBLENDINGOFEXCIPIENTSDURINGTHEACTUALEXPERIMENTSONTHEACCURACYOFTHERESULTSTHERAPIDCONTENTANALYZERINSTRUMENTMANUFACTUREDBYFOSSNIRSYSTEMSSILVERSPRING,MDANDVISIONSOFTWAREVERSION21ISUSEDFORTHEANALYSISTHESAMPLESAREPREPAREDBYWEIGHING1GOFMIXTUREINTOSEPARATEOPTICALSCINTILLATIONVIALSKIMBLEGLASSINCVINELAND,NJUSINGABALANCEWITHANACCURACYOF001MGNEARIRSPECTRAARECOLLECTEDBYSCANNINGINTHERANGE11162482NMINTHEREFLECTANCEMODEPARTIALLEASTSQUAREPLSREGRESSIONISUSEDINCALIBRATIONMODELDEVELOPMENTUSINGTHESECONDDERIVATIVEMATHEMATICALPRETREATMENTTOMINIMIZETHEPARTICLESIZEEFFECTSASSHOWNINFIG1,EXCELLENTAGREEMENTISACHIEVEDBETWEENTHECALIBRATEDANDPREDICTEDVALUES河南理工大学万方科技学院本科毕业论文5FIG1FIG1NEARINFRAREDNIRSPECTROSCOPYVALIDATIONCURVETHEEQUATIONUSEDTOPREDICTACETAMINOPHENCONCENTRATIONISVALIDATEDBYTESTINGSAMPLESWITHKNOWNAMOUNTSOFACETAMINOPHENCONCENTRATIONTHEYAXISREPRESENTSTHECONCENTRATIONCALCULATEDFROMTHEEQUATIONANDTHEXAXISREPRESENTSTHEACTUALCONCENTRATIONTHUSAPERFECTLYSTRAIGHTLINEAT45WOULDREPRESENTTHEBESTCALIBRATIONMODELEACHPOINTONTHEGRAPHREPRESENTSASINGLESAMPLETHECONCENTRATIONOFACETAMINOPHENEXAMINEDHERERANGESFROM0TO822BINBLENDERSUSEDINTHISSTUDYUNIAXIALBLENDERBLENDER1,BIAXIALBLENDERBLENDER2DUETOITSWIDESPREADUSE,ACYLINDRICALBLENDER1WITHACAPACITYOF30LISCHOSENASAREFERENCEBLENDERINTHESTUDYASSHOWNINFIG2,THISBLENDERHASACIRCULARCROSSSECTIONANDTAPERSATTHEBOTTOMITCANBEUSEDWITHORWITHOUTBAFFLES,WHICHAREMOUNTEDONAREMOVABLELIDINTHISSTUDYALLTHEEXPERIMENTSARECONDUCTEDWITHOUTTHEUSEOFBAFFLESMIXINGPERFORMANCEINTHISDEVICEISUSEDTOPROVIDEABASELINEFOREVALUATINGTHEMIXINGPERFORMANCEOFANEWLYDEVELOPEDBLENDER2WITHACAPACITYOF40L,WHICHISALSOCYLINDRICAL,INORDERTODETERMINETHEEFFECTOFDUALAXISOFROTATIONONMIXINGPERFORMANCETHEBLENDERSHOWNINFIG2BHASTWOAXISOFROTATIONTHESPINNINGRATEOFPRECESSIONRELATIVETOTHECENTRALAXISOFSYMMETRYISGEAREDTOBEHALFOFTHATOFTHERATEOFROTATIONAROUNDTHEHORIZONTALAXIS河南理工大学万方科技学院本科毕业论文6FIG2FIG2PICTORIALREPRESENTATIONOFABINBLENDER1ANDBBINBLENDER2SHOWINGTHECORRESPONDINGAXISOFROTATION23EXPERIMENTALMETHODTWOTYPESOFINITIALPOWDERLOADINGUSEDINTHEEXPERIMENTSTOPBOTTOMLOADINGANDSIDELOADING,WHICHARESCHEMATICALLYREPRESENTEDINFIG3TOAVOIDAGGLOMERATION,THEAPI,ACETAMINOPHEN,WASDELUMPEDPRIORTOLOADINGITINTOTHEBLENDERBYPASSINGITTHROUGHA35MESHSCREENINORDERTOCHARACTERIZEMIXINGPERFORMANCE,AGROOVESAMPLERWASUSEDTOEXTRACTSAMPLESFROMTHEBLENDERSAT75,15,30,60,120REVOLUTIONSTHETHIEFWASCAREFULLYINSERTEDINTHEBIN,ANDACOREWASEXTRACTEDATEACHPOINTOFINSERTIONEACH“STAB”MINIMIZINGPERTURBATIONTOTHEPOWDERBEDREMAININGINTHEBLENDERAPPROXIMATELY7SAMPLESARETAKENFROMEACHTHIEFSTAB,ANDATOTALOFFIVESTABSAREUSEDATEACHSAMPLINGTIME,ASSHOWNINFIG4SOATOTALOF35SAMPLESARETAKENATEACHSAMPLINGPOINTFIG3FIG3SCHEMATICOFTHELOADINGPATTERNUSEDINTHESTUDYINTOPBOTTOMLOADING,AVICELISLOADEDFIRSTINTOTHEBLENDERFOLLOWEDBYLACTOSEONTOPOFITANDFINALLYACETAMINOPHENISUNIFORMLYSIEVEDOVERINSIDESIDELOADINGAVICELISPLACEDATTHEBOTTOMANDTHENACETAMINOPHENISONLYSIEVEDONLYINHALFPARTOFTHEBLENDERANDISSANDWICHEDBETWEENLACTOSEANDAVICELFIG4FIG4ATHIEFSAMPLERBTOPVIEWOFTHESAMPLINGPOSITIONSCHEME河南理工大学万方科技学院本科毕业论文7THEEXPERIMENTALPLANUSEDINTHISSTUDYISASFOLLOWSFILLLEVELBLENDER160FILLLEVELBLENDER260,70,80LOADINGPATTERNBLENDER1SIDESIDELOADING,TOPBOTTOMLOADINGLOADINGPATTERNBLENDER2SIDESIDELOADING,TOPBOTTOMLOADINGSPEEDBLENDER115RPM,20RPM,25RPMSPEEDBLENDER2ROTATIONAL/SPINNING15/75RPM,20/10RPM,30/15RPMSAMPLINGTIMEBLENDER1,BLENDER275,15,30,60,120REVOLUTIONS3RESULTSTHEHOMOGENEITYINDEXUSEDISTHERSD,WHERECISTHECONCENTRATIONOFEACHINDIVIDUALSAMPLE,C_ISTHEAVERAGECONCENTRATIONOFALLSAMPLESANDNISTHETOTALNUMBEROFSAMPLESOBTAINEDATAGIVENSAMPLINGTIMEWEEXAMINETHEEFFECTOFFILLLEVELONMIXINGPERFORMANCEPREVIOUSLYTHEREHAVEBEENSTUDIESONTHEEFFECTOFFILLLEVELINTHEBOHLEBINBLENDER,GALLAYBINBLENDERANDVBLENDERANDDOUBLECONEBLENDER11,12AND13ALLTHEAFOREMENTIONEDBLENDERSHAVEONLYONEAXISOFROTATION,THEREFORETHEOBJECTIVEOFTHISSTUDYISTOEXAMINEHOWDUALAXISIMPACTMIXINGPERFORMANCESATHIGHFILLLEVELSTOAVOIDREPETITION,STUDIESFORFILLLEVELARENOTCONDUCTEDFORBINBLENDER1RESULTSAVAILABLEFROMAPREVIOUSSTUDYUSINGMGSTASATRACERSHOWEDTHATMIXINGINAUNIAXIALBLENDERSLOWEDDOWNQUITEDRAMATICALLYASTHEFILLLEVELEXCEEDED70MOREOVER,RESULTSFORACETAMINOPHENCANBEASSUMEDTOBESIMILARTOTHOSEOBTAINEDINPREVIOUSWORKBYMUZZIOETAL11AND13,FORASINGLEAXISRECTANGULARBINBLENDER11,WHICHHAVE河南理工大学万方科技学院本科毕业论文8SHOWNTHATEVENAFTERFEWHUNDREDREVOLUTIONSHOMOGENEITYACHIEVEDWITHA80FILLLEVELISVERYPOORASCOMPAREDTO60FILLLEVELTOEXAMINETHEEFFECTOFFILLLEVELINADUALAXISBLENDER,EXPERIMENTSWEREPERFORMEDINBLENDER2WITHTHETOPBOTTOMLOADINGPATTERNFORAROTATIONALSPEEDOF15RPMANDWITHSPINNINGSPEEDOF75RPMTHEFILLLEVELSEXAMINEDARE60,70AND80RESPECTIVELYANDSAMPLESARETAKENAFTER75,15,30,60,120REVOLUTIONSTYPICALRESULTSARESHOWNINFIG5,WHICHSHOWSTHERSDVSNUMBEROFBLENDERREVOLUTIONSASEXPECTEDFORNONAGGLOMERATINGMATERIALS,THECURVESSHOWARAPIDLYDECAYINGREGIONTHESLOPEOFTHECURVESINTHISREGION,INSEMILOGARITHMICCOORDINATES,ISUSEDTODEFINETHEMIXINGRATETHECURVESTHENLEVELOFFTOAPLATEAUTHATINDICATESTHEMAXIMUMDEGREEOFHOMOGENEITYTHATISACHIEVABLEINTHEBLENDERFORAGIVEMATERIALFIG5FIG5MIXINGCURVESFORDIFFERENTFILLLEVELSINBLENDER2THERSDOFACETAMINOPHENISPLOTTEDASAFUNCTIONOFNUMBEROFREVOLUTIONSTHELOADINGPATTERNINTOPBOTTOMANDTHEBLENDERROTATIONALSPEEDIS15RPMWITHSPINNINGSPEEDOF75RPMSIMILARTOPREVIOUSSTUDIESWITHOTHERTUMBLINGBLENDERSWEOBSERVETHATBLENDINGPERFORMANCEISADVERSELYAFFECTEDBYINCREASINGFILLLEVELSASSHOWNINFIG5,THECURVEFOR80FILLPERFORMSMOREPOORLYTHANTHOSEFOR60AND70FILLASFILLLEVELINCREASES,RSDCURVESDECAYMORESLOWLY,SIGNIFYINGASLOWERMIXINGPROCESSHOWEVER,THEEFFECTISNOTASPRONOUNCEDASINOTHERBINBLENDERSANDAFTERABOUTONLY100REVOLUTIONS,THESAMEPLATEAUTHESAMEASYMPTOTICBLENDHOMOGENEITYISACHIEVEDFORALLTHREEFILLLEVELSNEXT,THEEFFECTOFROTATIONALSPEEDISINVESTIGATEDINTHEBLENDER1河南理工大学万方科技学院本科毕业论文9WITHONEAXISOFROTATIONANDISCOMPAREDTOTHEBLENDER2WITHDUALROTATIONAXISEXPERIMENTSWERECONDUCTEDFORBOTHBLENDERSWITHTOPBOTTOMANDSIDESIDELOADINGEXPERIMENTSWEREPERFORMEDAT60FILLLEVELANDTHEROTATIONSPEEDSCONSIDEREDFORBLENDER1ARE15RPM,20RPMAND25RPMRESPECTIVELYASSHOWNINFIG6ANDFIG7,WHENPLOTTEDASAFUNCTIONOFBLENDERREVOLUTIONS,THEREISNOTMUCHOFANEFFECTOFROTATIONSPEEDONTHEHOMOGENEITYINDEXRSDOFACETAMINOPHENAT60FILLLEVELITISOBSERVEDTHATMIXINGPERFORMANCEAT20RPMAND25RPMISSLIGHTLYBETTERTHANAT15RPM,HOWEVERTHEDIFFERENCESINTHEPERFORMANCEOFTHEBLENDERUNDERDIFFERENTSPEEDSAREPROBABLYTOOSMALLTOBESIGNIFICANTRSDCURVESDECAYWITHTHESAMESLOPE,INDICATINGSIMILARMIXINGRATESINTHESTUDYREPORTEDHERE,THEFILLLEVELISONLY60,ANDALLTHEROTATIONALSPEEDSAREENOUGHTOACHIEVEHOMOGENIZATIONTHEAFOREMENTIONEDSTUDIESWERECONDUCTEDAT85FILLLEVELFORSUCHAHIGHFILLLEVEL,ATLOWSPEEDS,ASTAGNANTCOREISKNOWNTOOCCURATTHECENTEROFMANYBLENDERS,REQUIRINGHIGHERSHEARSTRESSPERUNITVOLUMETOACHIEVEHOMOGENIZATIONMOREOVER,THEFLOWPROPERTIESOFMGSTAREKNOWNTOBESTRONGLYDIFFERENTTHANTHOSEOFMOSTMATERIALS,ANDAREKNOWNTOHAVEADEEPIMPACTONTHEFLOWPROPERTIESOFTHEMIXTUREASAWHOLEFURTHERMORE,MGSTISFAMOUSLYKNOWNTOBEASHEARSENSITIVEMATERIALTHUSANEXPECTATIONTHATLUBRICATEDANDUNLUBRICATEDBLENDSWOULDSHOWSIMILARBEHAVIORWITHRESPECTTOSHEARISPROBABLYUNWARRANTEDFIG6FIG6MIXINGCURVESFORTOPBOTTOMLOADINGEXPERIMENTSWITH60FILLLEVELRSDISPLOTTEDASAFUNCTIONOFNUMBEROFREVOLUTIONSDOTTEDLINESCORRESPONDTOEXPERIMENTSINTHEBLENDER1,WHILESOLIDLINESREPRESENTDATAPOINTSFROMTHEBLENDER2河南理工大学万方科技学院本科毕业论文10FIG7FIG7CURVESFORSIDESIDELOADINGEXPERIMENTSWITH60FILLLEVELRSDISPLOTTEDASAFUNCTIONOFNUMBEROFREVOLUTIONSDOTTEDLINESCORRESPONDTOEXPERIMENTSINTHEWHILESOLIDLINESREPRESENTDATAPOINTSFROMTHE2SUBSEQUENTLY,EXPERIMENTSWEREPERFORMEDUSINGTHEBLENDER2ATTHREEROTATIONSPEEDS15RPM,20RPMAND30RPM,ANDASEXPLAINEDBEFORE,THECORRESPONDINGSPINNINGSPEEDSWERE75RPM,10RPMAND15RPMFILLLEVELCONSIDEREDFORBOTHSIDESIDEANDTOPBOTTOMLOADINGWAS60AGAIN,ITWASOBSERVEDTHATVARYINGROTATIONANDSPINNINGSPEEDSDIDNOTMAKEMUCHDIFFERENCEINMIXINGRATEASSHOWNINFIG6ANDFIG7,MIXINGCURVESFORBLENDER2VARYONLYSLIGHTLYWITHROTATIONSPEEDFORTHETOPBOTTOMLOADINGPATTERNITAPPEARSTHATMIXINGIMPROVESSLIGHTLYWHENROTATIONSPEEDISINCREASEDTHEPLATEAUISSLIGHTLYLOWERFORHIGHERROTATIONSPEEDS,INDICATINGANIMPROVEMENTINTHELEVELSOFASYMPTOTICHOMOGENEITY,BUTNOSIGNIFICANTCHANGESWITHSPEEDAREOBSERVEDINSIDESIDELOADINGPATTERNTHEBLENDINGPERFORMANCEOFBOTHBLENDERSISCOMPAREDATDIFFERENTROTATIONSPEEDSFORBOTHSIDESIDEANDTOPBOTTOMLOADINGPATTERNSTOMAKEAFAIRCOMPARISON,THEFILLLEVELWASKEPTAS60FORBOTHBLENDERS,ACONDITIONFORWHICHBOTHBLENDERSACHIEVEEFFECTIVEMIXINGATLONGENOUGHTIMESDUETOGEOMETRICSIMILARITYOFTHETWOBLENDERS,THISCOMPARISONHELPEVALUATETHEEFFECTOFSPINROTATIONWITHRESPECTTOTHECENTRALSYMMETRYAXISONMIXINGPERFORMANCEASSHOWNINFIG6,THEMIXINGCURVESFORTHEBLENDER2LIEBELOWTHOSEFORTHEBLENDER1FOREACHROTATIONRATE,INDICATINGFASTERMIXINGNOTETHATTHEFINALRSDASYMPTOTE河南理工大学万方科技学院本科毕业论文11REACHEDFORBOTHBLENDERSISALSODIFFERENT,WITHTHEBLENDER2SHOWINGALOWERASYMPTOTEBETTERFINALMIXEDSTATE,PRESUMABLYDUETOALESSEREFFECTOFTHESLOWMIXINGMODEINTHEHORIZONTALDIRECTIONTHANBLENDER1SIMILARRESULTSWEREOBTAINEDFORTHESIDESIDELOADINGPATTERN,ASDISPLAYEDINFIG7THERSDCURVESFORTHEBLENDER1FORALLTHETHREEROTATIONRATESLIEABOVETHEBLENDER2ITISTHEREFORECONFIRMEDTHATSPINNINGABLENDERINDIRECTIONPERPENDICULARTOTHEROTATIONAXISHELPSINENHANCINGMIXTUREHOMOGENEITYHOWEVER,FORTHEMATERIALSEXAMINEDHERE,THEROTATIONRATEDOESNOTHAVEMUCHEFFECTONMIXINGPERFORMANCEFINALLY,ACOMPARISONISMADEBETWEENTHETWOLOADINGPATTERNSFORBOTHBLENDERSAGAIN,TOACHIEVEAFAIRCOMPARISON,ALLEXPERIMENTSAREPERFORMEDAT15RPMAND60FILLLEVELASEVIDENTINFIG8,INBOTHBLENDERSTOPBOTTOMLOADINGGIVESAMORERAPIDDECAYOFTHERSD,INDICATINGFASTERHOMOGENIZATIONASCOMPAREDTOSIDESIDELOADINGPATTERNHOWEVER,FORBOTHLOADINGMODES,BLENDER2ACHIEVESFASTERHOMOGENIZATIONFIG8FIG8COMPARISONBETWEENTHEMIXINGCURVESOFTHEBLENDER2ANDTHEBLENDER1FORTOPBOTTOMANDSIDESIDELOADINGPATTERNDOTTEDLINESCORRESPONDTOEXPERIMENTSINTHEBLENDER1,WHILESOLIDLINESREPRESENTDATAPOINTSFROMTHEBLENDER2EXPERIMENTSAREPERFORMEDAT15RPMWITH60FILLLEVELASREPORTEDINPREVIOUSSTUDIES,ALLTHERSDCURVESINTHISPAPEREXHIBITACOMMONTRENDWITHRESPECTTOTIME,CHARACTERIZEDBYANINITIALPERIODOFRAPIDHOMOGENIZATIONDUETOCONVECTIVEMIXING,FOLLOWEDBYAPERIODOFMUCHSLOWERHOMOGENIZATIONTYPICALLYCONTROLLEDBYDISPERSIONORSHEARTHISTRENDISSHOWNSCHEMATICALLYINFIG9THEFIRSTREGIMEISAFASTEXPONENTIALDECAYANDTHESECONDONE河南理工大学万方科技学院本科毕业论文12ISASLOWEXPONENTIALASYMPTOTETOALIMITINGPLATEAUTHEFIRSTPARTREPRESENTSARAPIDREDUCTIONINHETEROGENEITYDRIVENBYTHEBULKFLOWCONVECTIONTHESLOPEOFTHERSDCURVE,INSEMILOGARITHMICCOORDINATES,ISTHECONVECTIVEMIXINGRATETHESECONDPARTISDRIVENBYINDIVIDUALPARTICLEMOTIONDISPERSIONORBYTHESLOWEROSIONOFAPIAGGLOMERATESDUETOSHEARFIG9FIG9ATYPICALMIXINGPLOT,WITHRSDPLOTTEDAGAINSTNUMBEROFREVOLUTIONSTHETWOSOLIDLINESEMPHASIZEONTHETWODISTINCTIVEMIXINGREGIMESWHENONLYONEMIXINGMECHANISMISPRESENTASITUATIONTHATCANBEACHIEVEDBYCAREFULCONTROLOFTHEINITIALLOADINGPATTERN,ASIMPLEMASSTRANSFERMODEL,REPRESENTEDINEQ1CANBEUSED,ASINPASTSTUDIES14,TOCAPTURETHEEVOLUTIONOFTHERSDINPOWDERSYSTEMSINTHISMODEL,ANEXPONENTIALCURVEDECAYINGTOWARDSAPLATEAUISFITTEDTOTHEMIXINGCURVES,WHEREISTHESTANDARDDEVIATION,THEFINALSTANDARDDEVIATION,AISANINTEGRATIONCONSTANT,SIGNIFIESTHEMIXINGRATECONSTANT,ANDNISTHENUMBEROFREVOLUTIONSTHISMODELPREDICTSTHATTHEEXPERIMENTALVARIANCEWILLDECAYEXPONENTIALLYWITHTIMEASITAPPROACHESTHERANDOMMIXTURESTATEINORDERTOCHARACTERIZENUMERICALLYTHE“MIXINGRATE,”HASTOBECOMPUTEDFOREACHBLENDINGEXPERIMENTAENTHEVALUESFORPARAMETERSAANDARECALCULATEDBYMINIMIZINGTHESUMOFSQUARESOFERRORSBETWEENTHEDATAANDANEXPONENTIALFUNCTION河南理工大学万方科技学院本科毕业论文13THEVALUEOFFINALSTANDARDDEVIATIONISTAKENASTHELOWESTVALUEOFTHEVARIANCEACHIEVEDINTHEMIXINGSTUDIESTHEVALUESFORARECOMPUTEDFORBLENDINGEXPERIMENTSWITHDIFFERENTPERCENTAGEFILL,ANDLOADINGPATTERNANDTHERESULTSAREPLOTTEDINFIG10ANDFIG11ASSHOWNINFIG10,THEMIXINGRATECONSTANTDECREASESWITHINCREASEINPERCENTAGEFILLLEVELABROADERCOMPARISONWITHTWOOTHERBINBLENDERSISPROVIDEDINFIG11,WHICHDISPLAYSTHEMIXINGRATEFORTHEBLENDER2,FORTHEBLENDER1WITHANDWITHOUTBAFFLES,ANDFORACOMMERCIALLYAVAILABLERECTANGULARBLENDERTHEFIGUREALSOILLUSTRATESTHEEFFECTOFLOADINGPATTERNONTHESEFOURBINBLENDERS,ALLOFTHEMROTATEDAT20RPMITISEVIDENTTHATBLENDER2WITHDUALAXISOFROTATIONHASTHEHIGHESTMIXINGRATECONSTANTOFTHEENTIREGROUPFORALLBLENDERSUSEDINTHISSTUDY,THEREISALSOANEFFECTOFLOADINGPATTERNONMIXINGITWASFOUNDTHATTOPBOTTOMLOADINGPATTERNGIVESBETTERMIXINGPERFORMANCETHANSIDESIDELOADINGFIG10FIG10MIXINGPERFORMANCEWASEVALUATEDATTHREEDIFFERENTFILLLEVELSFORBLENDER2EXPERIMENTSWEREPERFORMEDAT60,70AND80FILLLEVELSAT15RPMWITHTOPBOTTOMLOADINGMIXINGRATECONSTANTVALUESISPLOTTEDASAFUNCTIONOFFILLLEVELANDFOUNDTOINCREASEWITHDECREASEINFILLLEVELFIG11河南理工大学万方科技学院本科毕业论文14FIG11MIXINGPERFORMANCEOFBINBLENDERSALONGWITHLOADINGPATTERNARECOMPAREDAT20RPMWITH60FILLLEVELMIXINGRATECONSTANTVALUESPLOTTEDFORDIFFERENTLOADINGPATTERNSINBINBLENDERSWITHANDWITHOUTBAFFLEANDASSHOWNABOVE,BLENDER2GIVERSABETTERMIXINGPERFORMANCEASCOMPAREDTOBLENDER