Toshiro Miyahara

Yasuharu Akagi

Yuji Ymada

アカギ ヤスハル

ミヤハラ トシロウ

ヤマダ ユウジ

宮原 敏郎

山田 裕史

赤木 靖春

宮原, 敏郎

ミヤハラ, トシロウ

Miyahara, Toshiro

山田, 裕史

ヤマダ, ユウジ

Yamada, Yuji

赤木, 靖春

アカギ, ヤスハル

Akagi, Yasuharu

AROUS Academic Repository of Okayama University of Science / 岡山理科大学学術リポジトリ

ＴＨＥＢＵＬＬＥＴＩＮＯＦＯＫＡＹＡＭＡＵＮＩＶＥＲＳＩＴＹＯＦＳＣＩＥＮＣＥＮｏ､３６App211-216(2000）Ｅ定fCcto丘ParticleSizeonFiltrationResistanceinCrossflowMicrOnltrationToshiroMIYAHARA,YlljiYAMADAandYasuharuAKAGIDepα'･ｍｅ"rqn1pp/jedCﾉbe"z肋ｙＦｎｃＬｌ/bWE昭j"eermgO“)'α､α助加αＭ)WScje"ceI-1,Ｒ蜘卜cﾉｶ０，Olhzyama700-000ユノヒＷ〃（ReceivedNovemberl，2000）K2yWDMs:SolidLiquidSeparation,CrossnowMicrofiltration,FiltrationResistance,SubmicronParticle,OvermicronParticleExperimentswerecarriedouttoinvestigatetheeffCctofparticlesizeonmtrationresistanceincrossflowmicrofiltrationbyvaryingtheparticlesizefrom０．１９脚、ｔｏ17.1〃mwhichcorrespondedtoso-calledsubmicromandovermicronparticles・FiltrationresistancecanbecalculatedfromDarcy,slawusingtimecourseresultsoffiltrationfluxundervariousoperatingconditions･Fromtheseresults,threeempiricalcorrelationequationsfbrthefUtrationresistanceofthecakelayerareobtaineddependingupontherangeofparticlesizes・Steadyandunsteadyfiltrationnuxｓｔａｔｅｓｃａｎｂｅｅstimatedusingthesethreeempiricalcorrelationequations．IntroductionCrossnowmicrofiltrationisarelativelynewprocessofgrowingimportancewhichallowsseparationofsmallparticlcsathigherpermeatenuxesthanconventionaldcad-endfiltration・Intheprocess，thefluidstreamflowstangentiallytothemembranesurfacc；theshearingactionofthefluidpreventsthedevelopmentofthickfiltercakesatthemcmbranesurface・Primaryusesforthistcchnologyincludeclarificationoffmitjuices，treatmcntofindustrialwastewater，andconcentrationofmaterialssuchasfermenterbroths，especiallyasolid-liquidseparationtechniqueinthedownstreamprocessingofbio-productsfrommicrobialsources（NakanishiandTanaka，1994;TanakaelIaL，1994)．Recently,thistechnologyhasalsobeenappliedtotheseparationofoilywater（Muellererα/､，1997)．Whileitisgenerallyacceptedthattheshearstressassociatedwithtangentialnowisresponsiblcforkeepingcakegrowthtoaminimum,ｔｈｅshearactionisnotclcarlydefined（BlakeaqL，1992;Nassehi，1198;ChellamandWiesner，1998;ＨｗａｎｇｅＭﾉ.，1996;IritaniaaJ.，1991;StamatakisandTien,1993;WangeMJ.,1995)．Inthepresentstudy，theeffectofparticlesizeonfiltrationresistanceincrossnowmicrofiltrationforfour kindstheseparationofofpolymcthylmethacrylate（ＰＭＭＡ）particlesandtwokindsofpolystyrene（PS）particlcswasinvestigated・ThefiltrationresistanccincrossflowmicrofiltrationwascalculatedfromDarcy，slawusingtimecourseresultsof‐filtrationfluxandthrceempiricalcorrelationequationsforthefiltraUonresistanceofthecakelayerobtainedaccordingtotherangeofparticlesizes・Furthermorc，steadyandunstcadyfiltrationfluxstateswereprcdictedusingthreeempiricalcorrelationequationsforthetestedsamples，LExperimentalAschematicdiagramofthccrossnowmicrofiltrationsystemisshowninFi9.1．ItisFiItrationp旧sswe=39.2-156.8ｋＰａＣのss-fIowveIocity=0.28-1.11ｍ/ｓ３】Ｋｒ刀②■Ⅱ」r⑨目星Ⅲ、弓ｎｎＩｕｎＦFig.１Schematicdiagramofcxperimentalapparatus212 ToshiroMIYAHARA,YUjiYAMADAandYasuharuAKAGIボー⑪凶⑪ロ⑩君野のＥ呵昌⑪⑪のMp-1451ＭＲ１０００ＭＰ､1400ＭX･500ＳＧＲ７０ＣﾛﾛF10w(0.5cｍ n㎡Ｂｏｎ田nＦｂ－ＦｏｒＢＢＩｚＢｕ 9９goFeedinIet仁◇FeedoutIet こ○毎。⑪廷柄寓戸巨。Ｅ①夛負ロヨＥ。。5０ⅡＶ lateく＝Filt厄teoutIet ００５２１FiItrataJ回０．１ 0.5１ｄｐｌＬｍ］５１０Fig.２Crossflowmicrofiltrationmodulccomprisedofafeedcirculationsystem，acrossnowfiltrationmoduleandacomputersystemtomeasurethefiltrａｔｅＦｉｇｕｒｅ２ｓｈｏｗｓｔｈｅａｓｓｅｍｂｌｙｏｆｔｈemoduleTY1emodulewasconstructedwiththreeassemblies（Ａ，ＢａｎｄＣ)．ThefeedsolutionwaspumpedintothenowchannelthroughthcAandBassemblies・Thedimensionsoftheflowchannelwere:ｄｅｐｔｈ５ｎⅢn,width5cmandlength35clnAnuclepoｒｅｍｅｍｂｒａｎｅｗｉｔｈａｐｏｒｅｓｉｚｅｏｆＯ２〃ｍ(Polycarbonate，NolnuraMicroScienceCo.，Ｌｔｄ）wassetonthebronzcsupportofaporoｕｓｐｌａｔｃＴｈｅｅffectivemembraneareaforthefiltｒａｔｅｗａｓ７５ｃｍ２、Thecrossflowvelocity，〃，ｗａｓｖａｒｉｅｄｆｒｏｍＯ､２８ｔｏＬ１１ｍ/s、Thefiltrationpressure，△Ｐ，wasvariedintherangeof39､Ｚ－１５６８ｋＰａ・TheconcentrationofthesuspensionsrangedfromO15kg/ｍ３ｔｏＬ５０ｋｇ/ｍ3．ＦｏｕｒｋｉｎｄｓｏｆＰＭＭＡｐａｒｔｉｃｌｃｓａｎｄｔｗｏkｉｎｄｓｏｆＰＳｐａｒticleswcreusedasshowninTablelTTleparticlesizeinTablelwasevaluatedusingaparticlesizeinstruｍｅｎｔ（modelELS-80R，OtsukaElectronicsCo.)andanopticalmicroscopeFig.３ParticlesizcdistributionprovidesasatisfactoryreprescntationofthemeasureddistributionThereforc，theparticlesizedistribution雛;:職臘;:繍搬淵習･塞灘鯛…-歳扉仰|響。(1)Twoparametersarerequiredtodeterminethemeanparticlesize,ｔｈａｔｉｓ，‘！ｐｃａｎｄｓｃ・Thcycanbeobtainedfromthedataas`,G=(`,rdp2…`")''〃 (２）andTablelCharacteristicsofparticlesemployedinthisstudy …[Ｚ{mcwh]Ⅲ (3)DensiIy[kgm3］voIumelrlcmBandIamBterUJLm］RemarksParticIeWhere`jpcisthegeomctricmeandiamctcrandscisthegeometricstandarddeviationTY1erelationshipbctween‘ljianddhcofalog-normalprobabilitydistributionis(MugeleandEvance,1959）0.190.480.864.071１８３１１８３１１８３１１８３MP-1451MP-1000MP-1400MX-500PoIymeIyImethacryIate(PMMA）功F`,cexp{(ﾉ+i)(皿.)2/2｝（４）1２．０１７．１ 1０５０１０５０ＳＧＰ－７０ＣＳＧＰ１００Ｃ PoIyslyrene(PS）ITlevolumetricmeandiameterofeachparticleemployed,d3o,canbecalculatedusingEqs．(2)，（３）and(4)．ＴｈｅｒｅｓｕｌｔｓａｒｅａｌｓｏｓｈｏｗｎｉｎＴａｂｌｅＬDistilledwaterwasusedtosuspendtheseparticlcs．Figure3showsparticlesizcdistributiononlog-normalprobabilitydistributionplots、Asshowninthisfigure，forallkindsofparticles，thelinearitysuggcststhatthelog-normalprobabilityfunction 2.ResultsandDiscussion2･lTimecourseoffiltrationfluxEffectofParticleSizeonFiltrationResistanceinCrossflowMicrofiltration 2130.0004Ｆｉｇｕｒｅ４ｓｈｏｗｓｔｈｅｄａｔａｆｏｒｔｈｅｔｉｍｅｃourseoffiltrationnuxunderallconditionsinthisstudy・Asteadystatewasrcachedwhenthefiltrationnuxrcmainedconstant・Ａｓｓｈｏｗｎｉｎｔｈｉｓｆｉｇｕｒｅ，thesteadystateforeachoperatingconditionwasreachedwithinaround4hours・TherefOre，themeasuringtimcforfiltrationfluxwassetwithin4hours．0．０００３皆００００２つ0．０００３ 0．０００１△PmIMA,ＰＳ,－－□ ＡＰ=39.2-156.8kＰａｕ=0.28-1.11ｍ/ｓ ００ 3600'晏毛=::柵ｌＷｌ蕊7200 1０８００0．０００２(a）［豊弓 0．０００４４hours ＰＳＡＰ＝117.6ｋＰａＣ=0.45kg/ｍ３ｄｐ=１２．０１A、鵬砿岫疵８５３１２５８１瓠幻釦司ｕｕｕｕロｏ△◇0.0001 鷺 ０．０００３￣（ＤＥＣ､０００２－つ｡:Ｉ菫，､｡０ ０３６００７２００１０８００１４４００１８０００ｔ[s］ ０．０００１Fig.４Timecourseoffiltrationflux００ 3600 ７２００１０８００14400ｔ[s］Figure5(a)ａｎｄ５(b)showexamplesoftheeffectofcrossnowvelocity,Lu,onthefiltrationnux,LforPMMAandPSparticlesuspensionsThescfiguresshowthatthereisasmalleffectofcrossflowvelocityinincreasingthefiltrationnux，Ｊ、However，theeffectofcrossflowvelocityfoｒｔｈｅＰＩＶｎⅦAsuspensionwaslargecomparedtothatforthePSsuspension、TY1isindicatesthatthecakelayerofthePSparticles(largeparticleinsize)ishardtoremovebyshearforccinducedbycrossflowThecffectsoffiltrationpressure，△Ｐ，onfiltrationnuxareshowninFig､６(a)(fOrPMMA)ａｎｄ6(b）（fOrPS)，respectively・Asshowninthesefigures,increasingthefiltrationpressureenhancesthefiltrationfluxandtheeffectwaslargeonthePIVnVIAsuspensionTY1iswasprobablyduetothesamemechanismastheeffectofcrossflowvelocityAsamatterofcourse，decreasingtheconcentrationofthesuspensionenhancedthefiltrationnux2.2FiltrationresistanceGenerally,thefiltrationflux,Ｊ,isgivenbyDarcy，slawas(Murkes,1990）(b）Fig.５EffCctofcrossflowvelocityonfiltrationfluxfiltrationresistanceofthecakelayer、Figure7showsthefiltrationresisｔａｎｃｅｏｆａｍｅｍｂｒａｎｅｉｎｔｈｅａｂｓｅｎｃｅｏｆparticles，ｔｈａｔｉｓ，inthecaseoffeedingdistilledwateronlyFromthisfigure，thefiltrationresistanceofthcmembraneliesinorderoflO8m-1・TY1efiltrationresistanceofthecakelayer,Ｒｃ，canbccalculatedfromEq.(5)usingthetimecourseoffiltrationfluxandtheresultsforthemembranefiltrationresistanccshowninFi9.7．Figure8(a)ａｎｄ8(b）showexamplesofthetimecourseofthecakelayerfiltrationrcsistancclnthesefigures,RcliesinorderofaroundlOl2m~1．Ｔｈｉｓｉｍpliesthatthccrossnowmicrofiltrationiscontrollingthcfiltrationrcsistanceofthecakelayer、2.3ＣorrelationofthecakelayerfiltrationresistanceAsmentionedabove，asthecrossnowmicrofiltrationinthisstudywascontrollingthefiltrationresistanceofthecakelayer・Ｔｈｕｓ，weobtainedthefollowingcorrelationequationsforRcwhichareshowninFi9.9．For必=019-086瓜、△Ｐノー－，u(R,"＋R`） (5)where必istheviscosityofliquid，Ｒ,〃isthefiltrationresistanceofthemembraneandRcisthe214 ToshiroMIYAHARA,YujiYAMADAandYasuharuAKAGI00004 1Ｘ1０１３ＡＰ=117.6kPa譲〆□ｕ=0.28ｍ/ｓ0．０００３ 1Ｘ1０１２［Ｅ夛一◎に￣芒０．０００２＝ lＸ１０１１Ｏｕ=0.55ｍ/ｓ△ｕ=0.83ｍ/Ｓ◇ｕ=1.11ＷＳ０．０００１1Ｘ1０１００3600７２００１０８００ｔ[s】（a）1ｘｌＯｏｌｘｌＯ１１ｘｌＯ２１ｘｌＯ３１ｘｌＯ４１ｘｌＯ５ｔ【s］（a）0．０００４ 1Ｘ1０１３ＰＳ￣ｕ=0.55,ＶＳＣ=0.45kg/ｍ３ｄｐ=１２．０１A、ロ△P=39.2kＰａｏ△P=78.4kPa△ＡＰ＝117.8kPa◇△P＝156.8kＰａＰＳ蹟Ujili;鹸鉾００００３ 1Ｘ1０１２量００００２つ 盲ミニロ区。ロ1ｘｌｏｌｌ 硴硴砿岫２５８１８５３１釦釦釦司ｕｕｕｕ□ｏ△◇０．０００１０ 1Ｘ1０１００３６００７２００１０８００14400ｔ[S】 1ｘ１０ｏｌｘｌＯ１１ｘｌＯ２１ｘｌＯ３１ｘｌＯ４１ｘｌＯ５ｔ【s］（b）(b）Fig.８EffectofcrossflowvclocityonthefiltrationresistanceofthecakelayerFig.６Effectoffiltrationpressureonfiltrationflux1ｘｌＯｌ３ＰＭＭＡ,ＰＳ△P=392-156.8kＰａｕ=0.28-1.11ｍ/Ｓｃ=015-1.50kg/ｍ３ｄｐ=0.19-17.11ｍ1.Ox1091Ｘ1０１２百ミニロに［Ｅ夛一Ｅ正 ｡;ニラ/』DistiIIedwaterMembraneporesizeＯ２Ｕｍ 1Ｘ1０１１ ０迄｡灘,/((且ｚｉ蝋揺Eq.(8)1Ｘ1０１０ｌｘｌＯ１２１ｘｌＯ１３１ｘｌＯ１４１ｘｌＯｌ５１ｘｌＯ１６１ｘｌＯｌ７１ｘｌＯｌ８１ｘｌＯｌ９ｔＡｐ1.34u･0.373ＣＯ､93.p-1.11Fig.９Correlationofthefiltrationresistanceofthecakelayer1.Ox108 ０３９．２７８．４１１７．６１５６．８ＡＰ[kPa］Fig.７FiltrationresistanceofthemembraneEffectofParticleSizeonFiltrationResistanceinCrossflowMicrofiltration 215Rc＝414x103im△po67``-o187CM65妬川（６）for処=407〃ｍＲｃ＝383×10-5凶pL34"~o373Cql3巧川（７）andfoml,=120-17.ＭｍＲｔ》＝2.87×104t05△po67L`-ol87Co465d戸川（８）1Ｘ1０－４の声．こ］｜ｐｏｌの「ItisinfelTedthatthescthreccquationsdependontherangeofsuspendedparticlesizcSUsually,particleslcssthanl似mshowcolloidalbehaviorandparticlesgreaterthanl必mhavesedimcntationbchavior・Ｅｑ.(7)ｆｏｒ必=407〃mshowsthcprobabletransitionbetweenthecolloidalandsedimentatioｎｂehaviors、2.4PredictionoffiltrationfluxintheunsteadystateFigurelOshowsthecomparisonofmeaSuredfiltrationnuxesinthcunsteadystatewiththecalculatedresultsusingEqs．(5)，(6)，（７）ａｎｄ(8)．Thecalculatedcurvesfitwcllwiththemeasurements．1Ｘ1０－５ｌｘｌＯ－５ １xlO-4JS-eXp[ＷＳ］Fig.’1Parityplotforfiltrationfluxinthesteadystatefiltrationresistanceincrossflowmicrofiltration，experimentswereconductedvaryingthcparticlesizefromO19tol7.’〃ｍ・Asaresult，thefollowingconclusionsweredraｗｎｌ)ThesteadystateinfiltraUonfluxisreachedwithin４hours2）Increasingthecrossflowvelocityandthcfiltrationpressure，anddecreasingtheconcentrationofthesuspensionenhancethefiltrationflux，3）ThecrossnowmicrofiltrationinthisstudycontrolledthefiltraUonresistanceofthecakelayer、4)Threeempiricalcorrclationequationsforthefiltrationresistanceofthecakelayerareobtaineddependingontherangeofparticlesizcs、5）BothsteadyandunsteadyfiltraUonfluxstatcscanbeestimatedusingtheseempiricalcorrelationequations．0．０００４ｍ、ｍ、ｍ２４８４菰引幻幻幻司、ｍ、ｍｍ卿岬噸卿廻幅叩帽循帽】圀團回国０．噸聴砿聴砿帥露顕串弱弱ｕ却却釦餉釦副帥帥帥牝帥一一一一一一［】一一⑬。。△ロ0.0003caIcu:００００２－つ秒鋤ロ０．０００１ ロ０ AcknowledgmentThisworkwassupportedbytheYakumoFoundationforEnvironmentalScience．0 3600 ７２００ 10800t[s］Fig.１０Comparisonofthecalculatedfiltrationnuxintheunsteadystatewithmeasurements NomenclatureC＝concentrationofsuspensi0,,ｋｇ/ｍ３必＝particlcdiameter,ｍｑｌｉ ＝generalmcanparticlediameter,、｡〉ｃ ＝geometricmeanparticlediameter,ｍｄ３Ｏ ＝volumetricmeanparticlediameter,ｍノ＝filtrationflux,ｍ/ｓＪ,."ノ ーcalculatedvalueoffiltrationfluxatsteadystate,ｍ/ｓＪ,."， ＝experimentalvalueoffiltrationnuxatsteadystate,ｍ/ｓ△Ｐ＝filtrationpressure,Ｐａ2.5PredictionofmtrationfluxinthesteadystateAsmentionedbefOre，thesteadystateforeachoperatingconditionwasreachedwithinarounｄ４ｈｏｕｒｓＦｉｇｕｒｅｌｌｓｈｏｗｓｔｈｅｐａｒｉｔｙｐlotforthefiltrationnuxinthesteadystateusingEq.(5)withRcvaluesaftcr4hours・ItshOwsgoodagreementwiththemeasurements．ConclusionToclarifytheinfluenceofparticlesizeonToshiroMIYAHARA,YujiYAMADAandYasuharuAKAGI216Mueller,Ｊ,,Ｙ鰯-ＷＣｅｎａｎｄＲＨ・Davies;``Crossnowmicrofiltrationofoilywater,，，.ＺＭＥ川６ｍ"ｅＳｃｊ.，１２９，221-235（1997）Mugele,Ｒ､Ａ・ａｎｄＨ､DEvance;“Ｄropletsizedistributioninsprays,，Ｗ１．.肋9.Che川.,43,1317‐１３２４(1951）Murkes,Ｉ;``Fundamentalsofcrossnowfiltration,，，ＳＧＰα'･qrjo"αＭＰＵ"-(/iicqrjoM化伽０６，１９，１－２９（1990）Nakanishi,Ｋ・andTTanaka;“Crossnowfiltrationofmicrobialsuspension,"ﾉVMppo"Sho伽j"ＫＤｇｙｏＧａＡｋａＭｊ,41,578-584(1994）Nassehi,Ｖ・;“ModelingofcombinedNavier-StokesandDarcyflowsincrossflowmembranefiltration,”。z川.Ｅ７ｚｇＳｃｊ.,53,1253-1265（1998）Stamatakis,Ｋ､ａｎｄＣ､Tie､;“Asimplemodelofcross-flowfiltrationbascdonparticleadhesion,，，ＡＩｄ２ＥＬ３９,1292-1302(1993）Tanaka,Ｔ､,Ｋ・Abe,Ｈ､Asakawa,Ｈ､YoshidaandK・Nakanishi;“Filtrationcharacteristicsandstructureofcakeincrossflowfiltrationofbacterialsuspension,”ノ$凡'”e"伽jo〃α"dBjoe"gj"eerj"8,78,455-461（1994）Ｗan9,Ｗ.,ＸＪｉａａｎｄＧ.Ａ､Davies;“Atheoreticalstudyoftransientcrossnowfiltrationusingforcebalanceanalysis,，,C71em.Ｅ'ｚｇノ.,60,55-62(1995）＝filtratiollresistanceofthecakclayer，１/ｍ＝filtrationresistanceofthemcmbrane，１/ｍ＝geometricstandarddeviation＝filtrationtime,ｓ＝crossnowvelocity,ｍ/ｓＣ〃、－ぬｎＫSＧｌｌＬｌ＝viscosityofliquid,Ｐａｓ〃ReferencesBlake,Ｎ､Ｊ､,１．Ｗ･CummingandMStreat；‘`Prcdictionofsteadystatecrossnowfiltrationusingaforcebalancemode１，，，ノｌＭＥ机blzu"ｅＳｃｊ.，68,205-216(1992）Chellam,Ｓ､ａｎｄＭＲ､Wiesner;“Evaluationofcrossnowfiltrationmodclsbasedonsheared‐induceddiffusionandparticleadhesion：Complicationsinducedbyfeedsuspensionpolydispersivity,，，.ﾉ1Ｍどれｂｍ"ｅＳｃｊ.,138,83-97（1998）Hwang,1,,.-J､ＣｈａｎｇａｎｄＣ－Ｈ・Chen;``Steadystatcpermcatcfluxforparticlecross-flowfiltration,，，C71e川.肋8.Ｊ.,61,171-178(1997）Iritani,Ｅ,Ｔ,HayashiandT､Murase;“Analysisoffiltrationmechanismofcrossnowupwardanddownwardultrafiltration,ＭＣｈｅｍ.肋８.ノヒ柳"，24,39-44(1991）

Effect of Particle Size on Filtration Resistance in Crossflow Microfiltration

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Effect of Particle Size on Filtration Resistance in Crossflow Microfiltration

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