Static mixers: Mechanisms, applications, and characterization methods – A review

Static mixers: Mechanisms, applications, and characterization methods – A review

Akram Ghanem

, Thierry Lemenand

, Dominique Della Valle

, Hassan Peerhossaini

aLUNAMUniversité,LaboratoiredeThermocinétiquedeNantes,CNRSUMR6607,44306Nantes,France

bONIRIS44322Nantes,France

cUnivParisDiderot,SorbonneParisCité,InstitutdesEnergiesdeDemain(IED),Paris,France

a bs t r a c t

Staticmixersandmultifunctionalheatexchangers/reactors(MHE/R)arequalifiedasefficientreceptaclesforpro- cessesincludingphysicalorchemicaltransformationsaccompaniedbyheattransferduetotheirhighproductivity andreducedenergyexpenditures.Thepresentworkreviewsrecentconceptualandtechnologicalinnovationsin passivestaticmixersandcontinuousin-linereactors.Currentindustrialapplicationsarediscussedfromaprocess intensificationperspective,focusingonmixingandmasstransferperformance.Typicalexperimentaltechniques employedtocharacterizeandquantifythemixingprocessareexplored.Theworkiscomplementedbyareviewof mixingfundamentals,knowledgeofwhichallowsthedevelopmentoftheoreticalmodelscrucialfortheanalysisof experimentaldata,likethechemicalprobemixingassessmentmethod.Consideringthedevelopmentofcontinuous flowequipmentinnumerousprocesses,advancesinthisfieldwillcertainlybeofincreasinginteresttothescientific andindustrialcommunities.

©2013TheInstitutionofChemicalEngineers.PublishedbyElsevierB.V.Allrightsreserved.

Keywords:Processintensification;Passivemixing;Staticmixer;Continuousmultifunctionalheatexchanger/reactor;

Mixingassessment

1. Introduction

Staticmixersandmultifunctionalheatexchangers/reactors (MHE/R) are being increasingly incorporated in process industries for their mixing and heat transfer capabilities.

Process intensification is a chemical engineering purpose that consists in seeking processes with higher productiv- ity, safer operating conditions, reduced waste production, andlowerenergyconsumption.Newapplicationsarebeing exploredandnewon-lineexchanger/reactordesignsarebeing developed offering several advantages compared to batch processingandmechanicallystirredvessels.Thesmallspace requirement, low equipment operation and maintenance costs,sharpresidencetimedistribution,improvedselectivity throughintensifiedmixingandisothermaloperation,byprod- uctreduction, and enhanced safety are the mainfeatures that have promoted the use of these devices in chemical,

∗ Correspondingauthor.Tel.:+33607533161.

E-mailaddress:[email protected](H.Peerhossaini).

Received16December2012;Receivedinrevisedform5May2013;Accepted15July2013

pharmaceutical,foodprocessing,polymersynthesis,pulpand paper, paintandresin,watertreatment, andpetrochemical industries(Anxionnazetal.,2008;Bayatetal.,2012;Ferrouillat etal.,2006a,b;Shietal.,2011;Thakuretal.,2003).

Characterizing mixing in industrial processes is an important issue for various economic and environmental considerations (Anxionnaz et al., 2008; Lobry et al., 2011;

Stankiewicz and Moulijn, 2000)since it governs byproduct effluents and consequently process efficiency. In addition, due to the wide range of applications of mixers and micro-structuredmixers,suchashomogenization,chemical reaction,dispersionandemulsification,andheatingorcooling processes, the mixing efficiencyinthese devicesis adeci- sivecriterionforoverallprocessperformance.Indeed,mixing affectsvariousprocessparametersincludingheatandmass transferrates,processoperatingtime,costandsafety,aswell asproductquality.

0263-8762/$–seefrontmatter©2013TheInstitutionofChemicalEngineers.PublishedbyElsevierB.V.Allrightsreserved.

http://dx.doi.org/10.1016/j.cherd.2013.07.013

gates are reduced in size by the turbulent cascade to the Kolmogorovscale,micromixing startsbyengulfment inthe smallestvortices;itisthenachievedintheviscous-convective subrangebylaminarstretchingandfolding,associatedwith thickness reductionbystriation, up to molecular diffusion atsub-Batchelorscalesthatrapidlydissipatestheconcentra- tionvariances(Batchelor,1953).Theturbulencemicro-scales aredirectlyrelatedtotheturbulenceenergydissipationrate ε(Hinze,1955;Lemenandetal.,2005;Streiffetal.,1997).In thissense,theKolmogorovscaleisakeyparameterforthe selectivityofchemicalreactionsintheturbulentregime,since thelimitingmechanismofthewholemixingprocessoccurs atthesmallerturbulencescale,hencegoverningspeciescon- tactatthemolecularscale,(BaldygaandBourne,1988,1989, 1999;BaldygaandPohorecki,1995;FalkandCommenge,2010;

Guichardonand Falk,2000;Komoriet al.,1991;Villermaux, 1986).

Qualitativeinvestigationofthemixingprocessusingopti- cal techniques can give valuable information on the flow hydrodynamics.However,understandingandquantifyingthe mixingmechanismisessential indesigningindustrialpro- cessesinvolvingfastreactionsthatcanpresentcharacteristic reactiontimessmallerthan thecharacteristicmixingtime.

Thisfundamental property of the turbulent field (Wallace, 2009) can be determined byclassical velocimetry methods suchaslaserDoppleranemometry,particleimagevelocime- try, or hot-wire anemometry, all of which give access, in three-dimensionalspace,tothecontributionsoftheturbulent energydissipationrate.Alternativemethodstocharacterize mixing based on observations of a chemical system have been recentlydeveloped,especiallybyBaldyga andBourne (1990), Bourne et al. (1992a,b), and Fournier et al. (1996a):

Villermaux–Dushmanreactionsortheiodide/iodatemethod (BaldygaandBourne,1989;Durandaletal.,2006;Dushman, 1904; Guichardon and Falk, 2000; Guichardon et al., 2000;

MohandKaci,2007;OatesandHarvey,2006;WheatandPosner, 2009).Thesetechniques,called“chemicalprobemethods”,are basedonthe competitionbetweenmixingand wellknown chemicalkineticsbythestraightforwardobservationofreac- tion selectivitythrough monitoring the secondary product concentrations.Underoptimalconditions,theslowestreac- tiontimeisequaltothemixingtime.Fromtheknowledgeof themechanism,kinetics,andstoichiometryofthechemical reaction,thelocalturbulentenergydissipationratecanreadily bederivedfromthemeasuredselectivitybyusingphenomen- ologicalmixingmodels(Bourneetal.,1992a;Fournieretal., 1996a;GuichardonandFalk,2000).

Thefollowingsectionspresentanoverviewofstaticmixers andmultifunctionalheatexchangers/reactors,theirapplica- tionsandmixingcapabilities.Thenmixingfundamentalsand experimental techniques developed for its assessment are

geometricalconstructionthatinfluencestheflowstructurein amannertopromotesecondarytransverseflowsthatenhance massandheattransferinthecross-section.Anothertypeof staticmixerconceptistheinsert-typeconfigurationinwhich thetypicaldesignisaseriesofidentical,stationaryinserts, calledelements,andthatcanbeinstalledinpipes,channels, orducts.Thepurposeoftheelementsistoredistributethe fluidinthedirectionstransversetothemainflow,theseare theradialandtangentialdirections.Staticmixersdivideand redistributestreamlinesinasequentialfashionusingonlythe pumpingenergyoftheflowingfluid.

Theinserts canbetailoredand optimized forparticular applicationsandflowregimes.Commercialdesignstypically usestandardvaluesforthevariousparametersthatprovide highperformancethroughouttherangeofpossibleapplica- tions.

Staticmixerswerenotwidelyusedintheprocessindus- trybeforethe1970s,althoughsomepatentsaremucholder.

A patent dating to 1874describes asingle-element, multi- layer motionless mixer used to mix gaseous fuel with air (Sutherland,1874);AnearlyFrenchpatentusedstaged/helical elementstopromotemixinginatube(LesConsommateurs dePetrole,1931),andanothershowsamulti-elementdesign forblendingsolids(Bakker,1949).Intheearly1950s,staged elements designedtopromoteheattransferwere patented (Lynn, 1958). Since then, major petrochemical companies made developmentefforts and presumablyusedtheir own designs,beforeanycommercialization(Stearns,1953;Tollar, 1966;Veasey,1968).

Therearemorethan2000U.S.patentsand8000literature articlesdescribingmotionlessmixersandtheirapplications (Thakuretal.,2003).Nowadays,staticmixershavebecome standardequipmentintheprocessindustry.Theyareusedin continuousprocessesasanalternativetoconventionalagita- tionsincesimilarandsometimesbetterperformancecanbe achievedwithlowercost.Motionlessmixerstypicallyexhibit lowerenergyconsumptionandreducedmaintenancerequire- mentsbecausetheydonotincludemovingparts.Theyrequire smaller space,lower equipment cost,and nopowerexcept pumping.Theycanprovidehomogenizationoffeedstreams witha minimumresidencetime andcan bemanufactured from mostmaterialsofconstruction soastomeet various standardsandtoadaptwithharshworkingconditions.

However,stirredvesselsremainpowerfultoolsinprocess industryandfindvastapplicationsespeciallyforprocessing highly viscous products (Aubin and Xuereb, 2006; Cabaret etal.,2007).Numerousrecentstudiesinvestigatetheirhydro- dynamicswithNewtonianaswell asrheologically complex fluids (Alliet-Gaubert et al., 2006; Aubin et al., 2000, 2001;

Fangaryetal.,2000;Torréetal.,2007).Newimpellerandmixing vesselconfigurationsandinnovativeoperatingmethodsare

Fig.1–Stirred-tankreactorbatchmixing,(a)ModelVMC-100multishaftvacuummixer(RossEngineering,Inc.)and(b) advancedimpellerdesigns(Robbins&Myers,Inc.).

Fig.2–GreercoPipelineMixer(Chemineer,Inc.):ahybrid high-shearcontinuousin-linemixerwith

mechanically-drivenparts.

beingintroducedtoenhancetheirmixingefficiency, safety, andoverallproductivity(Aubinetal.,2006;Fentimanetal., 1998;Torréetal.,2008).Multishaftbatchmixers(Fig.1a)can simultaneouslycarryoutagitation,dispersion,andhigh-shear emulsificationoperations. Fig. 1(b)shows modern impeller designsoptimizedforspecificconsiderationsincludinghigh shearrequirement,energyefficiency,closeclearance, parti- clesizeconstraints,highviscosityandrheologicalsensitivity, foulingpotential,cleanability,interchangeability,andeaseof installation.

In addition, some processes require high productivities thatcannotbeprovidedbybatchmixers,togetherwithhigh shearinglevelsthatexceedthe capabilitiesofin-linestatic mixers.For thispurpose,hybridmixerdesignsthatcan be mountedin-lineandincorporatemechanically drivenparts havebeendeveloped(ChemineerInc.,2004).Fig.2showsthe GreercoPipelineMixer(Chemineer,Inc.)providingtheadvan- tagesofbothcontinuousandbatchprocessingfordemanding applications,thoughatgreatermanufacturingandoperating costs.

Commercial static mixers are of various types: open designs with helices (Helical Kenics (Chemineer, Inc.),...), open designs with blades or vortex generators (Low Pres- sure Drop (RossEngineering, Inc.),Custody Transfermixer (Komax Systems, Inc.), High-Efficiency Vortex (Chemineer, Inc.),...),corrugated-plates(SMV(Sulzer,Inc.),...),multi-layer designs(SMXandSMXL(Sulzer,Inc.),...),closeddesignswith channelsorholes (InterfacialSurfaceGenerator(RossEngi- neering,Inc.),...),ordesignsbasedonmetallicfoaminserts (Ferrouillat et al., 2006c), offset strip fins, or microstruc- turedparallelplates.Fig.3illustratessomeoftheavailable commercial designsand Table 1 lists the top static mixer manufacturers.

The applications of these devices can range from mix- ing of miscible fluids to interface generation between immiscible phases (high shear rate dispersive mixing), in additiontoheattransferoperationandthermalhomogeniza- tion.

Motionless inserts such as blades or corrugated plates inducechangesinthefluidstreamlines.Inserts withholes, channels, helicalelements, and oblique blades cause local accelerationandstretchingofthefluid.Theysplittheincom- ingfluidintolayersandthenrecombinethelayersinanew sequence. Multilayer designs with blades and baffles split the fluid in multiple layers. These various mixing actions cause distributive mixing, by convectionrather than diffu- sion;althoughtotheextentthatdistributivemixingishigh, diffusionisbetterabletoachievehomogeneityonamolec- ularscale.Thestriationthickness(Mohretal.,1957)isused toquantifydistributivemixinginlaminarflowsandtheRTD (residencetimedistribution)forbothlaminarandturbulent regimes.

At Reynolds numbers (based on the plain tube diame- ter) greater than afew hundreds, flowinstabilities leadto downstreamoscillationsandpseudorandombehavior.Even in creeping flow, mixing elements inseries asymptotically approachaconditionknownaschaoswherethedownstream locationofafluidelementbecomesessentiallyunpredictable basedonitsupstreamlocation.

Fig.3–Commerciallyavailablein-linestaticmixers.

Theindustrialapplicationthusgovernsthechoiceofthe device.Inthissense,laminarandturbulentflowsmustbedis- tinguishedbecausethebasicmixingmechanismsvarywidely betweenthetwoflowregimes.

2.1.1. Mixinginlaminarflows

Laminarflowsareencounteredinthecaseofhigh-viscosity fluids like in food, paint, dairy, cosmetic, polymer, adhe- sive, and detergent industries. The low levels of mixing

Table1–Commerciallyavailablestaticmixersandtheircorrespondingmanufacturers.

Manufacturer Staticmixermodels

Chemineer KM,HEV,KMX,KME,Thermogenizer,Ultratab,WVM

Sulzer SMF,SMN,SMR,SMRX,SMV,SMX,SMXL,SMI,KVM,CompaX

RossEngineering ISG,LPD,LLPD

KomaxSystems Komax,CustodyTransfer,OzoneMixer,GGM,FRP,ChannelMixer,TripleActionMixer

AlfaLaval ARTPlateReactor

WestfallManufacturing Model2800PlateTypeMixer

Fluitec CSE-XR

ZelenTech ZT-MX

WymbsEngineering HV,LV

Lightnin InlinerSeries45,InlinerSeries50

EMI Cleveland

BranandLuebbe N-form

Toray Hi-TorayMixer

Prematechnik PMR

UET Heliflo(Series,I,IIandIII)

Noritake N10,N16,N26,N60

Fig.4–SimulationsoflaminarmixingintwoSARconfigurations,(a)SAR-1and(b)SAR-2withnthenumberofsplitting andrecombinationsteps(Ghanemetal.,2013b).

inundisturbedlaminarflowhavetheobvious consequence of giving spatial non-homogeneities in composition. In low-Reynolds-numberflows, forviscosity orresidence-time purposes,itisnecessarytoprovidesolutionsbasedonkine- matic mixing through the primary flow topology, such as split-and-recombine reactors (SAR). The concept is based on passive liquid stream division, then rotation in bends ofopposite chiralities,and finallyrecombination,achieving stretching/folding following the baker’s transform. Mixing is efficiently ensured by diffusionwithout generating pro- hibitivepressuredrops.Fig.4illustratestheSARprinciplein twolaminatingmixerconfigurationsshowingthecreationof additionalintermaterialareawitheachstep,promotingfluid mixingbymoleculardiffusion(Ghanemetal.,2013b).

Conventional static mixersare designed tohomogenize the fluid by redistributing it in the radial and tangential directions.Undisturbedlaminarflowalsogivestemporalnon- homogeneitiesinthesensethatmoleculesleavingthetube atagiveninstanthaveenteredatdifferenttimes.Thesame fluidredistributionthatgivesspatialmixingalsogivestempo- ralmixing.Intheidealcaseofplugflow,enteringsegregated phaseswillbeuniformlyredistributedwhentheyleavethe mixer,andallthemoleculesleavingtogetherwillhaveentered together.Theextenttowhichactualstaticmixersarecloseto idealcanbecharacterizedusingtheresidencetimedistribu- tionfortemporalvariations(Castelainetal.,1997;Aubinetal., 2005)andusingthestriationthicknessdistributionforspatial variations(SokolovandBlumen,1991;Aubinetal.,2005).

Chaoticadvectionisaphenomenonthatcanbecreated inlaminarflowsbygeometricmodificationsofclassicalcon- figurations, for instance the alternation ofbend chiralities in simple ducts (Le Guer and Peerhossaini, 1991; Mokrani etal., 1997)inorder toobtain complex flowtrajectories in whichparticlesfollowradialandtangentialpathsthathave been shown to produce global enhancement of transport phenomena(Aref,1984;Jonesetal.,1989;Peerhossainietal., 1993;Carrière,2006).

2.1.2. Mixinginturbulentflows

Inturbulentflows,motionlessmixerspromoteturbulenceand generate intense radialmixing, even nearthe wall. When the turbulent regimecan beattained, eddy diffusion gives sufficientmixing formostindustrial processes. Mixerven- dorsoftenclaimthatstaticmixerscansignificantlyreduce contacttimeorincreaseheat transfercomparedtoaplain pipe.Thisenhancementismoreimportantforlaminarflow, andtherelativeintensificationdecreasesinturbulentregimes (Ghanemetal.,2013a).Itistrue,however,thatstaticmixers canincreasethe levelofturbulencewithout changingpipe diameterand flowrate,albeitwithahigher pressuredrop.

Inturbulentflows,motionlessmixersaregenerallyusedfor

process intensification.Thatis,theyallowthe sameopera- tions tobeperformedwithasomewhatsmaller,in-process inventory. Three important applications are gas mixing in theturbulentregimes,blendingofaqueoussolutionsintur- bulent flow, especially for water treatment, and blending ofpolymermelts orsolutions. They are alsousedasreac- tors,particularlyforpolymerizations.Thepresenceofinserts andperturbatorsusuallyproducesacomplexvortexsystem inwhichconcomitant phenomenasimultaneously enhance massand heattransfer. Anexample ofsuchsystem isthe High-EfficiencyVortexHEV(ChemineerInc.,1998)staticmixer andheatexchanger(Ghanemetal.,2013a;Lemenandetal., 2010).Similarly,Fig.5illustratesthedifferentmixingmecha- nismsintheKomaxTripleActionMixer.

2.1.3. Puremixinginindustrialapplications

Themostcommonuseofstaticmixersinindustryisinmix- ingofmisciblefluids.Twoormorefluidsorareactingmixture areblendedtoreduceandeveneliminateconcentrationgra- dients(Goldshmidetal.,1986),forexampletoincorporatethe enzymeinmilkinmakingyogurt.Staticmixerscanbeused forsolidblending,inwhichtheyarefedbygravity,andforthe blendingofparticulatesolidssuchascerealgrains,breadand cakemixes,andconcretecomponents(Baker,1991;Bakker, 1949).Sprayevaporation, gasmixingand gas/liquiddisper- sionlikeozonationofpotablewaterarecommonapplications inmodernindustry.Fig.6showsstaticmixerconfigurations commonlyusedingas-handlingprocessesthatprovideeffec- tivecontact,smallbubblesize,andglobalhomogeneitywith minimumlengthrequirement(seeFig.7).

Homogenization in laminar flows is another common process. Additives such as plasticizers and internal lubri- cants,stabilizers,colorants,fillersandflame retardantsare

Fig.5–Tripleactionmixer(KomaxSystems,Inc.)andthe associatedmixingmechanisms.

Fig.6–Staticmixerdesignsforhandlinggaseous-phasefluids.

Fig.7–Gas/liquiddispersionandcontactingexperiments,(a)SulzerSMV-typeelementsand(b)OzoneMixer(Komax Systems,Inc.).

commonlyblendedintopolymermelts.Thecompactadditive- dosing mixers shown in Fig. 8 provide efficient solutions formanypolymer-relatedprocessesand many otherappli- cations. Secondary fluids are injected into the main flow andrapidlymixedbyacombinationofvortexsheddingand shearzoneturbulence.Someofthemodelscanbeinstalled between pipe flanges and feature very small length and spacerequirements.Thetypicalcombinationofagearpump and motionless mixer replaces an extruder at the end of

apolymerizationline.Suchoperationsare closelylinkedto applicationsofthermalhomogenizationdiscussedlatersince thesamedevicesimultaneously homogenizesbothconcen- trationandtemperature.Motionlessmixersarealsousedto process glues(Schneideretal.,1988),andafamiliar house- holdapplicationistheuseofdisposablestaticmixerstoblend two-partepoxyresins.

Applications of static mixers in the food industry are numerous. Food products are typically highly viscous and

Fig.8–Compactstaticmixerswithadditive-dosingfeatureforsecondaryfluidinjection.

Fig.9–Insert-typestaticmixersadaptedforthefoodindustry.

non-Newtonian(Holdsworth,1993)andareusuallyprocessed inthelaminarregime.Cybulskiand Werner(1986)reported thatstaticmixersare usedtomixacids,juices,oils,bever- ages,chocolate,milkdrinks,orsaucesinfoodformulations.

Fig.9showssomestaticmixersadaptedforthefoodindustry.

Theirsurfacesareusuallyelectropolishedandtheyaremostly madefrom316stainlesssteelandhousedinsanitarytubings ofsimilarmaterials.

Waterclarificationandsludgetreatmentcanalsomakeuse ofthesedevices.Turbidityinpotablewateriscausedbysus- pendedsolidparticlesatlowconcentrations.Staticmixersare usedtodisperseaflocculatingagent,suchasalginate,asa firststepinclarification.Inthiscaseflowsareintheturbulent regime,butexcessiveshear,asmightbecausedbymechan- icalagitation,candamagetheflocculates,leadingtohigher consumptionoftheflocculatingagent.

2.1.4. Mixinginpresenceofchemicalreaction

Staticmixersare alsogood toolsformixinggasesandpre- vaporizedliquidfuelspriortoareaction.Indeed,thisisthe firstrecordeduseofastaticmixer(Sutherland,1874).Despite thehighdiffusivitiesofgases,mixturesdonotimmediately achievehomogeneityandadditionalmixingmaybeneeded forgoodcombustion.Increasingtheresidencetimeafterthe gaseshavebeenmeteredtogetherwillaccomplishtheneces- sarymixing,butthisalsoincreasesthein-processinventory andcanleadtosafetyproblemsintheeventofabackfire.

Additional active mixing is therefore required. Static mix- ersare oftenusedforpre-reactorfeedblendingtoimprove reactionyields.Baker(1991)discussedtheiruseinnitricacid production.Staticmixersplacedupstreamofareactortomix airwithammoniaincreasenitricacidyieldandeliminatehot spots that can damagethe costly platinum catalyst. Many chemical reactions involving gases can beimproved using staticmixers,suchasthoseformakingvinylchloride,ethyl- enedichloride,styrene,xyleneandmaleicanhydride(Baker, 1991).Staticmixershavebeenreportedtohavegreatpotential inreducingNOemissionincombustors(Braunetal.,1998).

Aconventionalapplicationofastaticmixerisfoundinthe nuclearindustrytoimprovesamplingandanalysisofcontam- inantsinanairflow(McFarlandetal.,1999).

Applicationsofstaticmixersinpolymerizationreactions havebeensuggested(Grace,1971;Phillipsetal.,1997).Sulzer designedapolystyreneprocessthatmakesextensiveuseof motionlessmixers,particularlyofthe SMRtype; Teinetal.

(1985)reportsomedetailsofthisprocess.Staticmixersare alsousedinpost-reactorsandindevolatilizationpre-heaters inotherpolystyreneprocesses.Anacademicstudyonstyrene polymerizationinastaticmixerreactorwasreportedbyYoon andChoi(1996).Fleuryetal.(1992)studiedthepolymerization ofmethyl methacrylatewhileBaker(1991),Khac Tienetal.

(1990), Myers et al.(1997), and Schott et al.(1975) describe theuseofmotionlessmixersinmakingpolystyrene,nylon, urethaneandsulfonatedcompounds.

Most of the applications concern highly exothermic polymerizations.However,themajorityofindustrialinstal- lations concern the reaction injection molding (RIM) of polyurethanes,forwhichthereactionismoderatelyexother- mic.CommercialRIMmachinesuse animpingementmixer followedbyastaticmixertoblendthereactivecomponents quickly(Kolodziejetal.,1982).AnacademicstudybyHoefsloot et al. (2001) treated polypropylene degradation in a static mixer-reactor.Othertypesofchemicalreactionscanbenefit from the useofstaticmixers. Areactiveextrusion process forglycol glucosidesynthesiscanbeimprovedusing static mixers(SubramanianandHann,1996).Anapplicationtothe lactasetreatmentofwholewheyhasbeenreported(Fauquex etal.,1984;Metzdorfetal.,1985),andLammersandBeenackers (1994) investigatedusing astatic mixer-reactor forproduc- ingstarchetherssuchashydroxypropylstarchforthefood andpulpandpaperindustry.GrafelmanandMeagher(1995) reportedliquefactionofstarchusingasingle-screwextruder andapost-extrusionstaticmixerreactor.Cultivationofatten- uatedhepatitisAvirusantigeninatitaniumstaticmixeris described byJunkeret al.(1994).Reactionapplicationssug- gestedforstaticmixersincludecrackingofheavyandcrude oils(Jurkias,1998)orthecontrolledhydrolysisofwheypro- teinsbytrypsin(Margotetal.,1998).

2.2. Heattransferinstaticmixers

Staticmixersconstituteapartofabroaderfamilyofdevices introducedaboveasmultifunctionalheatexchangers/reactors (MHE/R)inwhichmixing,chemicalreaction,andheattrans- fer can occur simultaneously in the same apparatus. Food processing productionlines oftenincorporatesuch devices forcooking, cooling,sterilization, orpasteurization offood products.Theyarealsousedforthermalregulationandheat injectionorevacuationincatalysisoresterificationprocesses orany otherapplicationsinwhichheattransferiscoupled withreaction.

Many traditional designs such as stirred tanks already involve heattransfergenerally atthevesselwall; however, inthesedevicesthereisoftenasignificantdistancebetween theheat-transferdeviceandthesiteofthechemicalreaction whereheatisgeneratedcausingconsiderablethermalnon- homogeneitieswithinthevesselmakingisothermaloperation difficult.Theaimoftheheatexchanger/reactor(HEXreactor) istoeliminatethis distancebysupplyingorremovingheat almostasrapidlyasitisabsorbedorgeneratedbythereaction.

One application is the traditional thermal homogeniza- tionand heattransferinheatexchangersinvolvingviscous

Fig.10–Commercialstaticmixersqualifyingasmultifunctionalheatexchangers/reactors.

fluids in the laminar regime, such as polymer solutions.

Static mixing elements canalso beused inturbulent flow toreducethe exchanger sizeand increasethe intensity of turbulentsystems.Theycanbeusedforhighlyexothermal chemical reactions where rapidheat evacuation is critical forsafetyreasons andproductquality(Phillipsetal.,1997).

Thesedevicesfunctionintwoways.Theyincreasethemetal tofluid surface area ina manneranalogous to the use of externally finned tubes. They also change the hydrodyna- micsbyredistributingtheflowwithinthetubecross-section, andthecombinationofeffectscansignificantlyincreaseheat transfercoefficients.Fig.10showssomestaticmixerconfigu- rationswithheattransfercapabilitiesthatthusqualifyasHEX reactors.

2.2.1. Thermalhomogenization

For an undisturbed laminar flow in a plain pipe, thermal diffusionisthe onlyheattransfermechanismintheradial direction. A great variety of motionless inserts have been usedtopromoteradialflowandthusreduceradialtemper- aturegradients inprocess fluids.One commonapplication

is the installation of a static mixer immediately down- streamfromascrewextruderinordertoobtainathermally homogeneouspolymermelt.Atypicalapplicationofthermal homogenizationisforfilmblowingorsheetextrusionbecause thermoplasticsrequireauniformtemperaturedistributionto eliminateposition-dependentvariationsintheproduct(Chen, 1975).Fig.11 isaschematicdiagramillustrating theuseof Sulzer SMVmixing elements ina through-air-drying(TAD) systemtoprovideuniformairtemperature,adecisivefactor infinalproductquality.

Schottetal.(1975)suggestedusingmotionlessmixersfor polyethylene,polypropylene,andpolystyreneprocessing,and such uses ofmotionless mixersin extrusion havebecome standard practice.Their mainpurposeisthermal homoge- nizationbut theycanalsoalleviatecompositiondifferences resulting from polymerblending and coloring.Theneedis primarilyforradialmixing,butflowpatternsinclassicextrud- ersproducepolymersthatlacktangentialsymmetry.Thus, sometangentialmixingisneededaswell,andthisisautomat- icallyprovidedbymostmotionlessmixers.Myersetal.(1997) reported applications in the turbulent regime to enhance

Fig.11–Schematicdiagramillustratingathrough-air-drying(TAD)systemincorporatingSulzerChemtechSMVmixing elements.

thermal homogenization. Some typical uses of static mix- ers/heatexchangersinthepolymerindustryinclude:

• heatingandcoolingofpolymerandpolymersolutions;

• heatingpolymersolutionspriortodevolatilization;

• coolingpolymermeltsbeforefillingplantstoavoidthermal damagetopackaging;

• meltviscosityadjustmentbytemperaturevariationforopti- malprocessconditions;

• coolingpolyestermeltsbetweenthereactorandthefiber spinningunit;and

• coolingpolymermeltsbeforegranulationtoraisethevis- cosity.

Mixingelementsaremostbeneficialindeeplaminarflow (IshikawaandKamiya,1994;Joshietal.,1995),andmostappli- cationshavebeeninthisarea.Literaturedescriptionsoftheir uselargelyconcernthereactiveflowscoveredinthenextsec- tion.Staticmixershaveadistinctadvantageoverplaintubes insuchapplicationsbecausetheyprovideamoreuniformres- idencetimedistribution.Ifinterestislimitedpurelytoheat transfer,insertsspecificallydesignedforthis purposeseem betterthangeneral-purposedevices(Habchietal.,2012a).The greatestinteresthasbeeninhelicaltwistedtapeandoffset stripfins(Bergles,1995).Thesedevicescanbeusedforturbu- lentflowandboilingheattransferaswellasforlaminarflow toimproveheattransfercoefficients.

2.2.2. Heattransferinpresenceofchemicalreactions Inadditiontothepolymerization,LammersandBeenackers (1994)suggestedusingacontinuoustubularreactorcontain- ingstaticmixerstoproducestarchethersforfoodandpulp.

Static mixers can be used in turbulent flow reactors, for examplein thecatalysttubes ofa reformerfurnace.Static insertsaresaidtoincreaseheattransfercoefficients,eliminate channelingwithinthe catalyst bed,avoid cocking, prevent catalyst deteriorationdue to hot spots and improve yield.

Applications tocondensation (Fanet al., 1978) and boiling heattransfer(AzerandLin,1980)havebeenreported.Another example isprovidedbyGoughand Rogers (1987),who dis- cussedthetreatmentofcoaltaroilresiduesusingstaticmixer heatexchangers.Theresiduescontainheat-sensitivepheno- liccompoundsthatcanreadilypolymerize.Similarresidues resultfromdistillatebottomsfromnaphthacrackingandcan eventuallyincludecarbonsolids.Thesefluidsarepreheated before being burned in a reducing atmosphere to pro- ducecarbonblack.Motionlessmixersarepotentialsolutions to many problems encountered in heat exchanger opera- tions.Incoolingprocesses,skinning duetoboundary-layer

solidificationmaybealleviatedduetothebetterradialmix- ing(Baker,1991).Foulinginreactivesystemsiscausedbylong residencetimesinthewallvicinityandhightemperaturedif- ferencesbetweenthewallandthebulkfluid.Crystallization, polymerizationorbiologicalgrowthmayoccur,andtheresult- ingfilmshavelowthermalconductivityandcausesignificant resistance to heat transfer. Gough and Rogers (1987) have shownthatstaticmixerscansignificantlyreducetheabove effects.

Furthermore, by integrating heat exchanger technology intothestaticmixercontinuousflow,high-ieldreactorsthat go beyondbatchreactorlimitations tomake possiblesafe, environmentallyfriendlyandcost-effectiveprocessintensifi- cationcanbedeveloped.Inmodernprocessingitisimportant thateachindividualmoleculebeexposedtoanidentical,care- fully controlled processingenvironment inorder toensure consistentproductpropertiesandhighproductivity.TheART PlateReactor(AlfaLaval)showninFig.12isanexampleofsuch devices;hereaserpentinechanneldesigncomprisingmultiple directionchangesprovidesuniformplugflowandresidence timedistribution.Highheattransfercapacityallowsoptimal thermalcontrolofexothermicreactions,improvingsafetyand productquality.

However,forprocessintensification,properoptimization shouldconsidertheoverallexpectedgain.Mixinginsertshave several significant disadvantages compared to plaintubes:

higher pressure drop, greater potentialfor fouling,relative difficultyofcleaningandgreatercost.Notethatthermaldiffu- sivitiesareseveralordersofmagnitudehigherthanmolecular diffusivities,sothatmostheattransferoperationsarefeasi- bleusingtubesofreasonablediameterandlengthandwith reasonableresidencetimes.Theuseofmixinginsertsisjus- tified when there is astrong needto minimize in-process inventory.Examplesincludetheneedtosuppressdetrimental reactionswhen theprocessmaterialisparticularlydanger- ousorexpensive.Fig.13depictssomeofthelarge-scalestatic mixerandheatexchangerapplicationswheretheequipment sizeintensifies thelosses and complicatesimplementation andmaintenance.

Thepresentstudyfocusesontheusageofthesedevices as staticmixers/reactors rather than heatexchangers. The following sectionintroduces the basicmixing mechanisms encounteredinthecorrespondingflows.

3. Mixing fundamentals

Mixing isa centralissuein processengineering and many industrialfields.Infact,thewayinwhichreagentsaremixed,

Fig.12–ARTPlateReactor37(AlfaLaval,AB),(a)globalview,(b)serpentineprocessplate,and(c)workingprinciple.

whetheratthereactorscale,affectedbytheflowstructures,or atmolecularscales,influencestheselectivityandhencethe productivityofreactions.

3.1. Energyanalysis

Tounderstandthemixingmechanismsthroughanenergetic approach,wedistinguishtwomechanismsbywhichenergy is dissipated inturbulent flow: the energy dissipation due toboundarylayersatthewallsandsurfacesofinserts,and theenergydissipationinthebulkfluid,thatistheregionof approximatelyhomogeneouscoreturbulence.Itisthissecond formofenergydissipationthatismostimportantindistribu- tivemixing (Goldshmid et al., 1986). Consider an unmixed feedstreamcontainingblackandwhiteliquid.Turbulencewill quicklyintermingletheinitiallyunmixedfeedanddisperse it downtothe size ofthesmallest eddies. Inconcept, the fluidinthesesmallesteddiesremainsblackorwhitebefore becoming graydue to moleculardiffusion. Thesize ofthe

smallesteddiesisproportionaltotheKolmogorovlengthscale, K:

K=

(1)

whereistheviscosity,isthedensity,andε¯isthepower dissipationperunitmassoffluid.Theweakdependenceon powerdissipation,whichistothe0.25power,meansthatK

variesoverarelativelynarrowrange,from5to50␮mforthe greatmajorityofindustrialprocesses.Ithappensthatthecon- stantofproportionalitybetweentheKolomogorovscaleand thesmallesteddysizeisoftheorderof1bydefinition.Given typicaldiffusioncoefficientsforlowviscosityfluids(thosefor whichturbulenceispossible),completemixingwilloccurin milliseconds.Exceptforveryfastreactions,thereactionrate willbegovernedbytheintrinsickineticsregardlessofmix- ingeffects.Thetotalpowerdissipation,ε,¯ isdividedintotwo

Fig.13–Large-scaleapplicationsofstaticmixerswithgaseousandliquidmedia.

parts:ε1intheboundaryregionandε2inthecoreregion(Eq.

(2)).

¯ε=ε1+ε2 (2)

Onlythesecondcontribution,ε2,enhancestherateoffast chemicalreactions.Theaimisthereforetoachieve highε2

valuesatalow pressure droplevel, which meansthat the ratioε2/¯εmustbehigh(Bourneetal.,1992b).Bourneandhis co-workers havedevised aset offast, competitive consec- utivereactions, theselectivityofwhichisverysensitive to mixingonthemolecularscale.Theyusedthesereactionsto showthatε¯ inaplainpipeisabout5W/kg,whileSMVand SMXLstaticmixerscangeneraterespectivelyabout800and 500W/kgwhenthefluidvelocityis2m/s.Forthesemixers,ε2

valuescalculatedbyBourneetal.(1992b)were33%and66%

oftheε¯valuesrespectively.ThisshowsthattheSMVmixer, whichusesacorrugated-platedesignandcausesthehighest pressuredrop,islessefficientforreactionenhancementthan theSMXLmixer,whichusesamultilayerdesign.

3.2. Mixingscales

Mixing,asaphysicalphenomenon,isacomplexprocess.For adeeper understanding, it is inevitable todistinguish and describesomesimplerstagesofmixing,namelymacromixing, mesomixing,andmicromixingillustratedinFig.14(Baldyga andBourne,1986,1992,1999;Fournieretal.,1996a).

3.2.1. Macromixing

Mixingonthescaleofthewholevesseliscalled“macromix- ing”. This determines the environment concentrations by convectingthefluidparticlesintheflowdomain.Themix- ingprocessdependsdirectlyonthetransferefficiencyofthe

“mean”flowatdifferentscales(BaldygaandBourne, 1999).

Macromixingconsistsinthedispersivecapacityoftheflow attheheatexchanger/reactorscale,andisgenerallycharac- terizedbytheresidencetimedistribution(RTD)methodasa signatureofvelocityfield uniformity(Castelainetal.,1997;

Habchi et al., 2009a;Villermaux, 1986). In fact, the RTD is directlyrelatedtotheglobalmotionoftheflowsinceitrep- resentsthetimethefluidparticlestaketomigratefromthe deviceinlettotheoutlet.Thislarge-scalemotion,causedby themeanflowvelocity,drivesthefluidparticlesbetweenhigh- and low-momentum regionsinthe heat exchanger/reactor volume,determiningthelarge-scaleconvectivetransfercalled macromixing.

The RTD sharpness, hence the macromixing, can be enhanced by generating a radial convective transfer, for instance longitudinalvortices(vortex generators) orbaffles thatperturbthefluidpath(Mutabazietal.,1989;Fiebig,1995;

PeerhossainiandBahri,1998;Ajakhetal.,1999;Toeetal.,2002;

Lemenandetal.,2003,2005;Momayezetal.,2004,2009,2010;

Ferrouillatetal.,2006a;MohandKacietal.,2010;Habchietal., 2010,2012b).

3.2.2. Mesomixing

Atthe intermediate scale,mesomixing reflectsthe coarse- scale turbulent exchange between the fresh feed and its surroundingsgovernedbytheturbulentfluctuations(Baldyga etal.,1995);afastchemicalreactionisusuallylocalizednear thefeedpoint,formingaplumeoffreshfeed.Thisplumeisat intermediatescalebetweenthemicromixingscaleandthatof thesystemorthereactor.Spatialevolutionoftheplumecan beidentifiedwiththeprocessofturbulentdiffusion.Another aspect of mesomixing is related to the inertial-convective processofdisintegrationoflargeeddies.Mixingbyinertial- convectivedisintegrationoflargeeddiesproceedswithoutany directeffectofmolecularmixing.However,thereisaneffect ofinertial-convectivemixingonthemicromixingprocess.

Fullyunderstandinganddescribingmesomixingisnota simple task. Several approaches can be adopted since the inertial-convectivemixingprocessdependsonvariousparam- eters including turbulent kinetic energyk, length scale of turbulent fluctuations L, and their combination inthe tur- bulent diffusivityD_t. Locally, it isalso sensitiveto specific operatingconditionslikepipediameter,ratiooffeedstream velocitytomeanvelocityofflowsurroundingthefeedpoint

Fig.14–Threedifferentmechanismsofthemixingprocessandtheircorrespondinglengthscales.

andeventualback-mixingintothefeedpipe(Baldygaetal., 1993).Twomechanismshavebeenproposed:aturbulentdis- persionmechanismandaninertial-convectivedisintegration mechanism. Further details can be found in Baldyga and Bourne(1999).

The simplest models (Pohorecki and Baldyga, 1983;

Villermaux and David, 1983) of inertial-convective mixing assumeerosivediminishing ofthe blobsoffreshfeed,fol- lowedbymicromixing.Inthemorecomplexmodels(Baldyga, 1989;BaldygaandBourne,1989;Baldygaetal.,1994),onlythe largeeddiesoftheinertial-convectivesubrangedeterminethe environmentformicromixing.

Intermediatestructures,whichcanbeturbulentcascade vorticesorfractalstructuresinachaoticlaminarflow(Aref, 1984; Habchi et al., 2009a,b; Jones et al., 1989; Lemenand and Peerhossaini, 2002; Muzzio et al., 1992), contribute to mesomixing.Inachaoticlaminarflow,thefractalstructures arecharacterizedbytheLyapunovexponent(Carrière,2006), whilein turbulent flows they can be characterizedby the TKEandtheReynoldsstrain-ratetensor(Habchietal.,2010;

MohandKacietal.,2009;Schäferetal.,1997).Mesomixingis thusbasicallygovernedbytheturbulentfluctuationsandthe randompathofthefluidparticlesexceptthemeanflow.Itis relatedtothemagnitudeofvelocityfluctuationsoftheeddies andthelengthscaleofthesefluctuations.Consequently,one of the simplest ways to capture the essential features of mesomixingistolinkit totheRMSofvelocityfluctuations ortheTKE,k(Habchietal.,2010):

k=1 2

u_iu_i (3)

3.2.3. Micromixing

Micromixing,thelastofthemixingstages,consistsofviscous- convectivedeformationoffluidelementsthatacceleratesthe aggregatesizereductionuptothediffusionscale(Baldygaand Bourne,1989).

The selectivity of chemical reactions depends on micromixing: how the reagents mix on the molecular scale (Baldyga and Bourne, 1999). This mechanism entails the engulfment and deformation of Kolmogorov micro- scaleeddiesand isthe limitingprocessinthereductionof localconcentration gradients. It can be characterizedby a micromixingtime thatisdirectly relatedtothe turbulence energydissipationrate(BaldygaandBourne,1999).Following

the Hinze and Kolmogorov theory, which is based on the ideaofenergycascade,thedropbreakupinmultiphaseflows can alsobe characterizedbythe turbulencekineticenergy dissipation rate(Hinze,1955; Lemenandet al., 2013;Streiff et al.,1997).Thus,anincreaseinturbulencekineticenergy dissipation favors the micromixingprocess, enhancing the selectivityoffastchemicalreactions andalsoreducing the maximum drop size in multiphaseflows. Thelocal turbu- lencekineticenergydissipationrate,ε,whichcanbeusedto quantifymicromixing,canberelatedtothestrainratetensor componentsby:

ε= 1 2

∂x_j+∂u_j

∂x_i

(4)

4. Methods to characterize mixing in continuous flows

Understanding and describing the degree of mixing is a crucialissue. Inaddition, process controlandoptimization sometimesnecessitateparameterization,measurement,and quantificationofmixing. Thisurgehas ledtothe develop- ment ofseveral qualitative and quantitative measurement techniquesthataresometimescase-specific;each ofwhich isadaptedtoacertaintypeofflow;someofthemhavebeen thesubjectofextensiveresearch,thelistofreferencescited hereafterisnotexhaustive.

4.1. Qualitativetechniques

Qualitativecharacterizationtechniquesaremostlyopticaland necessitatetransparentdevicesoratleastdeviceswithtrans- parentviewingwindows.Theinformationobtainedonmixing qualitycangiveanindirectapproximationofmixingtime.

4.1.1. Acid–baseorpHindicatorreactions

Thegenerationofcolorchangeinacid-basereactionsrelies onthepresenceofapHindicatorinthebasicoracidicsolu- tion.AnumberofdifferentpHindicatorshavebeenusedfor characterizingmixinginmicromixerslikemethylorange,bro- mothymolblue,andphenolphthalein.

Branebjergetal.(1995)estimatedamixingtimebyrecor- ding the time of color change. Kockmann et al. (2006) consideredamixinglengthdefinedasthedownstreamlength in the mixerwherecolor change was no longer visible.In thislatterstudy,mixingoftwofluidswasvisualizedwiththe

Fig.15–Flowvisualizationusingcoloreddyesindifferentstaticmixerconfigurations.

Fig.16–Photographsshowingacousticmicrostreamingvisualizationinamicrochamberatdifferenttimes,(a)0s,(b)28s, (c)67s,and(d)106s.

Source:Liuetal.(2002).

pH-indicatorbromothymolblueforgoodopticalcontrast.The redoxreactionofanalkalinesolutionofdi-sodiumhydrogen phosphate(pH8)withdeionizedwaterandbromothymolblue (pH7)resultedinamixturewithapHvalueof7.5,indicated byabluecolor.Theconcentrationofthereactantswasvery

lowtoavoidsignificantinfluenceonfluidproperties.Themix- ingtime,asdefinedinthiswork,indicatedwhenmixingwas complete.Thecolorchangeofthebromothymolbluesolution wasopticallyobservedtodeterminethemixinglength,where colorchangewasnolongervisible.Thisindicatedcomplete

Fig.17–LaminarmixingandhomogenizationefficiencyshownusingLaserInducedFluorescence(LIF),(a)SulzerSMXand (b)SulzerSMXplus.

4.1.2. Dilutionofcoloreddyes

Usingthismethod,concentratedsolutionsofcoloreddyeare contactedwith colorlesssolutionsor simplypure waterin thestudiedreactors.Fig.15 depictsthe visualevidencefor themixingprocessproducedindifferentcommercialdevices.

Mixing qualityand flowstructurescan beclearly observed atdifferentpositionsalongthemixer.Flowinstabilitiesand vorticescanalsobevisuallyspotted.

Suitableimagingtechniquesareneededtoaccompanythe developmentof transparentmicromixers. Themainissues are usually to achieve a simple, fast analysis rich in con- trastandcomplexininformationbasedonvisualinspection or microscopic imaging. Hessel et al. (2003) proposed an approachrelyingonaqueoussolutionswithhighconcentra- tionsofwaterblueandpurewater,whichwerefedthrough theinterdigitalmicromixers ofinterest.Theseblue-colored solutionsprovideexcellentcontrastduetohighdyesolubility andlargeextinctioncoefficient.Theyare,inparticular,suit- ableforimagingmultilaminatedsystemsarrangedparallelto thedirectionofobservationandmultiphasesystemssuchas gas/liquidandliquid/liquidflows.

Schönfeldetal.(2004)describedthismethodinwhichvisu- alizationofthe mixingprocess isconductedperpendicular totheflowdirection.Consequentlytheinformationobtained isspatiallyaveraged overthe micromixerdepth.Assuming alayerstructurethatishorizontalortiltedwithrespectto theobserver,itisdifficulttodistinguishperfectlymixedsys- temsfrom thecomplex multi-layeredmixingpatterns,and thisdifficultymayyieldoverlyshortmixingtimes.Another disadvantageofusingthewaterblueimagingisthat,dueto thelargemolecularweightofthisdye,itsdiffusioncertainly differsfromthatoflow-molecular-weightspecies.

Coloreddyesareappropriateforcharacterizingmixingin singleand two-phase systems. Thistechnique isalsouse- ful for monitoring the evolution of dynamic systems over timeoratdifferentprocesssteps.Fig.16illustratesthetran- sient evolution of the mixing process induced by acoustic microstreaminginamicrochamberbyusingacoloreddye.

4.1.3. Dilutionoffluorescentmaterials

Here,highenergylight(e.g.laser)isrequiredtoinducefluo- rescence,whichismonitoredusingfluorescencemicroscopy.

Typicalfluorescentmaterialsarefluoresceinandrhodamine B.

Usingconventionalmicroscopy,theresultinginformation isaveraged on the opticalaxis over the device depth.The method is associated with confocal scanning microscopy which enables point-wise measurement ofthe fluorescent dye through the depth of the micro device. Peerhossaini andWesfreid(1988)usedlaser-inducedfluorescence(LIF)for

Fig.18–Characterizationofdiffusivemixingbyfluorescent HydrodynamicFocusing(Knightetal.,1998).

visualizing,forthefirsttime,theGörtlervorticesembedded inaconcaveboundarylayer.Lemenandetal.(2003)usedthe sametechniqueforvisualizingthestreamwisevorticesgen- eratedbehindvortexgeneratorsinaHEVstaticmixer.Fig.17 illustratesthelaminarmixingprocessvisualizedbyLIFinthe SulzerSMXandSMX-plusconfigurations.

Afasteralternative toturbulent mixingistoreducethe lengthscaleoverwhichthefluidsmustdiffusivelymix.Knight etal.(1998)usedahydrodynamicfocusingtechniqueincorpo- ratingfluorescentspeciestocharacterizediffusivemixingina microfluidic,continuous-flowmixercapableofmixingtimes lessthan10msbymerediffusivelengthscalereduction.As showninFig.18,afluorescentdyelabelstheflowfromtheinlet channelandappearsbright,whilenonfluorescentbufferflows from thesidechannels. Thesideflowsqueezes,or “hydro- dynamicallyfocuses”,theinletflowintoathinstreamthat exitstheintersectionsheathedinbufferfluid.Atsuchsmall length scales,moleculesfrom the sideflow rapidly diffuse acrosstheinletstream,resultinginfastmixing.Fluidflowwas imagedusingstandardepifluorescenceandconfocalscanning microscopy.Inbothcases,theinletflowwaslabeledwiththe fluorescentdye5-carboxyfluorescein.

Johnsonetal.(2002)reportedusingfluorescenceimaging oftherhodaminedyethrougharesearchfluorescencemicro- scopeequippedwitha10×objective,amercuryarclamp,a rhodaminefilterset,andavideocamera.Theyalsoproposed elementarymixingquantificationthroughcalculationofthe percentageofmixedfluidusingEq.(5):

percentagemixed=

⎛

⎝

(1/N)

i=1(I_i−I^Perf.mix_i )²

(1/N)

i=1(I⁰_i −I^Perf.mix_i )²

⎞

⎠

whereN,I_i,I⁰_i,andI^Perf.mix_i arerespectivelythetotalnumber ofpixels,theintensityatpixeli,theintensityatpixeliifno mixingordiffusionweretooccur,andtheintensityoftheper- fectlymixedsolutionatpixeli.Theexperimentaldatafora perfectlymixedsolutionwereobtainedbyplacingthesame fluorescentbuffer,withhalfofthenormalrhodamineconcen- tration,inbothinletchannelsandthenapplyingthevarious electricfieldsunderinvestigation.

literaturetocharacterizeasplit-and-recombinemicromixeris thereductionofpotassiumpermanganateinalkalineethanol (Mensingeretal.,1995).

Anothertestreactionistheironrhodanidereaction,which hasbeenusedtocharacterizemixingininterdigitalmicromix- ers (Hessel et al., 2003). Mixing was recorded by digital recordingwithanopticalmicroscopeequippedwithavideo camera.Adefined illuminationwas establishedbyusing a light guide system with goosenecks. Equipment was cali- bratedforeachexperimentalrunwitheach mixerbyusing standarddyesolutionsofknownconcentration.Theimages ofbothcalibrationandexperimentalsolutionswereconverted togreyscaleformat.Therefore,theconcentrationdistribution wasgatheredbyanalyzingtheimagestakenwithfixedillu- minationwithimagesofthecalibrationsolutions,andthus concentrationprofiles alongthechannelcross-sectionwere obtained.

Differingfromtheclassicalcoloreddyedilutionandwater bluesolutions,theformationofthebrownishcomplexinthe ironrhodanidereactionpotentiallyprovidesinformationon fluidlayerformationbothattheverybeginningandduringthe courseofmixing.Theadvantageofthisreactionoverdilution- basedmethodsisthatthecoloredproductappearsonlyafter thereactantsare completelymixedatthemolecular scale.

Thisavoidsmeasurementerrorswithcomplexmulti-layered mixingpatternsortiltedlamellaethatareinherentinmost othervisualizationtechniques.

Thedrawbackinherentintheconventional imagingand microscopic techniques employed for visualization is that noinformationonthespatialmixingqualitythroughoutthe micromixerdepthcanbeobtained,whichcanleadtounder-or over-estimationofmixingtimesandlengths.Somereactions mayformasolidproduct,limitingtheiruseforcharacterizing micromixers.

Thelimitationsofanyonemethodcanbecompensatedfor byusingseveraltechniquestoexaminethesamecase.Inthis way,complementaryinformationcanbeobtainedfromeach technique,offeringabroaderviewonthecourseofmixing.For example,dilution-typeexperimentscanbecomplementedby reactivemethods.Fig.19showstheflowpatternsinasplit- and-recombinemixerobtainedbyusingthe dyewaterblue andthoserevealedbytheironrhodanidereaction.Comparing theresultshelpspointouttechnicalartifactsandpinpointthe realphysicalphenomenatakingplace.

4.2. Quantitativetechniques

Usingthesemethods,thecharacteristicmixingtimeislinked tosegregation levelsinareactive floworaflowcontaining chemicalspecieswhoseconcentrationsareinfluencedbythe mixingqualities.Theconcentrationsaremeasuredbyoptical techniques,andfollowingtheassociatedcase-specificphysi- calphenomena,themixingtimeiscalculatedusingphysical models.

One-dimensional profiles or two-dimensional maps of speciesconcentration,dependingonthemeasurementtech- niqueusedare obtainedtodetermineastriationthickness distribution, thus giving information about the scales of segregation.Forone-dimensionalconcentrationprofiles,the measurementisrepresentativeoftheconcentrationaveraged throughthe channelordevice depth.Itispertinentonlyif theflowstructureistwo-dimensionalandtheconcentrations are constant throughout the channel depth. Both typesof informationallowthecharacteristicfluidlamellaescaleinthe devicetobeidentified,whichinturncanberelatedtomixing time.

Thespeciesconcentrationistypicallydetectedusingpho- tometricandfluorescencemethods.Salmonetal.(2005)used Raman spectroscopy for the analysis of reaction–diffusion dynamics. ConfocalRaman imagingisanonintrusive tech- nique that can give the local concentrations of chemical speciesbyscanning asamplingvolumeofafewmicrome- tersinsizethroughouttheentiresystem.Ramanspectroscopy isroutinelyusedinchemicalanalysisandhasrecentlybeen coupledwithmicrofluidics.Salmonetal.(2005)analyzedinter- diffusion of pure liquids by coupling Raman imaging and microfluidics on quantitativegrounds. Raman spectra ata givenlocationinthemicrochannelwererecordedusingacon- focal Ramanmicroscope.Thesampleswere illuminatedby radiationfromanargon-ionlaser.Backscatteredlightwascol- lected bytheobjective,anda gratingdispersedthe Raman spectrumontoacharge-coupleddevice.Thelocalconcentra- tions ofthe fluidscould be probed from the intensitiesof nonoverlappingRamanbandsspecifictoeachliquid.Concen- trationmapswerethenobtainedusingx–ymicroactuatorsto displacethemicrochannelunderthemicroscopeobjective.

For photometric,fluorescence, andRaman (usingvisible light)detectiontechniques,thedevicemustbeopticallytrans- parent.Forinfrareddetection,thedevicemustbetransparent toinfraredradiationwavelengths.

4.2.2. Competingparallelreactions

This technique, namely the chemical probe, entails competitive-consecutive or competitive-parallel reactions, whicharebasedonthechemicalresultofthelocalinjection ofareagent instoichiometricdeficit inthemainflow.The principle istocarryout tworeactionsinparallel thatboth use a common reactant, which they compete for. One of thereactionsshouldbeveryfast(quasi-instantaneous)with characteristictimetr1,so thatit proceedsonlyif mixingis ideal (extremely rapid). The other reaction should be fast (butslowerthanthefirst)andtakesplacewhenthereisan excess ofthe common reactant, whenmixing is slow and non-ideal. The second reaction has characteristic time tr2

closetothemixingtimetm.Thelocalchemicalreactionthus results from a competition betweenmixing at microscales and the reaction kinetics. Quantitative informationcan be obtained on the yield of the secondary (slower) reaction.

Consequently, mixing performanceis characterized by the

Fig.19–Multi-laminationflowpatternsofasplit-and-recombinemixer,(a)dilution-typeexperimentusingthedyewater blueand(b)reaction-typeexperimentusingtheironrhodanidesystem(Schönfeldetal.,2004).

amountofsecondaryproductformed:thegreatertheyieldof thesecondaryreaction,thepoorerthemixingquality.

Nodirectinformationonmixingtimeisaccessibleandthe performancesofmixershavemostoftenbeencomparedon thebasis ofthe segregation indexXS,an indicatorofmix- ingquality.Inperfectmixing,thecommonreagentistotally consumedbythequasi-instantaneousreactionsothatXS=0.

Intotalsegregation,anoverconcentratedzoneoftheinjected commonreagentoccursandtheslowerreactioncanreactwith thiscommonreagent,sothatX_S=1,asshowninFig.21.The segregationindexcanberelatedfurthertothemixingtimeby usingphysicalmodels(BaldygaandBourne,1984,1989,1999;

Durandaletal.,2006;FalkandCommenge,2010;Fournieretal., 1996b).

Severaltypesofcompetingparallelreactionsystemshave beenreportedforthismethod.BaldygaandBourne(1990)first studiedthefactors determiningthe productdistributionof parallelreactionssuchasimperfectmixing, choiceofreac- tor,or sequence of reagent introduction.They carried out experimentsonthecompetitionforhydroxideionsbetween thereactionsofferrichydroxideprecipitationandthealka- linehydrolysisofethylchloroacetate.Inthesamework,the authors alsoreportedthe competitive nitrationofbenzene andtoluene.Othercompetingparallelreactionsystems,also basedonthealkalinehydrolysisreaction,werelaterproposed asmeansofcharacterizingmixingperformance.Bourneand Yu(1994)replacedtheFe³⁺usedbyBaldygaandBourne(1990) withH⁺.Brucatoetal.(2000)simulatedstirred-tankreactors throughcomputationalfluiddynamics,usingCu²⁺insteadof Fe³⁺. Computationalfluiddynamics andnumerical simula- tions(Fig.20)cangiveaccesstoqualitativeandquantitative informationconcerningmixingperformancethroughsimply followingparticletrajectories,byexaminingconcentrations orresidencetimedistributions,orevenbysimulatingcom- pletereactivesystems.Thepresentwork,however,focuseson theexperimentaltechniquesdevelopedinthefieldofmixing characterization.

Bourneetal.(1992a)alsoproposedusingthesimultaneous diazocouplingof1-and2-naptholwithdiazotizedsulfanilic

acid to characterize mixing. This is known as the second Bournereactionschemeandwasalsooriginallydevelopedfor studyingmicromixinginstirredtanks.Althoughthisreaction systemhasbeensuccessfullyappliedtocharacterizethemix- ersperformance(Ehlersetal.,2000),itisrelativelydifficultto usesinceitincorporatesfourconsecutivereactions.

Anothermethodisbasedontheprecipitationofbarium sulfatedevelopedbyBartholeetal.(1982),whichoffersthe advantageofusingnon-toxicandcheapreactants.However thereactiontimesarerelativelylong(oftheorderofseconds) making it difficult tocharacterize systems withgood mix- ingqualitieswheremixingtimesaremuchshorter(Mohand Kaci, 2007), which explains the preference for the Viller- maux/Dushmanmethod.

Thereactivesystem,knownastheVillermaux/Dushmanor theiodide/iodatemethodisbasedonatechniqueoriginally developed for the micromixing characterization in stirred tanks(Fournieretal.,1996a,b;GuichardonandFalk,2000)and has been the most commonlyused methodfor evaluating reactorperformance(AokiandMae,2006;Baccaretal.,2009;

Ehrfeldetal.,1999;FalkandCommenge,2010;Ferrouillatetal., 2006b;Keoschkerjanetal.,2004;Kockmannetal.,2006;Kölbl etal.,2008;MohandKaci,2007;Nagasawaetal.,2005;Panic etal.,2004;Schaeretal.,1999).

Thiscompeting-parallel-reactionschemicalprobemethod offersseveraladvantages:

• relativelysimplereactions;

• preciseknowledgeofthereactionmechanismandkinetics (Guichardonetal.,2000);

• product concentration accessible through simple spec- trophotometry;

• reactionratessufficientlyhighenablingshortmixingtime measurement;and

• better accuracy among other chemical probe methods (Durandaletal.,2006).

However,quantitativetreatmentoftheexperimentaldata requires a robust kinetic model. Comparison of published

Fig.20–Computationalfluiddynamics(CFD)asapowerfultoolformixinganalysis,(a)concentrationcontoursinthe ChemineerWVMpre-distributiontabconfigurationand(b)turbulentstreamlinesintheSulzerCompaXadditive-dosing mixer.

Fig.21–Schematicdiagramofthemicromixingprocessinthechemicalprobe.

models shows differences due to the sensitivity of the iodine-formingreactiontomixingconditions(ionicstrength, concentration, etc.). Theidealapproach isto re-determine thereactionkineticsusingthespecificparametersofthesys- temadoptedemployingmoderntechniquesforfastreactions (Bourne, 2008). Despite this fact, the Villermaux/Dushman methodforcharacterizingtheextentofmicromixingthrough examiningtheiodineyieldgivesqualitativelyconsistentand intelligibleresults. Withspecialattentiongiventothe uni- formity of reactive system characteristics, this method is suitable forranking different mixersor differentoperating conditions(Bourne,2008).Quantitativecomparisonofmixing timesmeasuredindifferentreactorconfigurationsusingdif- ferentmethodsremainsadelicateprocedurethatmusttake theaboveremarksintoconsideration.

5. Iodide/iodate chemical probe method

This chemical probe method, developedby Fournier et al.

(1996a,b)tostudypartialsegregationinstirredtanks,imple- ments asystem of parallel competing reactions producing iodine. The coupling of the borate neutralization and the Dushmanreactioninthis system allowsthemeasurement ofmixing efficiencyin reactors bymonitoring the amount of iodine produced. As mentioned before, this technique hasbeen extensively usedindifferent typesofreactors. A noveladaptiveprocedurerecentlydevelopedbytheauthors toimprovethereliabilityoftheiodide/iodatemethodwillbe presentedanddiscussed.

5.1. Chemicalsystemandmixingmodels

5.1.1. Iodide/iodatereactionsystem

In this method, borate neutralization (Eq. (6)) is quasi- instantaneous with characteristictime tr1; the second, the Dushmanreaction(Eq.(7))(Dushman,1904)isslowerandhas characteristictimet_r2 closetothemixingtimet_m.Thebal- ancedreactionscanbemodeledasfollows:

Reaction1:H₂BO₃⁻+H⁺↔ H₃BO₃ t_r1t_r2 (6)

Reaction2:5I⁻+IO3−+6H⁺↔ 3I2+3H2O tr2≈ ∼tm (7)

TheiodineI2furtherreactswithiodideionsI⁻,yieldingI⁻₃ ionsfollowingthequasi-instantaneousequilibriumreaction:

Reaction3: I⁻+I₂←→^KB I⁻₃ (8)

The kinetics of the three reactions was established by Guichardonetal.(2000).Thecharacteristictimesofreactions (1)and(2)are:

t_r1= Min([H₂BO⁻₃]₀; [H⁺]₀)

(r1)_t=0 (9)

t_r2= Min((3/5)[I⁻]₀; 3[IO⁻₃]₀; 1/2[H⁺]₀)

(r2)_t=0 (10)

For >0.166M: log₁₀(k2)=8.383−1.5112√

+0.23689 (13)

Theprincipleofthis methodistoadd,instoichiometric deficit,asmallquantityofsulfuricacidH⁺toaninitialmix- tureofI⁻,IO⁻₃,andH2BO⁻₃.Inperfectmixing,theinjectedH⁺ istotallyconsumedbythequasi-instantaneousreaction(1)in Eq.(6)andhencethereisnoformationofiodineI₂.Whenthe mixingprocessisnotsufficientlyfasttosustainreaction(1), thelocaloverconcentrationofH⁺producesiodineI2byreac- tion(2)(Eq.(7)),whichreactswithiodideionsI⁻toyieldI⁻₃ ions(Eq.(8)):itmodifiestheabsorbanceofthefinalsolution thatisdetectedbythespectrometer,usedtodeducethecon- centrationofproducedI⁻₃.Therefore,theselectivityinI₂isa measureofmolecular-scalesegregationandindicatesmixing quality.

ThecharacteristicsegregationindexXS isdefinedbythe expression:

XS= Y

Y_ST (14)

whereYistheratioofthequantityofH⁺transformedintoI2

followingthesecondreactiontothetotalquantityofinjected H⁺andYSTisthevalueofYinthecaseoftotalsegregation.XS

isgivenforopenloopflowsbyVillermaux(1986)as:

XS= 2([I2]+[I⁻₃]) [H⁺]₀

p

QH⁺ +1 [H2BO⁻₃] 6[IO⁻₃]₀ +1

(15)

whereQpandQ_H+arerespectivelytheflowrateofthemain streamandtheinjectedsulfuricacid.

ThemassbalanceoniodineI2atomsleadstothefollowing expression(Fournieretal.,1996a,b):

[I2]²−

5

[I⁻]₀−8 5[I⁻₃]

[I2]+3 5

[I⁻₃]

5KB =0 (16)

whereKBistheequilibriumconstantofreaction(3)(Eq. (8)) whichdependsonthesolutiontemperature:

log₁₀K_B=555

T +7355−2575log₁₀(T) (17) AtT=298KtheequilibriumconstantK_B=702mol⁻¹.

5.1.2. Adaptiveprocedure

Recently, the conventional chemical probe procedure was usedtocomparetwocurved2×4mmrectangularductswith differentradiiofcurvature(Habchietal.,2011).Afirstexper- iment, with distributed wall injections and a given set of speciesconcentrations fixing a“high rate” forreaction (2),

soastocaptureandtakeintoaccountallthemixingscales.

To meetthis challenge,anew protocol was proposed that involvespre-adjustingthemeasurementvolumetothediffer- entReynoldsnumbersbyadaptingthekineticsofreaction(2) toeachReynoldsnumber,leadingtomorerelevantresultsfor thesegregationindexX_S.Thesecondreactiontimetr2canbe adjustedbyvaryingtheinitialreagentconcentrations;how- ever,asitisquitedifficulttovarytheinitialconcentrations ofI⁻,IO⁻₃,andH2BO⁻₃constitutingtheinitialsolutionbecause theyarelinkedbythepH,thechoicewasmadetovarytheH⁺ concentrationsinjectedinto themainflow.Accordingly,for eachReynoldsnumber,thesecondreactiontimeiscalculated insuchawayastoobtainaconstantmeasurementvolume computedfromthelengthoverwhichreaction(2)takesplace, Lr2=Wtr2.Therefore,whentheReynoldsnumberandtheflow speedincrease,thesecondreactiontimeisdecreasedbythe samefactorbyincreasingtheH⁺concentration.Thismethod revealstherelativemixingimprovementwhentheReynolds numberisincreased,andallowscomparingdifferentreactor geometries.

Finally, themeasuredsegregation indexisrelatedtothe mixingtimebytheengulfmentmodel(BaldygaandBourne, 1989)for turbulent regimeand bythe stretching efficiency model(FalkandCommenge,2010)forlaminarone.

5.2. Micromixingmodels

The segregation index XS provides qualitative information on global mixing dependent on the chemical system. The relatedquantitativeparameteristheintrinsic mixingtime, tmindependentofthereactiveconditions,whichcanbeiden- tifiedthroughmixingmodelsdevisedonphenomenological grounds.

5.2.1. Engulfmentmodel

Severalmodelsexistfordeterminingmixingtimeandturbu- lentenergydissipationrate.BaldygaandBourne(1984,1989) havedevelopedacomplexmodel,theengulfmentmodel(E- model),basedontheassumptionoffirst-order-lawgrowthof the incorporatedreagent volumeinto spiralmarbledstruc- tures,showninFig.22,thatarelaterhomogenizedunderthe stretchingeffectsuntilnear-Batchelorscales,andthenmolec- ulardiffusion.

TheE-model isusedforthe turbulent flowregime.The firstofitsstepsisthegrowthofthevolumeV_icontainingthe speciesi:

dV_i

dt =EV_i (18)

wheretheengulfmentrateE,theinverseofthemixingtime, is relatedto the TKE dissipationrate, ε and the kinematic

Fig.22–Principleoftheengulfmentmodel.

AdaptedfromBaldygaandBourne(1999).

viscosity,followingthescalelawanalysisbyBaldygaand Bourne(1989):

E= 1 tm=0.05

(19)

ExpressingEq.(18)intermsofmassbalance,thegrowth oftheuniformmixingzoneofconcentrationc_iisgivenbythe temporaldifferentialequation:

dci

dt =E(ci−c_i)+R_i (20)

wherec_ireferstothemeanconcentrationvalueofiinthe environmentwhenmixingiscompletedandR_iistherateof formationofsubstanceibythechemicalreaction.

Tofindtherateofvariationofeachspecies,Eq.(20)must besolvedasafunctionoftimeforeachspeciesinvolvedin reactionsuntilthesulfuricacidconcentrationtendstozero resulting in a system of nine nonlinear equations for the differentreagentsintheiodide/iodatereactionsystem.The Newton–Raphsoniterativemethodisemployedandcomputa- tionsaremadewithMATLABsoftware.Thecalibrationcurve isobtainedbythesetofXSsolutionsfoundbysweepingthe mixing-timeparameter,tm.FromtheexperimentalXS value (Eq.(15)),themixingtimecanbedeterminedbytheinverse functionX_S=f(tm).Thecorresponding curvecanbeused to findthemixingtime,tmwhenthesegregationindexvalueis availablefromexperiments.

5.2.2. Stretchingefficiencymodel

In laminar shear flow, it is known that the characteris- tic dimension of the structure decreases in the direction orthogonalto theelongation. Diffusion andconvection are thencompetitiveprocesses,butaccordingtotheshearrate value,forlargesegregation scales,diffusionprocessisslow comparedtoconvectionandmixingisalmostcontrolledby stretching.Atfinesegregationscales,diffusionbecomesthe controllingstep.Thisproblemhasbeenaddressedbyseveral authors(BaldygaandBourne,1983;Lietal.,2005;OuandRanz, 1983a,b) and reinvestigated by Baldyga and Bourne (1984), whoconsideredthetotalmixingtimetobethesimultaneous contributionofthediffusiontimeand theshearstretching characteristictimeandproposedtocalculatethemixingtime ofintertwinedlamellaebyconsideringthestriationthickness andtheshearrateinthereactor.

Basedonthis approach, the stretching efficiencymodel proposedforlaminarregimes,byFalkandCommenge(2010)is usedtocalculatethemixingtime.BaldygaandBourne(1984)

suggest calculatingthe mixingtimeinlaminar flowbythe followingequation:

tm= arcsinh((0.76ı˙ ²₀)/Dm)

2˙ (21)

whereı0istheinitialstriationthickness,Dmthemoleculardif- fusionofwaterand˙the“efficient”generalizedshearratefor mixinginthereactor.Inthissense,˙isassumedtorepresent therateofcreationofintermaterialarea:

˙= 1 a_v

dav

dt (22)

whereavistheintermaterialareaperunitvolume.

However,determinationof˙ isnottrivialandnumerical oranalyticalsolutionsareneeded.FalkandCommenge(2010) estimatethe meanpowerdissipationrateper unitmassof fluidε¯ andthe “efficient”generalized shearrate forenergy dissipation˙minlaminarflowfromtheHagen–Poiseuillelaw.

Hence, ε¯ and ˙m can be derived in terms of the channel hydraulic diameter D_h, the mean flow velocityW, and the kinematicviscosityofthefluid:

ε¯=32W²

D²_h (23)

˙m=

2

(24)

Themean power dissipationrateper unitmassoffluid ε¯ canalsobecalculated,forall flowregimes,from the net pressuredropovertheentirereactorlength Pby:

ε¯=Q P

V (25)

whereQisthevolumeflowrateofthemainflowandVisthe totalfluidvolumebetweenthetwopressure-dropmeasure- mentpoints.

Theinitialstriationthicknessı0dependsinturn onthe experimentalprocedureandtheinjectionmode.Underopti- malconditions,theacidisinjectedinthedirectionofthemain flowwithanequalvelocitytoavoidajetimpactwiththeflow.

Inthiscase,theinitialstriationthicknesscanbeestimated using:

ı²₀

4 W=Qinj (26)