Quantifying Mixing using Magnetic Resonance Imaging.

0.94 MB·English

by  Tozzi, Emilio J.

JournalofVisualizedExperiments www.jove.com
VideoArticle
Quantifying Mixing using Magnetic Resonance Imaging
EmilioJ. Tozzi1,KathrynL. McCarthy1,LoriA. Bacca2,WilliamH. Hartt2,MichaelJ. McCarthy1
1Dept.FoodScienceandTechnology,UniversityofCalifornia,Davis
2CorporateEngineeringandTechnologyLaboratory,Procter&GambleCompany
Correspondenceto:[email protected]
URL:http://www.jove.com/video/3493/
DOI:10.3791/3493
Keywords:Biophysics,Issue59,Magneticresonanceimaging,MRI,mixing,rheology,staticmixer,split-and-recombinemix,
DatePublished:1/25/2012
Citation:Tozzi, E.J.,McCarthy, K.L.,Bacca, L.A.,Hartt, W.H.,McCarthy, M.J. QuantifyingMixingusingMagneticResonanceImaging.J.Vis.Exp.
(59),e3493,DOI:10.3791/3493(2012).
Abstract
Mixingisaunitoperationthatcombinestwoormorecomponentsintoahomogeneousmixture.Thisworkinvolvesmixingtwoviscousliquid
streamsusinganin-linestaticmixer.Themixerisasplit-and-recombinedesignthatemploysshearandextensionalflowtoincreasetheinterfacial
contactbetweenthecomponents.Aprototypesplit-and-recombine(SAR)mixerwasconstructedbyaligningaseriesofthinlaser-cutPoly(methyl
methacrylate)(PMMA)platesheldinplaceinaPVCpipe.MixinginthisdeviceisillustratedinthephotographinFig.1.Reddyewasaddedtoa
portionofthetestfluidandusedastheminorcomponentbeingmixedintothemajor(undyed)component.Attheinletofthemixer,theinjected
layeroftracerfluidissplitintotwolayersasitflowsthroughthemixingsection.Oneachsubsequentmixingsection,thenumberofhorizontal
layersisduplicated.Ultimately,thesinglestreamofdyeisuniformlydispersedthroughoutthecrosssectionofthedevice.
Usinganon-Newtoniantestfluidof0.2%Carbopolandadopedtracerfluidofsimilarcomposition,mixingintheunitisvisualizedusingmagnetic
resonanceimaging(MRI).MRIisaverypowerfulexperimentalprobeofmolecularchemicalandphysicalenvironmentaswellassample
structureonthelengthscalesfrommicronstocentimeters.Thissensitivityhasresultedinbroadapplicationofthesetechniquestocharacterize
physical,chemicaland/orbiologicalpropertiesofmaterialsrangingfromhumanstofoodstoporousmedia1,2.Theequipmentandconditions
usedherearesuitableforimagingliquidscontainingsubstantialamountsofNMRmobile1Hsuchasordinarywaterandorganicliquidsincluding
oils.TraditionallyMRIhasutilizedsuperconductingmagnetswhicharenotsuitableforindustrialenvironmentsandnotportablewithina
laboratory(Fig.2).Recentadvancesinmagnettechnologyhavepermittedtheconstructionoflargevolumeindustriallycompatiblemagnets
suitableforimagingprocessflows.Here,MRIprovidesspatiallyresolvedcomponentconcentrationsatdifferentaxiallocationsduringthemixing
process.Thisworkdocumentsreal-timemixingofhighlyviscousfluidsviadistributivemixingwithanapplicationtopersonalcareproducts.
VideoLink
Thevideocomponentofthisarticlecanbefoundathttp://www.jove.com/video/3493/
Protocol
1. Mixer design
1. UseaCADprogramtodesignthemixingsectionsofthestaticmixer.
TheSARmixeriscomposedofanumberofdifferentplategeometries;thesegeometriesareshowninFig.3.Eachlaser-cutPoly(methyl
methacrylate)(PMMA)plateis1.59mmthickandhasarectangularkeyatthebottomsothatitcanbealignedinaPVCpipewithanacrylicrod.
Thegeometryissimilartothosedescribedin[3,4],exceptthatthewallsintheexpansionsandcontractionsareformedbyaseriesofdiscrete
“staircase”stepsduetothealignmentofdiscreteplatesratherthansmoothdiagonalsurfaces.Althoughthematerialofconstructionhereis
PMMAandPVC,opaquenon-metallicmixerscanbeconstructedaswell.
2. Aligntheindividualplatestodeveloptherepeatingunitsofthemixer.Positiontheplatestightlywithina1½inchSchedule40clearPVCpipe.
3. Fig.4illustratesthestaticmixerviewedfromtheside.Noticethattwofluidsenterattheleftsideofthefigure.Theminorcomponent,shown
asthedarkregion,entersthroughthenozzle(PlateS,Fig.3)andformsastreamoftheminorcomponentinthe(colorless)major
component.TherepeatingunitstartsafterPlateSatthefirstPlateCandextendsdownstreamthroughPlate48,whichisalsoaPlateC.In
eachrepeatingunit,thetwofluidsflowinto8platesofopenchannel(PlateC).Thefluidisthenphysicallyseparatedintotwoverticalchannels
byeightplatesofPlateI,followedbytheactualmixingsection.Themixingsectionisatotalof16plates,fromupstreamtodownstream:
PlatesI,A,B,D,E,F,G,J,J,K,L,M,N,O,P,andH.Thefluidleavesthemixingsectionandflowsinto8platesofPlateH,inwhichfluidis
physicallysplitintotwohorizontalchannels.The“H”sectionisfollowedby8platesofopenchannel(PlateC).Thispatternof48platesis
repeated6timesinthemixer.TworepeatingunitsareillustratedinFig.4asPlates1-96.
2. Flow system with MR imaging system and a mixer
1. AssembleaflowsystemtopumpCarbopolsolutionthroughthein-linesplit-and-recombinestaticmixer.Beabletocontrolandrecordthe
massflowrateofthetestfluids.Inaddition,incorporateapressuretransducerupstreamofthemixertomonitorpressure.
Copyright©2012 CreativeCommonsAttributionLicense January2012| 59 |e3493|Page1of8
JournalofVisualizedExperiments www.jove.com
2. Positionthemixerinthemagnet(Fig.5).Themagnetispartofa1Teslapermanent-magnet-basedimagingspectrometer(AspectImaging,
IndustrialAreaHevelModi'in,Shoham,Israel),with0.3T/mpeakgradientstrengthThedimensionsofthemagnetenclosureare700x700x
600mm.
3. DopepartoftheCarbopolsolutionwithmanganesechloride(MnCl2).Thiswillbetheminorcomponent.Themajorcomponentisundoped
Carbopolsolution.Fig.6illustratesaschematicofflowsystem.
3. Characterization of the test fluid
1. Preparea0.2%w/wCarbopol(TheLubrizolCorporation)solutionbyslowlysiftingaweighedamountofpolymerintodeionizedwaterina
stirredtank.Thispolymerfamilyofproductsisbasedoncrosslinkedacrylicacidchemistryandiswidelyusedinpersonalcareandhousehold
productsasrheologicalmodifiers.Neutralizethecarbopolsolutionwitha50%NaOHsolutiontopH7;theneutralizationallowsthesolutionto
achieveitsmaximumviscosityasthepolymerswellsinwatertoformagel.PrepareasecondcarbopolsolutioncontainingtheMRcontrast
agentMnCl2toafinalconcentrationof0.040mM;thissolutionisreferredtoasthedopedtracerfluid.
2. Characterizetheflowbehavior,orrheology,ofthecarbopolsolutionswithaTAInstrumentsAR-G2rheometer(NewCastle,DE)witha
standardCouettegeometry(14mmdiam.x42mmheight)atafluidtemperatureof25°C.Forshearviscosity,useasteadystateshear
stresssweepfrom0.1500Painlogarithmicmodewith10points/decadeand5%tolerance.Methodsaredescribedin[5].
Inthiswork,therheologicalpropertiesofthetwosolutionswereindistinguishableandareillustratedinFig.7,datawerefittoapowerlawmodel
andshowshearthinningbehavior.
Characterizetheviscoelasticpropertiesofthe0.2%w/wcarbopolsolutionwithsmallamplitudeoscillatorytesting.Performthedynamictestingat
afixedstressof1Pa,whichcorrespondstothelinearviscoelasticregion.Measurestrainoverafrequencysweepfrom628-0.63rad/s(100-0.10
Hz)inlogarithmicmodewith10points/decade.
Thestorageandlossmoduli,G’andG”respectively,areshowninFig.8.ThecurvesarecharacteristicofagelsystemwithG’>G”andG’fairly
constant[5].Valuesoftan(δ)=G”/G’increasefrom0.05atlowerfrequenciesto0.3−0.5athigherfrequency.Thecorrespondingphaselag(δ)
followedthesametrend,withthelimitsbeingδ=0forHookeansolidsandδ=π/2forNewtonianfluids.
3. EvaluatetherelativecontributionofviscousforcestoinertialforcesduringflowusingtheReynoldsnumber.Sincethecrosssectionofeach
platevaries,theaverageflowratethroughtheplateandtheReynoldsnumberiscalculatedandgiveninTable1.
TheseReynoldsnumbervaluesaremuchlessthan1.0andcharacterizeflowsinwhichviscousforcesdominatetheinertialforces.Inother
words,themixingisbylaminarstretchingandshearingratherthanturbulence.
4. MR data acquisition
1. Selectanappropriateradiofrequencycoil.
Thisworkusesasolenoidwithfourturns,encasingacylindricalvolume60mmindiameterand60mmlong.ThiscoilcloselyfitsthePVCpipe
andachievedagoodsignal-to-noiseratioofthesignal.
2. Runamulti-slicegradientechosequenceandacquireMRimages.
Thispulsesequencewaschosensincethesignalintensityissensitivetomaterialspin-latticerelaxationtime.Therelativesignalintensity
betweentwomaterialswithdifferentrelaxationtimesiscalculatedfromanequation.Thesignalintensitydifferences,totalacquisitiontimeforthe
imagerelativetotheinfluenceofmoleculardiffusionduringtheimageacquisitionallneedtobeconsideredinselectingtheappropriate
experimentalparameters.Additionally,theconcentrationofthecontrastagent(MnCl2)ischosensuchthatthesignalintensitychangesresulting
fromcontrastagentconcentrationarelinear.TheadditionofMnCl2decreasesthespin-latticerelaxationtime(T1)ofthetestfluidfrom2.998s
(undoped)to0.515s(doped).ThedopedCarbopolsolutionappearsbrighterthantheundopedCarbopolsolutionintheimagessincethe
intensityishighlyweightedbythespinlatticerelaxationtime.Thepulsesequenceparametersareanechotime(TE)of2msandarepetitiontime
(TR)of30ms;thefieldofview(FOV)is64mmper128encodingswhichyieldsanin-planespatialresolutionof0.5mm/voxel.Withthis
multi-slicesequence,weacquire32crosssectionalslicesofthickness1.4mmperimagingslice.
5. Imaging the fluid
1. Pumpboththemajorandminorcomponentsthroughthemixeruntilsteadyflowisachieved.Therelativeflowrateofthemajorandminor
componentsis10:1.Simultaneouslystopthepumpsandimagethefluidinthemixer.TheMRsequencedoesnotincludeflowcompensation;
toavoidmotionartifacts,theimagingisperformedonquiescentliquid.Imagingtimeisontheorderof1-4minutes.
2. Repositionthemixerseveraltimestoimagecylindricalvolumesatdifferentaxiallocations.
Inthisstudy,severalcylindricalvolumesofthemixerareimagedandcanbelocatedinFig.9.Thevolumeischosenbyslidingthemixertube
axiallythroughthemagnet,untilthedesiredvolumeisinthesweetspotdefinedbythecenteroftheNMRcoilinthecenterofthemagnet.
3. AnalyzetheMRdatawithimageanalysisprocedurestodocumentthespatialdistributionofcomponentconcentrations.Therelationship
betweennormalizedsignalintensity(x)andthefractionofdopedfluid(y)inthisstudyisy=1.419x-0.482(R2=0.99).Thisrelationshipis
relevanttoanalyzethemixingprocess.ToillustratethepowerofflowvisualizationusingMRI,thefollowingresultsareselectedimagesat
differentaxiallocations.
6. Representative Results
Figure10illustratesimagesattheslitnozzle(injector)toshowthecrosssectionsasdopedandundopedenterthefirstrepeatingunit.These
imagesalsoclearlyshowthedifferenceinsignalintensitybetween100%dopedfluidandundopedfluid.
TheSARmixereffectivelyanduniformlysplitsflowasillustratedintheimagesoftheHPlatesdownstreamfromthe1st,2nd,and3rdmixing
sections(Fig.11,firstrow).Thenumberofdopedfluid“stripes”doublethrougheachmixingsection.ThesecondrowofFig.11illustratesthe
Copyright©2012 CreativeCommonsAttributionLicense January2012| 59 |e3493|Page2of8
JournalofVisualizedExperiments www.jove.com
imageanalysisprocedurethatthresholdstheimagesto“1”s(stripes)and“0”s(everythingelse).Theseprocessedimagesclearlyillustratethe
increaseofinterfacialareabetweenthedopedandundopedfluidsasthefluidsplitsandrecombines.
SequentialimagesthroughthesecondmixingsectionareshowninFig.12.

Table1.Crosssectionalareaofeachplateandaveragevelocitythroughthecrosssection,withcorrespondingReynoldsnumber(Re);defined
forapowerlawfluid(PL),usinganequivalentdiameter.

Figure1.Photographtoillustrateflowthroughasplit-and-recombinemixerusingCarbopoldyedredastheminorcomponentandundyed
Carbopolsolutionasthemajorcomponent.

Figure2.2Teslasuperconductingmagnet;forsizereference,theconveyorismoving3avocadosintotheimagingregion.
Copyright©2012 CreativeCommonsAttributionLicense January2012| 59 |e3493|Page3of8
JournalofVisualizedExperiments www.jove.com

Figure3.PlatetypesandletterdesignationsthatareusedtocreatearepeatingunitintheSARmixer.

Figure4.Schematicofthespilt-and-recombinemixer.
Copyright©2012 CreativeCommonsAttributionLicense January2012| 59 |e3493|Page4of8
JournalofVisualizedExperiments www.jove.com

Figure5.1Teslapermanent-magnet-basedimagingspectrometer(AspectImaging).

Figure6.Schematicofflowsystem.

Figure7.Apparentviscosityofthe0.2%Carbopolsolution.
Copyright©2012 CreativeCommonsAttributionLicense January2012| 59 |e3493|Page5of8
JournalofVisualizedExperiments www.jove.com

Figure8.Viscoelasticpropertiesofthe0.2%Carbopolsolution.

Figure9.RepeatingunitsoftheSARmixer.

Figure10.Twoimagesattheinjector:theupstreamsectionofthenozzlehasacircularcrosssectionforthedopedfluidwhichgradually
becomesaslitattheentrancetothefirstrepeatingunitoftheSARmixer.
Copyright©2012 CreativeCommonsAttributionLicense January2012| 59 |e3493|Page6of8
JournalofVisualizedExperiments www.jove.com

Figure11.Fluiddownstreamoffirst,second,andthirdmixingsections,illustratedatPlateH.

Figure12.Sequencesof16sequentialimagesthroughthesecondmixingsection.Pleaseclickheretoseealargerversionoffigure12.
Discussion
Magneticresonanceimagingisarapidandquantitativemethodforanalysisoffluidmixing.Themeasurementrequiresafewminutestomake
andprovidesconcentrationoffluidasafunctionofpositioninthesplit-and-recombinemixer.Thistechniqueissuitableforapplicationtoawide
rangeofmixingproblemsandgeometries[6-11].Limitationstothetechniquearethatanonmagneticmixermustbeconstructedandusedinthe
MRIequipment,andatleastoneofthematerialsmustprovideasufficientsignalfordataacquisition.AsufficientsignalrequiresanNMRactive
nucleiwithasufficientnumberdensity.
MRIcanalsobeusedtoquantifymixingofsolidsandliquids,twoliquidswithsignificantlydifferentrheologicalpropertiesaswellasmixingin
reactingsystems.ThemixingofsolidsintoaliquidwillyielddifferentimagesthanthoseoftheSARmixer.Inthemixingofsolidsthesolid
componentsignaldecaysrapidlyandisnotimaged;hence,thesignalisfromtheliquidonlyandtheconcentrationofsolidisderivedfromthe
signallosscomparedtopureliquidsignal.
Copyright©2012 CreativeCommonsAttributionLicense January2012| 59 |e3493|Page7of8
JournalofVisualizedExperiments www.jove.com
MRImixingimagesprovideanexcellenttestofcomputationalmixingexperiments.Theimagedataprovidesinsightontheimportanceoffluid
rheologicalpropertiesanddeviationsfromidealconditions.InFig.12thedeviationsfromideallyuniformlayersoffluidareevident.Theimages
obtainedthusprovidedetaileddatasetssuitablefordirectcomparisonwithnumericalpredictionsofcomplexflows.
Disclosures
AuthorM.McCarthyisaconsultanttoAspectImaging,Ltd.AuthorsL.BaccaandW.HarttareemployeesofProcter&Gamble,Co.
Acknowledgements
TheauthorswouldliketothankAspectImaging(IndustrialAreaHevelModi'in,Shoham,Israel)forthepulsesequencesusedinthestudy.This
workwaspartiallyfundedbyanawardfromtheCenterforProcessAnalyticalChemistryoftheUniversityofWashington(Seattle,WA,USA),as
wellasin-kindcontributionsandfinancialsupportfromProcterandGambleCompany.
References
1. Callaghan,P.T.PrinciplesofNuclearMagneticResonanceMicroscopy.ClarendonPress,Oxford,(1991).
2. McCarthy,M.J.MagneticResonanceImaginginFoods.Chapman&Hall,NewYork,NY,(1994).
3. Sluijters,R.Mixer.UnitedStatesPatentNo.3182965(1965).
4. vanderHoeven,J.C.,Wimberger-Friedl,R.,&Meijer,H.E.H.Homogeneityofmultilayersproducedwithastaticmixer.Polymer.Eng.Sci.41
(1),32-42(2001).
5. Steffe,J.F.RheologicalMethodsinFoodProcessEngineering.2ndEd.FreemanPress,EastLansing,MI,(1996).
6. Lee,Y.,McCarthy,M.J.,&McCarthy,K.L.Extentofmixinginatwo-componentbatchsystemmeasuredusingMRI.J.Food.Eng.50(3),
167-174(2001).
7. McCarthy,K.L.,Lee,Y.,Green,J.,&McCarthy,M.JMagneticresonanceimagingasasensorsystemformultiphasemixing.AppliedMagnetic
Resonance.22(2),213-222(2002).
8. Choi,Y.J.,McCarthy,M.J.,&McCarthy,K.L.MRIforprocessanalysis:Co-rotatingtwinscrewextruder.JournalofProcessAnalytical
Chemistry.9(2),72-84(2004).
9. Rees,A.C.,Davidson,J.F.,Dennis,J.S.,Fennell,P.S.,Gladden,L.F.,Hayhurst,A.N.,Mantle,M.D.,Muller,C.R.,&Sederman,A.J.The
natureoftheflowjustabovetheperforatedplatedistributorofagas-fluidisedbed,asimagedusingmagneticresonance.ChemicalEng.Sci.
61(18),6002-6015(2006).
10. Stevenson,R.,Harrison,S.T.L.,Mantle,M.D.,Sederman,A.J.,Moraczewski,T.L.,&Johns,M.L.Analysisofpartialsuspensioninstirred
mixingcellsusingbothMRIandERT.Chem.Eng.Sci.65,1385-1393(2010).
11. Benson,M.J.,Elkins,C.J.,Mobley,P.D.,Alley,M.T.,&Eaton,J.K.Three-dimensionalconcentrationfieldmeasurementsinamixinglayer
usingmagneticresonanceimaging.Exp.Fluids.49,43-55(2010).
Copyright©2012 CreativeCommonsAttributionLicense January2012| 59 |e3493|Page8of8