Modelling of mass transfer in Taylor flow: investigation with the PLIF-I technique

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OULOUSE

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Butler, Colin and Cid, Emmanuel and Billet,

Anne-Marie Modelling of mass transfer in Taylor flow:

investigation with the PLIF-I technique. (2016) Chemical

Engineering Research and Design, vol. 115 (Part B). pp. 292-302.

ISSN 0263-8762

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Modelling

of

mass

transfer

in

Taylor

flow:

Investigation

with

the

PLIF-I

technique

C.

Butler

,

E.

Cid

,

A.-M.

Billet

a_{LaboratoiredeGénieChimique,UniversitédeToulouse,CNRS,INPT,UPS,Toulouse,France} b_{FERMaT,UniversitédeToulouse,CNRS,INPT,UPS,INSA,Toulouse,France}

Keywords: Masstransfer Taylorflow Lubricationfilm PLIF-I Shadowgraphy Modelling

a

b

s

t

r

a

c

t

Anexperimentalinvestigationofmasstransferbetweenbubbles,slugsandlubricationfilms isperformedbymeansofopticaltechniquesforair–waterTaylorflowsina3mmglass chan-nel.Bubblesize,shapeandvelocity,aswellasslugsizeandfilmthickness,aremeasured byuseoftheshadowgraphytechnique.ThePLIF-Itechnique,withassociatedspecific tech-nicaladjustmentsandimageprocessingmethods,givesaccesstothedissolvedoxygen concentrationintheliquidphasewithhighspatialandtemporalresolutions.Valuesof con-centrationaremeasuredintheslugsand,forthefirsttime,inthelubricationfilms,leading tothequantificationofmasstransfercontributionsfromcapsandfromthecentralbubble body.Resultsforoverallmasstransferarecomparedtoliteraturemodelsbasedon volumet-riccoefficientkLa.AmongthemthemodelproposedbyVanBatenandKrishna(2004),which

considerscapandfilmcontributionstokLa.Theyarefoundtofailtoaccuratelypredictthe

experimentaldataofaverageO2concentrationintheliquidphaseforshortslugs(Ls<2dc).

Animprovedversionofthismodelisproposed,allowingcalculationofO2concentrationfor

filmsandslugsalongthechannel.Themodelneedsflowcharacteristics,whichareobtained byshadowgraphy.

1.

Introduction

Overthepastseveralyears,ithasbeenclaimedthatstructured reactorsofferinterestingpossibilitiesinthefieldofchemical reactionengineering.Amongstthem,monolithreactors,also knownas‘honeycombreactors’,haveappearedasa cutting-edgetechnologyforgas–liquidcatalyticreactorsinregardto conventionalreactors,whichsuffervariousdrawbacks.These includeliquidback-mixingandneedforcatalystseparation andrecycling(inslurrybubblecolumns),significantattrition of the catalyst (in fluidised-beds), and significant pressure dropanddiffusionallimitation(infixed-beds).Monolith reac-torshavebeenthefocusofconsiderablestudyforalmostfour decadesastheypromisetoovercometheseproblems.Aswell asother interestingpoints(suchaslow pressuredrop, low riskforfoulingorcloggingandforhotspots),monolith reac-torshostintheirchannelsspecificallytunablegas–liquidflow

∗_{Correspondingauthorat:LaboratoiredeGénieChimique,4alléeEmileMonso,CS44362,31030Toulousecedex4,France}

E-mailaddresses:[email protected](C.Butler),[email protected](E.Cid),[email protected](A.-M.Billet). regimes.Onesuchregime,theso-calledTaylorflow(or bubble-trainorslugflow)leadstointerestingvaluesofinterfacialarea andofratesofmasstransfer(Heiszwolfetal., 2001;Vandu etal., 2005), whichis particularlyconvenient as gas–liquid masstransferisthelimitingphenomenonwhenfast chem-icalreactionsareinvolved.Theoverallvolumetricgas–liquid masstransfercoefficient,kLa,wasreportedtobemuchlarger

in monolith reactors operating in the Taylor flow regime (0.1–1s−1_{)(Heiszwolfetal.,2001;Vanduetal.,2004)thanin} stirredtanks(0.03–0.4s−1_{),bubblecolumns(0.005–0.25s}−1_)or packedbeds (0.004–1s−1_{) (Yue et al., 2007). Thisenhanced} masstransferwasattributedtotheexistenceofathin liq-uidfilm(afew tensofmm)laying betweenthebubble and thechannelwall,aswellastotheefficientconvectivemixing withintheliquidslugsprovidedtheyareshortenough(Mehdi etal.,2013).Whatismore,thelubricationfilmcontributionto masstransferbecomescrucialwhenaheterogeneousreaction

occursatthecatalystcoatedwallbecauseasharp concentra-tiongradientislocallygeneratedinthiscase.Sofar,empirical correlationsforthevolumetric(liquidside)masstransfer coef-ficient, kLa, are available in literaturefor Taylor flows, but

knowledgeandunderstandingofthephenomenaoccurringat thelocalscalearestilllacking,whichcouldleadtopre-design rulesandscalinglawsformonolithreactors.

Inthepresentwork,masstransferisinvestigatedatthe bubble and slugscale in Taylorflow inachannel of3mm ofinternaldiameter,byuseofnon-invasivetechniqueswith highspatialandtemporalresolutions:shadowgraphyand Pla-narLaserInducedFluorescencewithdyeInhibition(hereafter PLIF-I).Theobjectivesare(i)tomeasuredissolvedgas concen-trationvaluesinliquidphase,(ii)tocomparethemtoexisting masstransfermodelsinordertosortthoseofmostrelevance, (iii)toquantifylubricationfilmandbubblecapcontributions inanattempttounderstandthephenomenatakingplace,and (iv)toproposeanimprovedmodel,allowingfortheprediction ofthedissolvedoxygenconcentration[O2]infilmsandslugs alongthechannel.Thismodel,basedonphenomenological considerations,isintendedasamethodforfastandeasy esti-mationofgas–liquidmasstransferforpre-designofmonolith reactors.

2.

State

of

the

art:

mass

transfer

in

Taylor

flow

2.1. Experimentalinvestigations

ItwasshownthatkLavaluesmeasuredinmonolithreactors

correlateratherwellwiththosepredictedfromsingle-channel models(Heiszwolfetal.,2001;Vanduetal.,2004).Mostworks ongas–liquidmasstransferhavebeendevotedtosingle milli-metriccapillaries(Vanduetal.,2005;Mehdietal.,2013;Berˇciˇc andPintar,1997;Irandoustetal.,1992;VanBatenandKrishna, 2004;Shaoetal.,2010;LiuandWang,2010;Hassanvandand Hashemabadi, 2012;Pan et al., 2014)and the experimental contributionshaveprovideddatameasuredattheinletand attheoutletofachannel.Therelativecontributionsof bub-blecapsandlubricatingfilmtothegas–liquidmasstransfer havebeenthoroughlydiscussed,butconclusionsweremainly drawnfornon-reactivesystemswherefilmsaturationwiththe transferringspeciesmayhinderitscontribution.No experi-mentalworkhasyetinvestigatedthespecificcontributions fromlubricationfilmsandfrombubblecapsandfew chem-icalengineeringmodelshavebeenproposedinliteratureto takeinto accountthosecontributions(Hatziantoniouetal., 1986;Nijhuisetal.,2001;Kreutzeretal.,2001).

Recently, non-invasive experimental methods have

appeared, allowing fully developed Taylor flows tobe suc-cessfully studied(Tanet al., 2012;Dietrichetal., 2013;Yao et al., 2014).However, someofthese methodsare suitable forspecificfluidsystemsonly,wherechemicalreactionand chemical enhancementfactor are implied, or are validfor verysmallreactorsonly.Whatismore,thesetechniquesdo notpermittheinvestigationofthelubricationfilm.

2.2. ExistingmodelsformasstransferinTaylorflows

AstheliquidphaseinTaylorflowconsistsofatrainofmixed slugs,it hasoftenbeenrepresented,formasstransfer pur-poses, using the plug flowmodel (Berˇciˇc and Pintar, 1997; Vandu et al., 2005; Shao et al., 2010; Yue et al., 2007). For this kindofmodel,uniform velocityandconcentrationare

assumedfortheliquidphaseoverthechannelcrosssection, regardlessoftheactualstructureoftheflow.Asinglevalueof

kLaisthenusedtoexpressmassexchangebetweengasand

liquidphases:

uTPdC

dz=kLa[C∗−C(z)] (1)

wherezistheaxialcoordinatealongthechannel,uTPisthe

totalsuperficialvelocityoffluids(gasplusliquid)inthe chan-nel,C(z)thecurrentconcentrationoftransferredgasinthe liquidphase,andC*_{thesaturationconcentrationofdissolved} gasintheliquid.Notethataisconsideredhereastheinterface surfaceperunitvolumeofchannel.Eq.(1)canbeintegrated into: C(z) C∗ =1−









Correlationsfor kLaestimation are found inliterature; the

majorones(i.e.mostoftencited)arelisted inTable 1. The majoradvantageoftheplugflowmodelassociatedwiththese correlationsforkLaisthatitcanbeappliedwiththe

knowl-edgeofphaseflowrates, channeldiameter,fluidproperties andbubbleandsluglengthsonly.TheBerˇciˇcandPintar(1997)

correlation(Eq.(A)inTable1)wasestablishedforlong bub-bleswithalmostsaturatedfilms.InthecorrelationsfromVan BatenandKrishna(2004)(Eqs.(B1)and(B2)),thecontributions from caps (left term inequations) and film (right term in equations)tomasstransferareevaluatedonthebasisofthe Higbiepenetrationmasstransfermodelandoffallingfilm the-ory,respectively.Notethatconditionsofestablishmentofthe correlationsproposedbyVanBatenandKrishna(2004) corre-spondtoshortcontacttimeoftheliquidfilm(f <0.1ı2_f/D). Eq.(B1)usestheexactdimensionsofbubble,filmandslug, unlikeEq.(B2)wherethesedimensionsareestimatedthanks totheoperationalparameters(forinstancefilmlength,L_f−b, isestimatedfromLUCandtheratioofbubbleandunitcell

vol-umes),andmayleadaprioritolessaccurateresults.Vandu etal.(2005) correlatedfilm contributiononly,based onthe (kL)f−bsuggestedbyVan Batenand Krishna(2004),wherea multiplicativevalueof4.5bestfittedtheexperimentaldataof airabsorptioninwaterin1–3mmdiametercapillariesof cir-cularandsquarecross-sections.Eq.(C1)shouldthenbevalid forTaylorflowsinwhichfilmcontributionisdominant.Shao etal.(2010)tunedthemultiplicative constantinEq.(C1) to matchCFDcomputedresultsforthecaseofCO2absorption intoanaqueoussolutionofNaOH.ThecorrelationfromYue etal.(2007)(Eq.(D))wasderivedfornarrowchannels(lessthan 1mm)inadditiontohighgasandliquidsuperficialvelocities (1m/s<uTP<12m/s).

Morerecentmodelstakeintoaccountthedetailed struc-tureofTaylorflow(Abiev,2013;Kececietal.,2009;Svetiovand Abiev,2015).Kececietal.(2009)derive,forrectangular chan-nels,atheoretical analysisofthe recirculation time inthe liquidslugsforlaminarflow,andproposedacorrelationfor thischaracteristictime.SvetiovandAbiev(2015)considerthe liquidslugasstratified inthreelayers:thefilmatthewall, andtheinnerandouterlayersintheTaylorvortex.Forthis model,hydrodynamicstermsareevaluatedfromthePoiseuille structureoftheliquidflowandfromthelubricationfilm thick-ness,ascorrelatedinliterature(Thulasidasetal.,1997).The masstransfer(ortransport)termsaredeterminedfrom dif-fusionlayerconsiderationandfromannularfilmtheory.This

Table1–CorrelationsfromliteratureforestimationofkLavalues(kLaisexpressedins−1,whereinterfacialais

expressedinm2_{pervolumeofunitcell).}

Authors Correlation Eq.

BerˇciˇcandPintar(1997) kLa=0.111

u1.19 TP

[(1−εV )LUC]0.57 (A)

VanBatenandKrishna(2004) kLa=2

√ 2 

q

q

VanBatenandKrishna(2004) kLa=2

√ 2 

q

q

q

q

Yueetal.(2007) ShLadc=0.084Re0.213G Re0.912L Sc0.5L (D)

Fig.1–Schematicrepresentationofunitcell,bubble,slug andfilm.

modelneedsadifferentialequationinspace(2-dimensional) andtimetobesolved,andcouldbeinterestinglycompared toexperimentalresults.Inaview offastandeasy estima-tion ofgas–liquidmasstransferforpre-designofmonolith reactors,thismodelhoweverrequiresasignificantamountof calculation.

3.

Calculation:

pre-design

model

for

mass

transfer

in

Taylor

flow

AsmentionedinSection2.2,theVanBatenandKrishna(2004)

modeldistinguishesthecontributionsfromfilmsandcapsto masstransferintheunitcell.AnoverallkLavalueisbuiltfor

theunitcellfrom2contributions:

kLa=(kLa)caps+(kLa)f−b (3)

where (kLa)caps=kL,capsacaps and (kLa)f−b=kL,f−baf−b. The termsacapsanda_f−barederivedinEq.(B2)inTable1.Theoverall

kLavalueisweightedinEq.(1)bytheaveragedriving

concen-trationdifferenceinthewholeunitcell.Asaconsequence, inthis model,actual volumesandconcentrations forfilms andslugscannotcontributetothecalculationoftheresulting dissolvedoxygenconcentration.

Inthiswork,theseparateuseofthetwocontributionsis preferred.Tothatpurpose,separateslugandfilmzonesare taken into account(see Fig. 1).A channel fedwith deoxy-genatedwaterandpureO2gasbubblesisconsidered.Focusis madeonaunitcellofvolumeVolUCandlengthLUC,travelling

alongthechannelatvelocityuTP (Fig.1).Theslugtravelsat

avelocityuTP (Thulasidasetal.,1995)andisassumedtobe

perfectlymixed.Forsimplification,itisconsideredtobethe samediameterasthebubble(db).Theslugreachestheaxial

positionzinthechannelatatimeinstanttdefinedas: t=_uz

TP (4)

Theslug isfedbymass transferfrom the bubble cap sur-facesandbymassexchangewiththeliquidfilmlayerclose tothewall.Theestimationofmasstransferbetweenbubble andslugisbasedonthevolumetriccoefficient(kLa)caps(per volumeofunitcell)asexpressedbyVanBatenandKrishna (2004)(leftterminEq.(B1),Table1);howeveruTP isusedin

thisrelationinsteadofub:theliquidvelocityprofileintheslug

isknowntoconformtothePoiseuillelaw(SvetiovandAbiev, 2015)whereuTPistheaveragevelocityintheslugs.Formass

exchangebetweentheslugandliquidfilmlayer,weconsider thattherecirculationinslugmeetsuniformconcentrationat filmboundary.Followingliteratureanalysisoffully-developed laminarflow inacircular channelwith aconstant bound-aryconcentration(IncroperaandDeWitt,2002;Das,2010),the assumptionismadethatSh=3.66,whereShistheSherwood number.ThevalueofShisaconstant,independentofRe,Sc, and axial location (Incropera and DeWitt,2002). Therefore, massexchangebetweenfilmlayerandslugisevaluatedon thebasisofavolumetriccoefficient(kL)f−s,definedas:

(kL)f−s= 3.66D

dc (5)

whereDisthediffusivityofdissolvedgasintheconsidered liquid.

DefiningCsandCfastheconcentrationsofdissolvedgasin

slugandfilmattimet(orpositionzinchannel),respectively, abalanceequationofdissolvedgasintheslugvolumeVolsis

thenderivedoveraninfinitesimaltimeinstantdt: Vols[Cs(t+dt)−Cs(t)]={(kLa)caps[C∗−Cs(t)]VolUC

+(kL)f−sAf−s[Cf(t)−Cs(t)]}dt (6) wherethe slugvolume,Vols,and thecontactareabetween

theconcentratedliquidlayeratthewallandslug,A_f−s,can becalculatedfrommeasuredvaluesofunitcellvolume, bub-ble volume,from slug lengthLs and film thickness ıf. The

valueofA_f−sisexpressedas2rbLf−sor2rb(1−εL)LUC,where

εL is defined as the ratio between the length of

lubrica-tion film(along the bubble)and the unit cell,L_f−b/LUC (see

Fig.1).

AsshowninFig.1,inthepresentworkthefilmconsists ofthethinlayeratthetubewallalongthewholeunitcell.It isfedbymasstransferfromthebubblelateralinterface,and connectedtopreviousandnextliquidfilmlayersbyaflowrate

evaluatedviathefollowingbalanceequationestablishedover asmalldistancedzalongthechannel:

qfCf(z+dz)=qfCf(z)+{(kL)f−baf−b[C∗−Cf(z)]

−(kL)f−saf−s[Cf(z)−Cs(z)]}dz (7) Thecoefficient(kL)f−bisexpressedfollowingthemodelofVan

BatenandKrishna(2004)by

(kL)f−b= 2 √ 

r

wherea_f−b anda_f−s arethecontactareasbetweenfilmand bubble, and film and slug, per unit lengthof the channel respectively.AsdzissmallcomparedtoLUC,theconsidered

elementoffilm(oflengthdz),dependingonitspositionz,can belocatedeitherclosetoabubbleorclosetoaslug. There-foreitisnecessarythata_f−bisexpressedas2rbεLanda_f−s

as2rb(1−εL).FollowingSvetiovandAbiev(2015),thevalueof

qfwasestimatedacrossfilmthicknessıfbylocally

integrat-ingtheliquidvelocityprofileintheslug,which,asmentioned earlier,isknowntoconformtothePoiseuillelaw:

qf=2

Z









Fromthe twocoupledEqs.(6)and(7), theevolutionof dis-solvedgasconcentrationsCfandCsalongthechannelcanbe

computedwithinitialvaluesCf(z=0)=Cs(z=0)=0.The

result-ingdissolvedgasconcentrationintheunitcell,CUC,issimply

calculatedastheweightedsumofCsandCf:

VolUCCUC=VolfCf+VolsCs (11)

4.

Materials

and

methods

Thetwo optical techniquesused to study the mass trans-fer in the channel are Planar Laser-Induced Fluorescence withInhibition(PLIF-I)andshadowgraphy.Both techniques arenon-intrusive.Shadowgraphyisawell-knowntechnique whichinvolvesilluminatingthesubjectofstudybyadiffuse lightsourceandrecordingimagesofitsshadow(Settles,2001). ThebasicprincipleofthePLIF-Itechniquelaysonthe exci-tationofafluorescentdyebylightataspecificwavelength whichthedyeabsorbs.Thedyethenemitslightatadifferent wavelengthandvaryingintensitiesduetodifferentinhibiting factors,suchasthepresenceofdissolvedmolecularoxygen (Danietal., 2007).When rigorouslyapplied,this technique allowsthecaptureofimagesofthedissolvedgas concentra-tionfield.ThePLIF-Itechniquehasbeenusedforadecadeand canbeappliedtovariousgas–liquidsystems,likefreerising bubbles(Danietal.,2007;Valiorgueetal.,2013;Häberetal., 2015; Jimenez et al., 2013a) or confinedinterfaces (Roudet, 2008;Jimenezetal.,2013b).However,thesignaltonoiseratio maybepoorifthelaserdoesnotexcitethedyeatan opti-mised wavelength. Furthermore,incident and fluorescence lightsmaybereflectedonwallandbubbleinterface,leadingto dataprocessingdifficultiesandnon-negligibleuncertainties.

Fig.2–Experimentalset-up.

Inthiswork,thelaserwavelengthhasbeenadjustedtothe dyeexcitationspectrum,andaspecificdataprocessinghas beendevelopedtotakelightscatteringintoaccount.General andspecificprinciplesofthetechniquesaredescribedinthe nextsections.

4.1. Experimentaltest-rig

The mono-channel is a calibrated glass tube with a

circular cross-section and has an internal diameter of

3mm±0.01mm.Thegasisinjectedinto theliquidthrough aT-mixerlocatedatthechannelinlet.Itcanbeset-upsothat theinletcanbeeitheratthetoporbottomofthechannelto allowascendingordescendingcon-currentflowstobe gener-ated.ThegasflowrateisregulatedbyaBrooksSLA5850Smass flowmeterconnectedtoaWest6100+digitalcontroller.The liquidphase,consistingofwateranddissolveddye,is sup-pliedfroma20Lreservoirtankandiscirculatedinaclosed loopbyaTuthillD-seriesgearpumpwiththeflowrate reg-ulatedbyaBronkhorstCORI-FLOWmassflowcontroller.The gasandliquidareseparatedattheoutlet.Thegasisexhausted toambientandtheliquidreturnstothereservoirtank.Agas injectionspargingsystemisincludedintheliquidreservoir tank.Thisenablestheliquidtobedeoxygenatedbynitrogen, orgivenaknownoxygenconcentrationforPLIF-Icalibration, describedlaterinSection4.3.Aschematicrepresentationof thesetupisshowninFig.2.

Duringthe masstransferexperiments,eitheroxygen or nitrogenwasusedasthegasphaseinthechannel,and nitro-gen gasissparged into the liquid reservoirto removeany dissolvedoxygen presentbeforeit entersthe channel. The oxygenconcentrationattheoutletofthechannelismeasured byaUnisenseOX-50microsensorconnectedtoaUnisense

Table2–Liquidphasephysicalpropertiesat21◦_C.

Density(kg/m3_{) 998}

Dynamicviscosity(mPas) 1.05 Surfacetensionwithair(mN/m) 71.2 Henry’sconstant(mol/m3_{/Pa)(Sander,2015) 1.22×10}−5

Massdiffusivity(m2_{/s)(HanandBartels,1996) 1.77×10}−9

PA2000amplifier.Thissensorwasusedtomeasurethetotal masstransferalongthechannellength.

4.2. Imagingandlasersystems

Thecamerausedforthe PLIF-Iandshadowgraphyimaging

wasaPCOEdge5.5sCMOScamerawhoseresolutionhasbeen reducedto2560×402pixelstoimagethechannelareaof inter-estonlyandtoenableahigherfrequencyofacquisition.It isfittedwithaNikon105mmMacrof/2.8lensandextended withaseriesofextensiontubeswithatotallengthof68mm. A540nmOD6high-passfilterisplacedinfrontofthecamera. Fortheshadowgraphyexperiments,a120×160mmPhlox LEDpanelisusedasthelightsource.Itispositionedbehind the channel, perpendicular to the axisof the camera.The imagedsectionofchannelissurroundedbyaglycerolfilled visualisation box. Asthe refractiveindices ofglycerol and glassarealmostidentical,anyrefractionorreflectionoflight as it passes throughthe channel walls becomesnegligible (SchröderandWillert,2008).Thecameraacquiresimagesat afrequencyof100Hzandwithanexposuretimeof100ms, effectivelyfreezingtheflow.

The light source used for the PLIF-I experiments is an

Opotek Opolette 355 tunable laser system. The advantage

of using this system is that it can generate wavelengths over a broad range and thus allowsfor the tuning ofthe

laser light to the maximum excitation wavelength of the

PLIF-I dyebeing used. Thedyeused in these experiments is Dichlorotis (1,10-phenanthroline) ruthenium(II) hydrate (C36H24Cl2N6Ru·xH2O)[CASNo.207802-45-7].Byexcitingitat itsmaximumabsorptionwavelength(max=450nm,E=5mJ),

theresultingemissionismaximisedand animagewithan excellentdynamicrangeisproduced.Duringthisstudy,ithas beenverifiedthatimagesproducedusingtheOpolettelaser

have adynamic range approximately 3times greater than

thoseproducedwhileusingafrequencydoubledNd:Yaglaser (=532nm,E=200mJ).The540nmfilterinstalledonthe cam-eraisdesignedtoblockthelightatthelaserwavelengthbut allowthe resultinglightatthe fluorescencewavelengthsto pass.Thedyeisdirectlysolubleintheaqueousphaseandis usedatalowconcentrationof50mg/L.Asaconsequence,it doesnotsignificantlyaltertheliquidphaseproperties,which havebeenspecificallymeasuredorcalculatedforthisstudy (seeTable2),and presents constantcalibration parameters (Jimenezetal.,2014).Additionaltestsalsoshowedthatthere wasnophotobleachingofthefluidduringexperiments.

Thelasersystem isequipped withalenssystem which producesadiverginglasersheetwithathicknessof280mm which was measured in-situ. Thelaser lightsheet is pos-itioned to pass through the centerline ofthe channel and perpendicular totheaxisofthe camera.Amotorised vari-ableattenuatorensuresstabilityofthelaserenergypulses. Thestandarddeviationsingraylevelintensityvaluesshow, forthreeindividualpixelsinasequenceofconcentration cal-ibration images,a timevariationofless than 5%from the mean.

ForthePLIF-Iimages,thecameraacquisitionistriggeredby thelaser.Thecameraacquiresimagesatafrequencyof20Hz andwithanexposureof100ms,withthecamerafrequency ofacquisitionlimitedbythemaximumrepetitionrateofthe lasersystem.

4.3. Experimentalprocedure

Thepresentedtestswereperformedat21◦_{Cand101.325kPa} respectively. Four oxygen concentration values along the channellengthcanbequantified:oneattheinlet,anotherat theoutlet(usingtheoxygensensor),andtwoatintermediate positions(usingPLIF-Itechnique).

Therecordeddataallowedthecompleteprocessingoffour Taylorflowregimes,amongthemthreeintheascending con-figuration and one in the descending configuration. Their correspondinggasandliquidphasesuperficialvelocitiesare presentedinTable3,togetherwiththeirmajor characteris-tics.

For each flow regime,sequences of 5000shadowgraphy

andPLIF-I imagesare recorded.Furthermore,forthe same regime,anadditional5000shadowgraphyandPLIF-Iimages arerecordedusingnitrogenbubblesinplaceofoxygen bub-bles.Astheliquidphaseenteringthechannelisdeoxygenated bynitrogenduringtheexperiments,nomasstransfertakes placesbetweentheliquidandnitrogengasbubblesandthere isthereforenodyequenching.Theseimagesareusedas ref-erence images in the image processing stage described in Section4.4.

For the imaging of a certain Taylor flow regime, the

experimentalset-upallowsfortheshadowgraphyandPLIF-I experimentstobeconducteddirectlyoneaftertheother with-outanymovementofequipmentordisturbanceoftheflowin thechannel.Itissimplynecessaryfortherequiredlightsource tobeactivatedandthecamerasettothecorresponding fre-quencyofacquisitiontorecordimageswithdifferentdynamic ranges.

Ateachpositionalongthechannel,calibrationsarealso acquiredso theimage intensitygrayvalues canberelated totheoxygenconcentration.Sinceoxygenmoleculesinhibit dyefluorescence(Jimenezetal.,2014),theirpresenceina liq-uidphasecaneasilybetrackedandquantifiedbasedonthe Stern–Volmerrelation:

I₀(x,y)

I(x,y) =1+KSV(x,y)·[O2](x,y) (12)

wherexandyarethecoordinatesoftheconsideredpixelin theimage,IisapixelgrayvalueatacertainO2 concentra-tion[O2],I0 isapixelgrayvalueintheabsence ofO2, and KSV istheStern–Volmerconstant.Thecalibrationprocedure

involvessaturatingtheliquidatknownoxygenconcentration valuesand recordingthe resultingfluorescencereceivedby theimagingsystem(Danietal.,2007).Thefiveconcentration valuesfortheoxygen-nitrogengasmixturesusedwere0%, 5%,10%,21%and100%(inoxygen).Foragivenconcentration value,100imagesareusedtocreateatime-averagedimage. ThevalueofKSVcanthenbedeterminedbyalinear

regres-sionfit ofthe data, pixel-by-pixel. This typeofcalibration procedurethereforeaccountsforlasersheetnon-uniformity, absorption,pixelresponsenon-uniformity,andlensvignette (Websteretal.,2001;Valiorgueetal.,2013).

Table3–RecordedTaylorflowregimesandtheirmajorcharacteristics.

Regime uGS(m/s) uLS(m/s) uTP(m/s) ub(m/s) LUC(mm) Ls(mm) Volb(mm3) εL(%) ıf(mm) AxialpositionofPLIF-I

z1(m) z2(m)

1(desc.) 0.056 0.161 0.217 0.240 10.2 9.63 16.8 5.6 43 0.595 0.93

2 0.103 0.143 0.247 0.283 12.7 9.89 33.2 22.7 55 0.245 0.625

3 0.045 0.079 0.124 0.140 15.8 12.50 36.4 20.8 46 0.195 0.505

4 0.222 0.118 0.339 0.395 9.7 5.90 38.7 39.3 112 0.195 0.505

Fig.3– PLIF-Iimagesofrecordedregime2(seeTable3)at

z_{=0.245m(t=0.99s):(a)instantaneousgrayvalueimage;}

(b)correspondinginstantaneous[O2]image;(c) correspondingtime-averaged[O2]unitcellhalf-image.

4.4. Imageprocessing

Inordertoextractthequantitativedatarelatedtothemass transfer taking place between the two phases, significant processingoftheimagesisrequired.Theprocessingincludes anumberofedgedetection,calibrationandcorrectionsteps, andisdescribedindetailinButleretal.(2016).Theprocessing isrealisedwithaself-developedMATLABcode. Computation-allyintensivetasksareperformedonagraphicsprocessing unit(GPU)byintegratingcustomCUDAkernels.

Theapplicationoftheimageprocessingonthe

shadowg-raphy images leads to the determination of channel wall

position, bubble interface, bubble radius, bubble and slug lengths,andbubbleaveragevelocity.

For the correctionof light scattering effects, two series ofPLIF-Iimagesarerecordedusingthesameflowrates:one seriesobtainedwithN2 bubbles(nomasstransferbetween liquid and gas, no fluorescence quenching) and the other seriesobtainedwithO2 bubbles(showingquenchingdueto masstransfer).Themostfrequentsluglength,i.e.themode, iscalculatedfromthecombinedO2andN2images.Thisvalue isusedtoensurethatamaximumnumberofinstantaneous images (at least 100) can be used to create time-averaged imagesinwhich allthe slug lengthsareexactly thesame. Before creating the time-averaged O2 images however, the instantaneousimagesarefirstconvertedfromgrayvaluesto [O2].Forthis,Eq.(12)isusedastheKSVcalibrationdescribed

in Section 4.3 is designed to work pixel-by-pixel. Fig. 3(a)

and (b) show an instantaneous gray valueimage recorded

bythecameraand theresultingimageconverted into[O2],

respectively.Fig.3(c)showsthecorrespondingtime-averaged [O2]unitcellimage.The[O2]imagecolourscalerangesfrom 0to39.524mg/L.ThismaximumvalueC* _{isthetheoretical} saturation[O2]calculatedfromHenry’slaw(Henry’sconstant isgiveninTable2).

InFig.3(a)and(b),thedatahiddenbythebubbleshadow cannotbeexploited(lowerhalfoffigures).However,theunit cellisexpectedtobeaxisymmetricalaboutthechannelaxial centreline.TocalculatethetotalmassofdissolvedO2inthe liquidphase,anintegrationofthe[O2]inthe halfunitcell (Fig.3(c))isperformedaroundtheaxialcentreline.The vol-umesofdiscscorresponding toeachpixelrevolvedaround theaxisarecalculatedusingmagnificationfactorsdetermined fromaspatialcalibrationstep.

Theliquidphaseisthenseparatedintotheslugandfilm areasinordertodeterminetheindividualcontributionsofthe filmandbubblecapstothetotalmassofdissolvedO2.Thefilm isdefinedasthethinregionalongthechannelwallandthe slugistheremainingliquidphase.Fig.4showstheunitcellfor regime2:thedashedlinedefinesthefilmboundary.Between thebubbleandchannelwall,thegas–liquidinterfacedefines thelocation ofthefilm.Inthe slugzone, thefilm location isdeterminedbydetectionofthelocationsofthemaximum gradientof[O2]closetothewall.

5.

Results

and

discussion

5.1. Geometricalandoperationalflowcharacteristics

For the four recorded Taylor flowregimes(one descending andthreeascending),geometricalandoperationalvaluesare

determinedfromthe shadowgraphyimagesand areshown

inTable3.Itcanbeobservedthatthedatashowscontrasted valuesofbubblevelocityub(0.14–0.40m/s),two-phase

superfi-cialvelocityuTP(0.12–0.34m/s),sluglength(5.9–12.5mm)and

bubblevolume(16.8–38.7mm3_{),leadingtocontrastedvalues} ofthegasholdupεLintheunitcell.Filmthicknessvariesin

therange43–112mm.

Thefilmthicknessıfiscalculatedastheaveragethickness

betweenthebubbleandchannelwallwherethebubble inter-faceanglerelativetothechannelwallwasbetween±5◦_.For thefirstthreerecordedregimes,thefilmthicknessisfound tobe55mm,43mmand46mmrespectively.Thesevaluesare foundtobewithin10mmwhencomparedtotherelationship ofAussillous and Quéré (2000)for relatively high Capillary number(Ca∼0.003).Forthefourthregime,showingveryshort slugs,asignificantdifferenceisobservedbetween measure-ment(112mm)andprediction(58mm).Someofthedifference maybeduetothefactthatthisrelationshipwasderivedfor bubbleswithlonglubricationfilms(5–10cm)ofconstant thick-ness,whichisnotthecasefortheregimespresentedhere. Furthermore,duetotheincreasedeffectofrefractioncloseto thetube,theuncertaintyofthefilmthicknessisrelativelyhigh

Fig.4–Measuredfilmboundaryforregime2.

Fig.5–Time-averagedPLIF-Iimagesofrecordedregimesatdifferenttravellingtimest_{:(a)Firstaxialposition;(b)Second}

axialposition.Theupperunitcellimageismirroredabouttheaxialcentreline.

aseachpixelinthisregionisequaltoapproximately11mm. Thefilmisapproximately3–6pixelswide.

5.2. Time-averagedconcentrationfields

Fig.5presentsthetime-averaged[O2]imagesforeachofthe fourrecordedTaylorflowregimes,attwoaxialpositionsalong thechannel.Theimagesarepresentedwithacommonscale sothatthedifferenceinflowcharacteristics(unitcelllength, bubblelength,etc.)canbeclearlyvisualised.Itisworth high-lightingthattheunitcell,andtheslugitself,arenotuniform inconcentration.Thezonesofgreatest[O2]arevisibleinfront ofthe bubble nose and along the channel wall(i.e. inthe film).Theeffectofslugrecirculationonconcentration distri-butionisclearlyobserved.Theobservedpatternsofoxygen iso-concentrationareasareverysimilartothepatterns

com-putedwithCFDbyHassanvandandHashemabadi(2012)for

millimetriccapillaries.However,somedifferencesincludethe areasrichindissolvedoxygeninthecentralpartofslug vor-tices,whicharenotobservedinCFDconcentrationfields.

Asexpected,inallcases,the overall[O2]increaseswith time.Itisinterestingtonotethatforregime4,corresponding tothehighestuTP and thesmallestLs, theaverage

concen-trationinO2almostreachessaturationinashorttravelling time.

5.3. Masstransferevolutionalongthechannel

ForeachrecordedTaylorflowregime,themeanconcentration ofdissolvedO2intheliquidphaseismeasuredatthe chan-neloutlet.InTable4,thesevaluesarepresentedintermsof achievedmasstransferrelativetocompletesaturationofthe unitcellindissolvedO2,andtherelativecontributionoffilms

totheachievedmasstransferisextractedfromtheprocessing ofthePLIF-Iimagesatz2(Fig.5(b)).

Itisclearlyevidentthatmasstransferbetweengasand liq-uidphasesinTaylorflowisthemostefficientwhentheuTPis

highandwhenLsisshort(regime4).Itcanalsobeobserved

thatfilmcontributiontooverallmasstransferremains mod-erate(less than 40%). Thismay be explained bythe short lengthoffilmwhichisincontactwiththebubble(lessthan 4mm),inallofthefourinvestigatedTaylorflowregimes. Film-bubblecontacttimesexceedthediffusivecriterion(0.1ı2

f/D) fromVanBatenandKrishna(2004)byafactorofatleast15. Theweakestfilmcontribution(21%)totheoverallmass trans-fercorrespondstotheshortestcontactlength(0.57mmfor regime1).

TheevolutionofconcentrationofdissolvedO2alongthe tubeandatchanneloutlet(measuredfromtheoxygenprobe), areshowninFig.6:themeanconcentrationsintheunitcell, film,andslugarenormalisedbyC*_{,andplottedattheir} cor-respondingaxialpositionsz(fromtubeinlet).Theerrorbars presentedinFig.6forthePLIF-Imeasurementsareestimated onthebasisofthemaximumfluctuationofthepixelgray val-uesthathavebeenusedtocreatethetime-averagedimages.

The resulting uncertainty was determined to be

approxi-mately±3%. However,thisvalueisprobablyhigherforthe PLIF-Imeasurementsmadeinthelubricationfilms,because oftheincreaseddistortioneffectinthevicinityofthetube wall,and oftherestrictednumberofpixelstodescribethe filmarea.Thelatterpointmakestheuncertaintyforfilm con-centrationdifficulttoquantify.Fortheprobemeasurements, theuncertaintywasfoundtobeapproximately±4%.

Concerning overall [O2] in the unit cell, the PLIF-I and probemeasurementsareseentobeingoodagreement.The slopeofthecurveisgreateratlowervaluesofzandreduces

Table4–RecordedTaylorflowregimesandtheirmajorcharacteristicsintermsofachievedmasstransferatchannel outlet.

Regime uTP(m/s) Lf−b(mm) Achievedmasstransfer(%,C*=39.5mg/L) Filmcontributionforz2(%) Slugresidencetimeatz2(s)

1 0.22 0.57 73 21 4.3

2 0.25 2.91 73 28 2.5

3 0.12 3.29 69 25 4.1

4 0.34 3.8 >99 38 1.5

Fig.6– EvolutionofdissolvedO2concentrationalongthechannelcomparedtoliteraturemodels:(a)Regime1;(b)Regime2; (c)Regime3;(d)Regime4.

significantlyastheflowtravelsalongthechannel,indicating thatahighproportionofthemasstransferoccursclosetothe inlet.Attheoutlet,theliquidisoftennotyetfullysaturated (exceptforregime4).Oxygenconcentrationsinfilms,which havebeenexperimentallymeasuredforthefirsttime,clearly outweigh concentrations in slugs. However, even if films enrich fasterthan slugs, theircontribution tooverall mass transferismoderateforregimes1to3becauseoftheirsmall volumes(forthesecases,Volf /Volsrangesfrom12%to28%,

whereasitreaches58%forregime4),andbecausetheircontact lengthwithbubbles,L_f−b,areshort,asshowninTable4.

5.4. ModelsformasstransferinTaylorflow

Theexperimentalvaluesofoverall [O2]inthe unitcell are usedtotestthekLamodelspresentedinTable1,whichare

basedontheassumptionofplugflow.For regimes1and2,

Fig.6(a)and(b)showthatthemodelfromYueetal.(2007)is ingoodagreementwiththeexperimentaldata(with respec-tivekLavaluesof0.215s−1and0.220s−1),andthatthemodels

fromVanBatenandKrishna(2004),BerˇciˇcandPintar(1997), andtoalesserextentVanduetal.(2005),givesatisfying ten-dencyfortheevolutionofconcentrationalongthechannel.

Fig.7–ComparisonoftheproposedmodelofseparateadditivecontributionstolocalexperimentaldataacquiredbyPLIF-I technique:(a)Regime1;(b)Regime2;(c)Regime3;(d)Regime4.

Forregime3however(longslugs,Fig.6(c)),modelfromVan BatenandKrishna(2004)over-estimatesmasstransfer.Model fromShaoetal.(2010)doesnotfitthedata.Forregime4(short slugs,Fig.6(d))allthetestedmodelsclearlyunder-estimatethe rateofmasstransfer.Werecallthatthesemodelsdonot con-sidertheactualstructureoftheflow,eventhemodelfromVan BatenandKrishna(2004)wherefilmandcapscontributions aredistinguishedbutthenmergedintoasinglekLacoefficient,

regardlessoflocalgradientsinconcentrations.

Theconsiderationoftheseparatemasstransfer mecha-nisms(Eqs.(4)–(11))allowsonetofollowtheevolutionofthe variouslocalconcentrations,aswellastheoverallunitcell concentration(Fig.7).Theflowcharacteristicsrequiredto cal-culatealltheparametersusedintheseequationsaredc,uTP,

Ls,L_f−b,LUC,andıf.Theyhavebeenmeasuredwiththe

shad-owgraphytechniqueonlyandarereportedinTables3and4. Asmentionedearlier,valuesof(kL)f−band(kLa)capsusedinthe modelarecalculatedinasimilarwaytothatproposedinthe

modelofVanBatenandKrishna(2004)(Eq.(B2)),otherthan theuseofuTPinplaceofub.

Fig.7showsthatthemodelofseparateadditive contrib-utions satisfactorilyfits the experimental data: this model predicts the evolution ofthe unit cell concentration along thechannelforthefourrecordedregimes.Inparticular,the fastincreaseofgasconcentrationatchannelentranceinthe caseof short slugs (regime 4, Fig. 7(d))is well reproduced

bythemodel, whereas the models basedon plugflow are

unabletodescribe[O2]evolutionforregime4(seethemodel ofVan Batenand Krishna (2004)shown in Fig.7(d)). What ismore,theevolutionsoffilm andslug concentrationsare alsowell reproduced bythe separate additive contribution model.

Asexpected,themodelissensitivetothevaluesof(kL)f−b, (kLa)caps, andqf, andtoalesserextent(kL)f−s.Itishowever importanttonote that,tofitthe experimentaldata, itwas necessary(i)todivide (kL)f−b byafactorof35 and(kLa)caps

Table5–Masstransfercoefficientsusedinthemodelof separateadditivecontributions.

(kLa)caps(1/s) (kL)f−b(m/s) (kL)f−s(m/s) Ls<2dc 2 √ 2 

p

q

p

q

byafactorof1.8forregimes1to3(longslugs),and (ii)to divide(kL)f−bbyafactorof3.5forregime4(shortslugs).This shows that the contributionoffilms derived byVan Baten and Krishna (2004) in Eq. (8) is greatly over-estimated for theregimeswithlongslugs(Ls>2dc),aswellasforregimes

withlongfilm-bubblecontacttimes(f >1.5ı2_f/D).Thismaybe explainedbytheorderofmagnitudeofthevelocityusedinthis equation,i.e.eitheruTPorub,thusconsideringstagnantfilmat

thewall,whereasvelocitiesinthefilmmaybenon-negligible, especiallyinthecaseofcontaminatedbubblesurface.Further measurementofadditionalregimesandlocalinvestigationby

meansofComputationalFluidDynamicsshouldpermitthe

fulldeterminationofthiseffect.Table5summarisesthe equa-tionsfordeterminationofthemasstransfercoefficientsused inthemodelofseparateadditivecontributions.

6.

Conclusions

MasstransfertakingplaceinTaylorflowinamillimetric chan-nelhasbeensuccessfullyquantified.Itisthefirsttimethe PLIF-I techniquehas been implementedto study this phe-nomenon.Thistechniquehasallowedforthemeasurementof thelocalgasconcentrationintheliquidslugsandfilms.Mass transferbetweengasandliquidphasewasfoundtobethe mostefficientforshortslugsandhightotalsuperficial veloc-ity.Amongseveralavailablemasstransfermodels,arelation estimatingtheoverallvolumetricmasstransfercoefficientkLa

fromthecontributionsoffilmsandcapstomasstransfer, pub-lishedbyVanBatenandKrishna(2004),wasfoundunableto accuratelydescribethe experimentalresultsinthe caseof small slugs(in thisstudy:Ls<2dc). Inthepresent work,an

improvedmodelwasproposed:asthemajorgeometricand

dynamic characteristics ofthe flow were known thanksto shadowgraphymeasurements,it waspossibletoderivethe actualseparatecontributionsbytakingintoaccount interfa-cialmasstransfertowardsfilmandslug(onthebasisofthe relationssuggestedbyVanBatenandKrishna(2004)for esti-mationoftherespectivemasstransfercoefficients),andmass exchangebetweenfilmandslug.Thismethodgives satisfy-ing resultsregardingoverall dissolvedgasconcentrationin the channel, andalsoallowsforavery good estimationof dissolvedgasconcentrationsinfilmsandslugs.Ithasbeen furthershownthattheinterfacialmasstransferbetween bub-bleandfilm(kL)f−bisover-estimatedbytherelationderived byVanBatenandKrishna(2004)andneedstobeadaptedby useofacorrectionfactor(aspresentedinTable5).

In futurework, moreTaylor flowregimes willbe

inves-tigated, showing contrasted geometrical and dynamical

characteristics.Regimeswithlongbubbleswillbeof partic-ularinteresttoemphasisefilmcontributiontomasstransfer. Inordertoestimatemoreaccuratelythefilmcontributionfor themodelofseparateadditivecontributions,theorderof mag-nitudeoftheliquidvelocityinthefilmwillbeinvestigatedvia CFDcalculations.

Nomenclature

A contactarea(m2₎

a contactareapervolumeofunitcellorperunitlength ofchannel(m2_/m3_,m2_/m)

C dissolvedgasconcentration(mg/L)

C* _{dissolvedgassaturationconcentration(39.524mg/L)}

Ca Capillarynumber(–)

D massdiffusivity(m2_/s)

d diameter(m)

I pixelgrayvalueintensity(–)

KSV Stern–Volmercoefficient(L/mg)

kL liquidphasemasstransfercoefficient(m/s)

L length(m) q volumetricflowrate(m3_/s) Re Reynoldsnumber(–) r radius(m) Sc Schmidtnumber(–) Sh Sherwoodnumber(–) t time(s) u velocity(m/s) uGS,uLS superficialvelocity(m/s) Vol volume(m3₎ x,y pixelcoordinates

z axialdistancefromchannelinlet(m)

Greek

ı thickness(m)

εL=L_f−b/LUC lengthvoidfraction(–)

εV=Volb/VolUC volumevoidfraction(–)

 contacttime(s)

Subscripts

b gasbubble

c channel

caps bubblecaps

f liquidlubricationfilm

f−b liquidlubricationfilmbetweenbubbleandchannel wall

f₋s liquidlubricationfilmbetweenliquidslugand chan-nelwall G gasphase L liquidphase TP twophase s liquidslug UC unitcell

Acknowledgments

TheauthorsthanktheAgenceNationaldelaRecherche(ANR) forfinancialsupport,andtheFédérationdeRecherche FER-MaTforfinancialandtechnicalsupport.

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