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

HAL Id: hal-01411112

https://hal.archives-ouvertes.fr/hal-01411112

Submitted on 7 Dec 2016

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Modelling of mass transfer in Taylor flow: investigation

with the PLIF-I technique

Colin Butler, Emmanuel Cid, Anne-Marie Billet

To cite this version:

Colin Butler, Emmanuel Cid, Anne-Marie Billet. Modelling of mass transfer in Taylor flow:

inves-tigation with the PLIF-I technique. Chemical Engineering Research and Design, Elsevier, 2016, vol.

115 (Part B), pp. 292-302. �10.1016/j.cherd.2016.09.001�. �hal-01411112�

O

pen

A

rchive

T

OULOUSE

A

rchive

O

uverte (

OATAO

)

OATAO is an open access repository that collects the work of Toulouse researchers and

makes it freely available over the web where possible.

This is an author-deposited version published in :

http://oatao.univ-toulouse.fr/

Eprints ID : 16171

To link to this article : DOI : 10.1016/j.cherd.2016.09.001

URL :

http://dx.doi.org/10.1016/j.cherd.2016.09.001

To cite this version :

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

Any correspondence concerning this service should be sent to the repository

administrator:

staff-oatao@listes-diff.inp-toulouse.fr

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:colin.butler@ensiacet.fr(C.Butler),emmanuel.cid@ensiacet.fr(E.Cid),annemarie.billet@ensiacet.fr(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.

References

Abiev,R.,2013.Bubblesvelocity,Taylorcirculationrateandmass transfermodelforslugflowinmilli-andmicrochannels. Chem.Eng.J.227,66–79.

Aussillous,P.,Quéré,D.,2000.Quickdepositionofafluidonthe wallofatube.Phys.Fluids12(10),2367–2371.

Berˇciˇc,G.,Pintar,A.,1997.Theroleofgasbubblesandliquidslug lengthsonmasstransportintheTaylorflowthrough capillaries.Chem.Eng.Sci.52(21),3709–3719.

Butler,C.,Cid,E.,Billet,A.-M.,2016.Investigationparinhibition defluorescencedesmécanismeslocauxdetransfertdemasse enécoulementdeTaylor.In:ProceedingsofCongrès

FrancophonedeTechniquesLaser,Toulouse,France,13–16 September2016.

Dani,A.,Guiraud,P.,Cockx,A.,2007.Localmeasurementof oxygentransferaroundasinglebubblebyplanar laser-inducedfluorescence.Chem.Eng.Sci.62,7245–7252. Das,S.,2010.FundamentalsofHeatandMassTransfer.Alpha

ScienceInternationalLtd.,Oxford,UK.

Dietrich,N.,Loubière,K.,Jimenez,M.,Hébrard,G.,Gourdon,C., 2013.Anewdirecttechniqueforvisualizingandmeasuring gas–liquidmasstransferaroundbubblesmovinginastraight millimetricsquarechannel.Chem.Eng.Sci.100,172–182. Häber,T.,Gebretsadik,M.,Bockhorn,H.,Zarzalis,N.,2015.The

effectoftotalreflectioninPLIFimagingofannularthinfilms. Int.J.Multiph.Flow76,64–72.

Han,P.,Bartels,D.,1996.Temperaturedependenceofoxygen diffusioninH2OandD2O.J.Phys.Chem.100,5597–5602.

Hassanvand,A.,Hashemabadi,S.H.,2012.Directnumerical simulationofmasstransferfromTaylorbubbleflowthrougha circularcapillary.Int.J.HeatMassTransf.55,5959–5971. Hatziantoniou,V.,Andersson,B.,Schoon,N.H.,1986.Mass

transferandselectivityinliquid-phasehydrogenationofnitro compoundsinamonolithiccatalystreactorwithsegmented gas–liquidflow.Ind.Eng.Chem.ProcessDes.Dev.25(4), 964–970.

Heiszwolf,J.J.,Kreutzer,M.T.,vandenEijnden,M.G.,Kapteijn,F., Moulijn,J.A.,2001.Gas–liquidmasstransferofaqueousTaylor flowinmonoliths.Catal.Today69(1–4),51–55.

Incropera,F.P.,DeWitt,D.P.,2002.FundamentalsofHeatandMass Transfer,5thed.JohnWiley&Sons,NewJersey,USA. Irandoust,S.,Ertlé,S.,Andersson,B.,1992.Gas–liquidmass

transferinTaylorflowthroughacapillary.Can.J.Chem.Eng. 70,115–119.

Jimenez,M.,Dietrich,N.,Grace,J.R.,Hébard,G.,2014.Oxygen masstransferandhydrodynamicbehaviourinwastewater: determinationoflocalimpactofsurfactantsbyvisualization techniques.WaterRes.58,111–121.

Jimenez,M.,Dietrich,N.,Hébrard,G.,2013a.Masstransferinthe wakeofnon-sphericalairbubblesquantifiedbyquenchingof fluorescence.Chem.Eng.Sci.100,160–171.

Jimenez,M.,Dietrich,N.,Hébrard,G.,Cockx,A.,2013b.

ExperimentalstudyofO2diffusioncoefficientmeasurement

ataplanargas–liquidinterfacebyplanarlaser-induced fluorescencewithinhibition.AIChEJ.59,325–333.

Kececi,S.,Wörner,M.,Onea,A.,Soyhan,H.S.,2009.Recirculation timeandliquidslugmasstransferinco-currentupwardand downwardTaylorflow.Catal.Today147,S125–S131.

Kreutzer,M.T.,Du,P.,Heiszwolf,J.J.,Kapteijn,F.,Moulijn,J.A., 2001.Masstransfercharacteristicsofthree-phasemonolith reactors.Chem.Eng.Sci.56(21),6015–6023.

Liu,D.,Wang,S.,2010.Gas–liquidmasstransferinTaylorflow throughcircularcapillaries.Ind.Eng.Chem.Res.50(4), 2323–2330.

Mehdi,S.,Billet,A.-M.,Chughtai,I.R.,Inayat,M.,2013.Overall gas–liquidmasstransferfromTaylorbubblesflowingupwards inacircularcapillary.Asia-Pac.J.Chem.Eng.8,931–939.

Nijhuis,T.A.,Kreutzer,M.T.,Romijn,A.C.J.,Kapteijn,F.,Moulijn,J., 2001.Monolithiccatalystsasefficientthree-phasereactors. Chem.Eng.Sci.56(3),823–829.

Pan,Z.,Zhang,X.,Xie,Y.,Cai,W.,2014.Instantaneousmass transferundergas–liquidTaylorflowincircularcapillaries. Chem.Eng.Technol.37,495–504.

Roudet,M.,(Ph.D.thesis)2008.Hydrodynamiqueettransfertde masseautourd’unebulleconfinéeentredeuxplaques. UniversitédeToulouse

http://ethesis.inp-toulouse.fr/archive/00000806/.

Sander,R.,2015.CompilationofHenry’slawconstants(version 4.0)forwaterassolvent.Atmos.Chem.Phys.15,4399–4981. Schröder,A.,Willert,C.E.,2008.ParticleImageVelocimetry:New

DevelopmentsandRecentApplications.Springer-Verlag BerlinHeidelbergGmbH,NewYork.

Settles,G.S.,2001.SchlierenandShadowgraphyTechniques: VisualizingPhenomenainTransportMedia.Springer-Verlag BerlinHeidelbergGmbH,NewYork.

Shao,N.,Gavriilidis,A.,Angeli,P.,2010.Masstransferduring Taylorflowinmicrochannelswithandwithoutchemical reaction.Chem.Eng.Sci.160(3),873–881.

Svetiov,S.D.,Abiev,R.S.,2015.MasstransferinTaylorflowin microchannels:modellingofconvectioneffects.In: Proceedingsof15thEuropeanConferenceonMixing,Saint Petersburg,Russia,28June–3July2015.

Tan,J.,Lu,Y.C.,Xu,J.H.,Luo,G.S.,2012.Masstransfer

performanceofgas–liquidsegmentedflowinmicrochannels. Chem.Eng.J.181,229–235.

Thulasidas,T.C.,Abraham,M.A.,Cerro,R.,1995.Bubble-trainflow incapillariesofcircularandsquarecrosssection.Chem.Eng. Sci.50(2),183–199.

Thulasidas,T.C.,Abraham,R.L.,Cerro,R.L.,1997.Flowpatternsin liquidslugsduringbubble-trainflowinsidecapillaries.Chem. Eng.Sci.52,2692–2947.

Valiorgue,P.,Souzy,N.,ElHajem,M.,BenHadid,H.,Simoëns,S., 2013.Concentrationmeasurementinthewakeofafreerising bubbleusingplanarlaser-inducedfluorescence(PLIF)witha calibrationtakingintoaccountfluorescenceextinction variations.Exp.Fluids54,1–10.

VanBaten,J.M.,Krishna,R.,2004.CFDsimulationsofmass transferfromTaylorbubblesrisingincircularcapillaries. Chem.Eng.Sci.59(12),2535–2545.

Vandu,C.O.,Ellenberger,J.,Krishna,R.,2004.Hydrodynamicsand masstransferinanupflowmonolithloopreactor:influenceof vibrationexcitement.Chem.Eng.Sci.59(22–23),

4999–5008.

Vandu,C.O.,Liu,H.,Krishna,R.,2005.MasstransferfromTaylor bubblesrisinginsinglecapillaries.Chem.Eng.Sci.60(22), 6430–6437.

Webster,D.R.,Roberts,P.J.W.,Ra’ad,L.,2001.Simultaneous DPTV/PLIFmeasurementsofaturbulentjet.Exp.Fluids30, 65–72.

Yao,C.,Dong,Z.,Zhao,Y.,Chen,G.,2014.Anonlinemethodto measuremasstransferofslugflowinamicrochannel.Chem. Eng.Sci.112,15–24.

Yue,J.,Yuan,Q.,Luo,L.,Gonthier,Y.,2007.Hydrodynamicsand masstransfercharacteristicsingas–liquidflowthrougha rectangularmicrochannel.Chem.Eng.Sci.62(7),2096–2108.