Comparison of porosity assessment techniquesfor low-cost ceramic membranes

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w w w . e l s e v i e r . e s / b s e c v

Comparison of porosity assessment techniques for low-cost ceramic membranes

Maria-Magdalena Lorente-Ayza

^a^,∗

, Olga Pérez-Fernández

^b

, Raquel Alcalá

^b

, Enrique Sánchez

^a

, Sergio Mestre

^a

, Joaquin Coronas

^c

, Miguel Menéndez

^b

aInstitutoUniversitariodeTecnologíaCerámica(ITC),UniversitatJaumeI,Castellón,Spain

bInstitutodeInvestigaciónenIngenieríadeAragón(I3A),UniversidaddeZaragoza,Zaragoza,Spain

cInstitutodeNanocienciadeAragón(INA),UniversidaddeZaragoza,Zaragoza,Spain

a r t i c l e i n f o

Articlehistory:

Received9February2016 Accepted6September2016 Availableonline29September2016

Keywords:

Membranes Porosity Shaping

Bubblepointmethod

Intrusionmercuryporosimetry

a bs t r a c t

Severalcharacterizationmethodswereappliedtolowcostceramicmembranesdeveloped forwastewatertreatmentinmembranebioreactors(MBRs)and/ortertiarytreatments.The membraneswerepreparedbyfourdifferentprocedures(uniaxialpressingandextrusion, bothwithandwithoutstarchadditiontogeneratepores).Theporesizeofthesesymmetric ceramicmembraneswasmeasuredbytwodifferentmethods:bubblepointandintrusion mercuryporosimetry.Agoodagreementbetweenbothmethodswasachieved,conﬁrming thevalidityofthebubblepointmethodforthemeasurementofthemeanporesizeof membranes.Airandwaterpermeationsoftheseceramicmembraneswerealsostudied.The relationshipbetweenthepermeationofbothﬂuidsisconsistentwiththeratioofviscosities, accordingtotheHagen–Poiseuilleequation.

Comparacióndetécnicasdemedidadelaporosidadenmembranas cerámicasdebajocoste

Palabrasclave:

Membranas Porosidad Conformado

Métododepuntodeburbuja Porosimetríadeintrusiónde mercurio

r e su m e n

En el presente trabajo se han caracterizado mediantediferentesmétodos membranas cerámicasdebajocostedesarrolladasparatrataraguasresidualesenreactoresbiológi- cosdemembrana(MBR)omediantetratamientosterciarios.Lasmembranasseprepararon mediantediferentesprocedimientos(prensadouniaxialyextrusión,conosinadiciónde almidón como material generadorde poros). Eltama ˜no delporode estas membranas cerámicassimétricassedeterminómediante2métodosdiferentes:puntodeburbujay porosimetríadeintrusióndemercurio.Losresultadosobtenidosmedianteambosmétodos mostrabanconcordancia,loqueconﬁrmalavalidezdelmétododepuntodeburbujaparala

∗ Correspondingauthor.

E-mailaddress:[email protected](M.-M.Lorente-Ayza).

http://dx.doi.org/10.1016/j.bsecv.2016.09.002

creativecommons.org/licenses/by-nc-nd/4.0/).

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medidadeltama ˜nodelporomediodelasmembranas.Además,sehaestudiadolapermea- bilidadalaireyaguadeestasmembranascerámicas:larelaciónentrelapermeabilidadde ambosﬂuidosesconsistenteconelratiodeviscosidades,deacuerdoconlaecuaciónde Hagen-Poiseuille.

Introduction

Membranebioreactors (MBR)combineabiologicaldegrada- tion process withthe direct separationof activatedsludge andliquid-solidbyﬁltrationmembranes[1].Inaddition,MBRs haveimportantadvantagessuchasspacereductionrelative toconventional activated sludge process,which leadsto a decreaseintheirenvironmentalimpact,thecapabilityofoper- ating withhigher concentrations ofsuspended solids, and theproductionofbetterqualityefﬂuent.However,oneofthe maindrawbacks ofMBR is membrane fouling.Despite the highcostofcommonlyusedceramicmembranes(madeof alumina,zirconiaortitania),itisknownthattheyaremore hydrophilicthan polymericmembranes, whichmeans that ceramic membranes have a lower membrane fouling rate.

Ceramicmembranesarealsomorechemically,mechanically andthermallyresistant.Othercharacteristicsthatinfluence membrane fouling are pore size and configuration (tubu- lar, flat or hollow fiber) [2,3]. Currently, polymeric hollow fiber membranes are the most widely used in the indus- trybecause themanufacturingcostofceramicmembranes basedonhighpurityoxidesishigherthanthatoftheirpoly- meric counterparts. However, hollow fiber membranes are morelikelytodevelophigherfoulingratesandconsequently giverisetohighermaintenancecosts[1].Asanalternative, lowcostceramicmembraneswhose compositionismainly basedonclaysandorganicporeformersarecheaper,similar tothecostofpolymericmembranes.Thepreparationoflow costceramicmembraneswasdescribedinapreviouspaper [4].

Thiswork attempts tocharacterize twokey parameters oflow cost ceramicmembranes: mean pore diameter and permeability.Severaltechniquescanbeusedtomeasurethe poresizedistributionandaverageporesize(d50)ofamem- brane:nitrogen adsorption,intrusion mercury porosimetry, permporometry,thebubblepointmethod,soluteresistance tests and electronic microscopy (SEM, TEM). In this work, wewillcomparethe resultsobtainedbyintrusionmercury porosimetryand thebubble pointmethod.Bothare simple andrapidtechniqueswhichhavebeenwidelyusedtoevalu- atetheporesizeofceramicmaterials.Theyarestandardized, repeatableandreproducibletestmethods.

Thegoal ofthis studyistodrawacomparisonbetween the average pore size results obtained using bubble point and intrusion mercury porosimetry characterization techniques applied to a set of low cost symmetrical ceramic membranes. Asmercury manipulationhasbeen restricted, this comparisoncould open up an alternative tointrusion mercury porosimetry. This work also addresses the relationship between the water and air permeabilities of the membranes.

Table1–Compositionalrangeusedtoobtainceramic membraneswithverydifferentporositycharacteristics (totalporevolumeandsizedistribution).

Rawmaterial Compositionalrange(wt%)

Clay 40–85

Chamotte 0–20

Feldspar 0–15

Calciumcarbonate 7–20

Starch(differentsources) 0–20

Experimental method

Membranepreparation

Lowcostceramicmembraneswerepreparedfromrawmate- rialsnormallyusedintheceramictilesector(clays,chamotte, feldsparandcalciumcarbonate)andorganicporeformers(dif- ferentstarchesprovidedbyRoquetteLaisaEspa ˜na,S.A.).The componentsweremixedinsuitableproportionssothatthey couldbeeasilyprocessedbyuniaxialdrypressingorextru- sion.Toobtainmembraneswithabroadrangeofporosityand poresizes,theformingmethodswerecombinedwiththeaddi- tionofdifferentproportionsofstarchtosomecompositions.

Table 1shows the compositional range usedto obtain the ceramicmembranes,wheretheproportionofclay,chamotte, feldspar,calciteandstarchhavebeenmodiﬁed.Fourdifferent groupsofmembraneswerepreparedinthisway,referredto asP,PS,EandES(Table2).

Theprocessforproducingthepressedmembranesstarted withdryhomogenization(manuallyandbymeansofanauto- matic mixer) ofthe different raw materials. The resulting compositionsweremoistenedto5.5kgH₂O/100kgdrysolid.

Cylindricaltestspecimens,0.7cmthickand5cmindiameter, wereformedfromthispowderbyuniaxialdrypressingusing anautomaticlaboratorypress(NannettiSpA,Italy).Thetest sampleswereoven-driedat110^◦Ctoaconstantweight.

Eachbatchofrawmaterialsfortheextrudedmembranes was kneaded to aconsistency of5kg, determined bypen- etrometry (usingacylinderwith1.5cmdiameter)(Analogic penetrometer Geotester0-6kg,NovatestS.r.l.,Italy)[5], and allowedtostandfor24htoachieveuniformmoistureinthe mass.Thewatercontentofthecompositionsvariesbetween 20and 32wt%.Testpieces1cmthick and5cmindiameter wereshapedfromanextrudedsheet,usingalaboratoryauger withade-airingchamber(Model050C,TalleresFelipeVerdés, S.A.,Spain).Thetestsampleswereweighedandafterwards driedatroomtemperaturefor24h,andoven-driedat110^◦C toaconstantweight.

Afterdrying,all thesampleswereweighedandthebulk densitywasmeasuredbythemercuryimmersionmethod[6].

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Table2–Membranesclassiﬁcation.

Membranesseries Formingmethod Composition Numberofspecimens

P Uniaxialdrypressing Withoutstarch 10

PS Uniaxialdrypressing Withstarch 4

E Extrusion Withoutstarch 2

ES Extrusion Withstarch 5

Next,the membraneswere sinteredwithdifferentthermal cycles,dependingontheir compositionand theﬁnalprop- ertiesrequired(sinteringtemperaturesrangedfrom1060to 1160^◦Canddwellingtimefrom6to120min).Aftersintering, the membrane properties were determined. These proper- tiesincludeddensity,thickness,microstructure(observedby ScanningElectron Microscopy,FEG-ESEM Quanta200F, FEI, USA),andairandwaterpermeability.Moreover,theaverage porediameterandporesizedistributionweredeterminedby twotechniques:intrusionmercuryporosimetryandthebub- blepointmethod.

Thepresentstudy was carriedout witha largenumber ofmembranes withdifferent pore sizes: 15 different compositions(classiﬁedinfourseries,asshowninTable2)and 36samplesweretestedtocompareaverageporesizevalues obtainedbybothmethods.Inordertocompare theperme- abilityforairandwater,9differentcompositionsand36tests werecarriedout.

Characterization:bubblepointandintrusionmercury porosimetry

The bubble point method allows the determination of membrane airpermeability and, unlike the mostcommon techniques used in the study of porous solids (nitrogen adsorption and intrusion mercury porosimetry), provides information about the pores that control the permeation [7–12].Thismethodisusedtomeasureporeswithsizeabove 50nmanditisstandardizedbyASTMF316-03[13],ISO2942 [14]andISO4003[15].Itconsistsofﬁllingtheporousstructure ofthemembranewithaliquidandmeasuringtheairpressure necessarytodisplacetheliquidinsidethepores.Themini- mumpressurenecessarytoblowtheﬁrstobservedairbubble correspondstothelargest poresizeofthe membrane;this valueisknownasthebubblepoint[15–18].Themathemat- icalrelationshipbetweenpressureandporesizeisgivenby Washburnequation:

P= 4cosϕ dp

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wherePisthepressuredrop(bar),d_pistheporesize(␮m), ϕisthecontactanglebetweentheﬂuidandporewallsand

istheliquidsurfacestress.Inordertobeabletousethe Washburnequation,theporesareassumedtobecylindrical.

Duringthebubblepointtest,liquidintrusionwillﬁrstoccur throughthelargest pores.Ifthe poreswerecylindrical,the ﬂow(m³s⁻¹)throughthemembrane,consideredaslaminar, wouldbegivenbyHagen–Poiseuilleequation[10,17,19]:

Qv=nr⁴P

8l (2)

whereQvisthevolumetricflowthroughthemembrane,Pis thetransmembranepressure,nisthenumberofpores,risthe poresize,istheliquidviscosityandlistheporelength.Ifthe aboveequationisemployedforagas,thevolumetricflowrate shouldbeexpressedatthemeanpressure,i.e.Qvshouldbe calculatedasthevolumetricflowmeasuredatPm,wherePm

isthemeanpressureatbothsidesofthemembrane.Thisis slightlydifferentfromtheusualwayofcalculatingthegasper- meationthroughporousmembranes(e.g.[20]).Inlaminarflow conditions,themolarflowrateisproportionalto(P12−P22), whereP1isthepressureintheretentateandP2isthepressure inthepermeate. However,if thevolumetricflowmeasured atthemeanpressure(P1+P2)/2isemployed,itmayeasilybe foundthatthisvolumetricflowrateisgivenbyEq.(2),where

Pis(P₁−P₂)(seeAppendix).Thisformulationofthegasper- meationallowsthesameequation(2)tobeusedforliquids andgases.

The average pore size (d50) is calculated using Eq. (1) from thepressure atthe intersectionpointofthe linethat represents 50% ofthe air ﬂow(mLmin⁻¹) through the dry membraneversusthe appliedpressure withtheequivalent curve forthe wet membrane(Fig. 1). Thepore sizescorre- spondingto16%and84%ofthedryﬂow(namedd16andd84) arecalculatedinthesamemanner,givinganinsightintothe standarddeviationoftheporesizedistribution.

IntrusionmercuryporosimetryisalsobasedontheWash- burnequation,butinthistechniquemercuryistheliquidused toﬁllthepores.Bythismethodthemercury intrusionvol- umeisrecordedasafunctionofpressureorporesize[8,21].

ThistechniqueisnormalizedwithinDIN66133andISO15901 [22], butrestrictionsonthe useofmercurymay leadtoits disappearanceinthenearfuture.Finally,thetotalvolumeof pores(V_f)andcharacteristicporediameters(d16,d50andd84) arecalculatedfromexperimentaldata.

Fig.1–Airﬂow-pressurerepresentation.

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Fig.2–Schemeofthebubblepointexperimental equipment.

Themain difference betweenboth methods isthat the bubble point, besides being a non-destructive technique, measures the air ﬂow through the pores, while intrusion mercuryporosimetry records the intrusionvolume ofmer- cury coming into the membrane pores. Intrusion mercury porosimetryworkswithhigherpressure,whichisconsidered a limitation because it can lead tosample deformation in thecaseofpolymericmembranes[9].Anotherlimitationin the caseofasymmetric membranes isthe inability ofthis methodtodistinguishbetweenthe poreswhich determine theﬂux(usuallyintheselectivelayer)andthelargerporesin thesupport[23].Inaddition,intrusionmercuryporosimetry alsomeasuresporesthatdonotparticipateinthepermeation (non-connectedpores).

Bubblepoint

Inordertomeasuretheporesizeofthemembranesbythe bubblepointmethod,twosetsofairflowmeasurementswere carriedout.Thefirstwasperformedwiththedrymembrane, measuringtheairflowthroughthemembranewhilethetrans- membranepressure(TMP)wasgraduallyincreased.Asecond setofmeasurementswasperformedwiththesameprocedure, buttheporousnetworkofthemembranewaspreviouslyfilled withwater(surfacetensionatthewater/airinterface, , is 72.75mN/mat20^◦C[24]);thismethodisbasedonthefactthat anairbubblewillpenetratethroughtheporewhenitsradius isequaltothatofthepore,meaningthatthecontactangleis 0^◦(andcosϕ=1)[25].Forthisprocedure,asteelmodulesuit- ablefordiskceramicmembraneswithadiameterof5cmwas madeandaset-upwasdesignedasshowninFig.2.Theseal- ingbetweenthemembraneandthemodulewasmadewith Vitono-rings.

Intrusionmercuryporosimetry

The pore size distribution for each membrane was also obtainedbyintrusionmercuryporosimetry(AutoporeIV9500, MicromeriticsInc.USA).Thistechniqueisbasedonthemea- surementof the intrusion volume of a non-wetting liquid inordertocalculatedatarelatedwiththeporestructureof thesample.Thus,theequipmentcontinuouslyregistersthe

variationoftheintrusionvolumeofthemercuryinsidethe sampledependingonthepressureappliedoverthesample.

Next,itcalculatestheporediameterwiththeintrusionpres- sure,bymeansoftheWashburnequation(surfacetensionat themercury/airinterface,,is487mN/mat20^◦Candcontact angle,ϕ,is135^◦),obtainingagraphicofcumulativeporevol- umeversusporesize.Finally,thecharacteristicporediameters (d16,d50andd84)arecalculatedfromexperimentaldata.

Permeability:airandwater

Airandwaterpermeabilitieswerecalculatedbymeasuringthe fluidflow(mLmin⁻¹)throughthemembraneatroomtemper- aturewhiletheappliedpressurewasgraduallyincreased.The permeationwasdeterminedfromtheslopeofthestraightline obtainedfromthegraphicalplotoftheair/waterfluxagainst appliedpressure,permembraneareaunit(m³h⁻¹m⁻²bar⁻¹).

Air permeability was measured in the same module as described forthe bubble point measurements,whilewater permeabilitywasdeterminedbymeansoftwodifferentpieces ofequipment:anautomaticliquidpermeameter(LEP-1101-A, PMI,Ithaca,NY,USA)formembraneswithhigherpermeability andamanualliquidpermeameterformembraneswithlower permeability.

Results and discussion

Membranestructure(SEM)

Micrographsofpolishedsectionsofexamplesofthefourtypes ofmembranesdescribedinTable2areshowninFig.3.Itcan beseenthatacontinuousporousstructurewascreated,the pores being larger when starch was employedas the pore generatorinthe preparationofthemembrane(membranes PS and ES, compared with those without starch addition, PandS).Theadditionofstarchincreasesporosityandpore sizeaswellasporeconnectivity,owedtotheincreaseinthe amount ofinterconnectedpores createdbystarchburnout, whichshouldresultinanincreaseinpermeability.Thiseffect hasbeenreportedpreviouslyintheliterature.Starchadditions greaterthan10wt%havebeenshowntoincreasetheamount ofinterconnectedporescreatedbystarchburnoutduringthe sinteringstep[4,26–28].

Samplesobtainedbyextrusion(EandES)havealowerpore sizethanthe pressedsamplesowingtothedifferentshap- ing processes (seeFig. 3).Fig. 4shows themicrostructures oftwomembranesofthesamecomposition(highclaycon- tentandnostarch),whichhavebeenobtainedbyextrusion and pressing.Ascanbeseen,theydiffermainlyintheori- entedandscarcelyconnectedporestructurewhichistypical from theextrudedmaterials.Poresfromthepressed mem- branearerounderandhighlyconnected,whereasporesfrom theextrudedmembraneshowalongshapeandreducedcon- nection.Thischaracteristicmicrostructureismoreevidentin thesurfaceofthemembranes,wheretheorientedclaypar- ticlescreateasuperﬁciallayerthatclosesmanyporesnear thesurface.Thiseffecthavealreadybeenobservedbyseveral authors[4,29,30],whohavereportedthatclayproductsman- ufacturedbyextrusionhaveamicrostructurecharacterized

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Fig.3–FEG-ESEMmicrographsofpressedandextrudedmembranes,withandwithoutstarchaddition(magniﬁcation:

400×).Porespresentadarkcolorinthemicrographs.

byanorientatedporedistribution.Thisisaconsequenceof themovementofthecolloidalclayparticlestravelingthrough theaugerextruderduringtheshapingstep.Moreover,these poreshaveareducedconnectivity.Inshort,boththeshaping

methodandthestarchadditionhaveagreatinﬂuenceonthe microstructureofthesupport,modifyingtheporesize,poros- ityandporeconnectivityand,consequently,thepermeability, asitwillbeexplainedinSection“Air–waterpermeability”.

Fig.4–FEG-ESEMmicrographsofpressedandextrudedmembraneswithhighclaycontent(magniﬁcation:1500×).Pores presentadarkcolorinthemicrographs.

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Fig.5–Comparisonofaverageporesizemeasuredby bubblepoint(BP)andintrusionmercuryporosimetry(MP) methods(2samplesevaluatedforeachpoint).

Bubblepointandintrusionmercuryporosimetry

Agraphical representation ofthe mean pore sizeobtained from the bubble point and intrusion mercury porosimetry characterization shows an approximate linear relationship betweenbothmethodswitha coefficientR² of0.93 (Fig.5) andaslopecloseto1(0.84).Thissuggeststhatbothmeth- odsprovidemeanporediametersofthesameorderinspite ofthedifferencesintheexperimentalapproach.Smalldiffer- encesbetweenthemeanporesizemeasuredbybothmethods areexpectedsinceinthebubblepointmethodthemeanpore diametercorrespondstoaflowofavalueofhalfasgreatas thatintheabsenceofwater(asithasbeenexplainedinFig.1), whileinintrusionmercuryporosimetrythemeanporediam- etercorrespondstothecutoffporesizeunderwhich50%of thetotalporevolumelies. Inaddition,sincetherealpores arenotcylindrical,parallelandequal,thedifferencesinboth methodswouldaffectthe calculationofthemean valuein differentways.Thebubblepointmethodmeasuresporesthat affecttheliquidflow,whichareporesthatareconnectedtothe surfaceandbetweenthem,butclosedporesarenotmeasured.

Ontheotherhand,intrusionmercuryporosimetrytechnique measures all pores that mercury can reach with pressure, bothopen and non-connected pores.Moreover,because of thehighpressuresused,intrusionmercuryporosimetrytech- niqueisabletoreachsmallerpores,whicharenomeasurable forthebubblepointmethod.Deviationbetweenbothmethods havealsobeenfoundbyotherauthors,butthenatureofthe measuredmaterialaffectstothisdeviation:Bhatiaetal.[31]

foundthatthemercurypore-sizedistributedresultsshowed muchlargerporesinthegeotextilesthandidthebubblepoint method, whereas Calvoet al. [9] observedthat mean pore diameterswerelowerfortheintrusionmercuryporosimetry curveswhenpolycarbonateﬁlterswereanalyzed.

Thegoodagreement,inspiteofthedifferencesbetween both methods, can be considered as conﬁrmation of the validityofthebubblepointmethod;whichallowsthereplace- mentofintrusionmercuryporosimetrytechniquebybubble pointmethodtoreducethemercuryuseincharacterization laboratories.

Finally,itisworthnotingthattheextrudedsamplesshow resultsclosertothelinearrelationshipthanthepressedsam- ples.Thiscouldbeduetothedifferentmicrostructurethat bothshapingmethodsgivetothesupports,asdescribedin Section“Membranestructure”.Supportsobtainedbymeans of theaddition ofstarch in theircomposition alsoshow a higherdeviationfromthelinearrelationship,probablyowing tothefactthatthebigporesgeneratedbythestarchprovide higher variability, being higher the error associated to the measurement.Asithasbeenstatedbefore,intrusionmercury porosimetyprovidethesamestatustoallpores;ontheother hand,bubblepointmethodmeasurestheeffectivediameter, which isaffected by the pore size, sinceit inﬂuences the necessary energy to empty the pores. This has also been reportedbyCalvoetal.[9],whoobservedabetteraccordance forbothcharacterizations(poresizedistributionsobtainedby intrusionmercuryposimetryandbubblepointmethod)when poresizedecreased.

Thecomparisonbetweencharacteristicdiameters(d16and d84)calculatedbybubblepointmethodandintrusionmercury porosimetryshowsthesametendthatd₅₀,soithasnotbeen plottedinthepresentpaper.Agoodagreementwasachieved betweenthevaluesobtainedbythesetwodifferentmethods, whichagainisconfirmationofthevalidityofthebubblepoint method.Itisclearthattheagreementwasachievedbecause these membranesare symmetric. Inthe caseofasymmet- ricmembranes,themeasurementofporesizedistributionby intrusionmercuryporosimetrywouldnotreflectthesizeof theporescontrollingtheflow.Inaddition,thed84poresgen- eratetheworstcorrelation(R²=0.919).Thiscouldbeexplained bythefactthatmercuryintrusioncanmeasureverysmalland non-connectedporesthattakenopartinthepermeation,as ithasbeendescribedpreviously.

Air–waterpermeability

AccordingtoEq.(2),aplotoftheairflow(usingthevolume measuredatthemeanpressure)versusthetransmembrane pressure(P)shouldshowastraightline(Fig.6a).Theslopes oftheselinesallowthepermeationofeachmembranetoair tobecalculated.Ontheotherhand,waterpermeabilityiscal- culatedbymeansoftheslopeofthestraightlinethatappears when thewaterflow isrepresentedversus P (Fig. 6b).As Fig.6aandbshows,pressedmembranesshowhigherslopes (andpermeabilities)thantheextrudedmembranes.Theper- meability of the membranesobtained byuniaxial pressing ishigher than those obtainedbyextrusion, confirming the resultsonmicrostructuralfeaturessetoutinSection“Mem- branestructure”:extrudedmembraneshavesmallerandless connectedporesthanpressedones,whichprovokesareduc- tion in water and air permeability, effect that have been reported bythe authors in previous works about low-cost ceramicmembranes[4].

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Fig.6–Plotofairﬂow(measuredatthemeanpressure)(a)andwaterﬂow(b)versustransmembranepressureforone exampleofeachkindofmembranes(1sampleevaluatedforeachcurve).

Theadditionofstarchtothe initialcompositiongreatly improvesthepermeability,becausecompositionswithstarch havehigherslopesthanthosewithoutstarch,ascanbeseen inFig.6aandb.Theresultsareconsistentwiththemicrostruc- tureobservedinSection“Membranestructure”,whereithas been stated thatthe addition ofstarch tothe membrane’s compositionincreasetheporesizeandtheconnectivityofthe pores,owedtotheporositycreatedwhenstarchisburntout duringthesinteringstep,increasingthemembrane’sperme- ability(airand water).Thisisespeciallyeffectiveforstarch percentageshigherthan10wt%,sinceaconnectedcoarsepore networkisdeveloped,ashasbeendetailedinpreviousworks [32].

Agraphical representationofairand waterpermeability obtainedfromtheexperimentalvaluesshowsalinearrela- tionshipbetweenbothmeasurementswith acoefﬁcientR² of0.96(Fig.7).Ashasbeenpointedoutpreviously,samples withhigherpermeability (membranesPS,shapedbypress- ingandwithstarchaddition)donotfollowthegeneraltrend aswell as the restof the samples.This isexpected, since thesesamplesexhibitpermeabilityvaluesthatare twiceor threetimeshigherthanthoseoftherestofsamples.Moreover, meanporesizeofPSsamplesfollowthesamepattern,since theydonotﬁttothegeneraltrendaswellastheothercom- positions.Similar conclusionshavebeenfoundinprevious researchescarriedoutbythesameauthors[4].

TheslopeofthestraightlineinFig.7(value63)conﬁrmsthe relationshipbetweenbothmeasurements. Therelationship betweenairandwaterpermeabilitiesisclosetothetheoretical valueof56calculatedfortheratioofairandwaterpermeation fromtheHagen–Poiseuilleequation,usingtheviscositiesofair (1.837×10⁻⁵Nsm⁻²)andwater(1.002×10⁻³Nsm⁻²)at20^◦C (Eq.(3)):

ftheor= Jair

Jwater =water

air

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wherefistheratioofairandwaterpermeation,Jistheﬂux andistheviscosityofeveryﬂuid(airorwater).

Thisgoodagreementbetweentheratioofpermeabilities forairandwaterwiththeratioofviscositiessuggeststhatit couldbepossibletoestimatethepermeabilityforaﬂuidfrom thepermeabilityexperimentallymeasuredwiththeotherand viceversa,asTable3conﬁrms.

Finally,theinfluenceoftheporesize(obtainedbythebub- ble point methodand intrusionmercury porosimetry) over thewaterandairpermeabilitycoefficient(Kp)hasbeeneval- uated. As reported in a previous research study [33], the Hagen–Poiseuille(Eq.(4))relatesthepermeabilitycoefficient

Fig.7–Comparisonbetweenwaterandairmembrane permeabilities(2samplesevaluatedforeachpoint).

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Table3–ExamplesofpermeabilityestimationbasedEq.(3)forcompositionsofeachseries.

Composition Experimental airpermeability (m³h⁻¹m⁻²bar⁻¹)

Calculated airpermeability (m³h⁻¹m⁻²bar⁻¹)

Deviation ratio(%)

Experimental waterper-

meability (m³h⁻¹m⁻²bar⁻¹)

Calculated waterpermeability (m³h⁻¹m⁻²bar⁻¹)

Deviation ratio(%)

P 231 269 17 4.3 3.7 14

PS 2280 2859 25 46.0 36.0 20

E 112 93 17 1.5 1.8 21

ES 483 526 9 8.4 7.7 8

Fig.8–Comparisonofwaterandairpermeabilitycoefﬁcientsversusd₁₆(a)andd₅₀(b)poresizemeasuredbybubblepoint (BP)method(2samplesevaluatedforeachpoint).

withthe poreradius(r),thewaterviscosity(),thesurface porosity(εsf)andthetortuosityfactor():

Kp= ε_sf

8r² (4)

Assuming that the ratio εsf/ varies little between the membranes, the model predicts an approximately linear relationshipbetweenKpand r².Thisrelationshiphasbeen representedinFig.8forbothd₁₆(a)andd₅₀(b),obtainedbythe bubblepointmethod.Thecorrelationisslightlybetterwiththe meandiameter(d50)obtainedwiththebubblepointmethod, whichindicatesthatd50isagoodparameterfordefiningthe properties ofthe support as a membrane. Thedifferences foundbetweenthistrendandthetrendobtainedintherefer- encedwork[33],wherethecorrelationwasslightlybetterwith thed16 parameter(obtainedwiththemercuryporosimeter), maybeduetothedifferentmeasuringtechniques.Sincemer- curyporosimeter measuresall the pores ofthemembrane (connectedandnon-connected),the porediameterd₁₆ rep- resentstheporesofbiggerdiameter,whicharetheporesthat havehigherinfluenceoverthefluidpermeability.Ontheother hand,bubblepointmethodmeasurestheporesthatpartici- pateinthefluidflux,sothed50isrepresentativeoftheeffective poresize.Thispossiblyexplainsthedifferencesobtainedin thediameterthatcorrelatesbetterwiththepermeability.

Conclusions

Astudy oftherelationship betweenmeanpore sizesmea- suredbytwodifferentmethods(bubblepointandintrusion mercuryporosimetry)hasbeencarriedoutusingasetoflow costceramicmembranespreparedusingdifferentprocedures and compositions. The airand waterpermeabilities ofthe testedmembraneswerecompared,achievingagoodcorrela- tionbetweenbothexperimentalvalues.Thesepermeabilities wererelatedbytheHagen–Poiseuillemodelwiththeratioof theviscositiesforairandwater.Moreover,bothpermeabili- tieshavearelationshipwiththesquareporediameter,asthe Hagen–Poiseuilleequationpredicts.

SEMimagesshowedahigherporosityofthemembranes preparedwithstarch,whichalsohadhigherpermeability.This resultconﬁrmsthesuitabilityofstarchasaporeformerin thepreparationoflowcostceramicmembranes.Membranes preparedwithuniaxialpressingprovidedhigherpermeability thanthoseobtainedbyextrusion,forthesamecomposition ofthestartingmixture.

To sum up, a good correlation between both methods wasfound.Theconsistencybetweenthetwomethodsopens up the possibility of replacing mercury intrusion in some applications.Goodagreementwasalsoobtainedinthemea- surementsoftheporesizedistributionwidth(d16andd84).

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Acknowledgements

ThispaperincludesresultsoftheNITRAMEM(IPT-2012-0069- 310000) project, funded with a total amount of 870,455.39 EurosbytheMinistryofEconomyandCompetitivenessand theEuropeanRegionalDevelopmentFund(ERDF)oftheEuro- pean Union, INNPACTO through the program, which the authorsshowtheirgratitude.

Appendix A. Appendix

TheHagen–Poiseuille equation (2) was deducedfor anon- compressibleﬂuid.Foracompressibleﬂuiditcanbeexpressed as:

Qv=nr⁴ 8

dP

dl (A.1)

Sincethegasiscompressible,thevolumetricflowvaries withthepressure,anditispreferabletogivethevolumetric flowasafunctionofthemolarflow.Accordingtotheidealgas equationwehave:

PQv=FRT (A.2)

whereFisthemolarﬂow.SubstitutingEq.(A.2)inEq.(A.1)we obtain:

FRT=nr⁴ 8

PdP

dl (A.3)

Byseparatingvariablesandintegrating,withP₂andP₁as thepressureinretentateandpermeatesiderespectively,we obtain:

F= nr⁴ 16RT

(P²₂−P²₁)

l (A.4)

Eq.(A.4) hasbeenextensivelyusedtodescribethelaminar flowinaporousmembrane(e.g.[20]).However,ifthevolu- metricflowmeasuredatthemeanpressure(Pm=(P1+P2)/2)is definedby:

Qm= FRT Pm

(A.5)

itispossibletorewriteEq.(A.4)as:

Qm= nr⁴ 8

(P2−P1)

l (A.6)

ThusEq.(A.6)allowsthesameformoftheHagen–Poiseuille equationemployedforliquids(Eq.(2)),butusingasvolumetric ﬂowthevaluecalculatedatthemeanpressureinthemem- brane(Eq.(A.5)).

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