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Particuology12 (2014) 2–12

ContentslistsavailableatScienceDirect

Particuology

journalhomepage:www.elsevier.com/locate/partic

Anexperimentalandnumericalstudyofpacking,compression,andcakingbehaviourofdetergentpowders

SubhashC.Thakura,b,HosseinAhmadianb,JinSuna,JinY.Ooia,?

SchoolofEngineering,UniversityofEdinburgh,King’sBuildings,EdinburghEH93JL,UK

NewcastleInnovationCentre,ProcterandGambleTechnicalCentreLtd,NewcastleuponTyneNE129BZ,UK

article

info

abstract

Articlehistory:

Received22April2013

Receivedinrevisedform21June2013Accepted27June2013

Keywords:

DiscreteelementmethodPowder?ow

CohesivematerialUniaxialtestPlasticity

Contactmodel

Thispaperpresentsanexperimentalandnumericalstudyofthepacking,compression,andcakingbehaviourofspraydrieddetergent(SDD)powderswithatwo-foldaim:anexperimentalprocessofobservationandevaluationofthepacking,compressionandcakingbehaviourofSDDpowders,andanumericalapproachbasedondiscreteelementmodelling(DEM).Themechanicalproperties,includingthestress–strainresponseandthecorrespondingporositychangeasafunctionofconsolidationstressinacon?nedcylinder,thestress–strainresponseduringuncon?nedshearingandthecakestrengthasafunc-tionofconsolidationstress,wereevaluatedandcomparedfordifferentSDDpowdersusinganextendeduniaxialtester(EdinburghPowderTester–EPT).TheexperimentsusingEPTshowedexcellentrepro-ducibilityinthemeasurementofpacking,compressionandcakingbehaviourandwerethereforeveryusefulfordescribingthehandlingcharacteristicsofthesepowderedproductsincludingscreeningnewproductsanddifferentformulations.Itwasfoundthatthesamplewithhighermoisturehadlowerbulkporositybuthighercompressibilityandcakestrength.Theporosity,compressibilityandcakestrengthwerefoundtovaryacrossdifferentsizefractionsofthesamesample.Thelargersieve-cutsampleshadhigherinitialbulkporosity,compressibilityandcakestrength.Itisrevealedthatmoistureplaysasig-ni?cantroleinpacking,compression,andshearingbehaviourofthepowder.Three-dimensionalDEMmodellingusingarecentlydevelopedelasto-plasticadhesive-frictionalcontactmodelshowedthatthecontactmodelisabletocapturethedetergentbehaviourreasonablywellandcanbeusedtomodelcomplexprocessesinvolvingthesepowders.

? 2013 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of

1.Introduction

Powderpacking,compressibility,and?owabilityareimportantmeasuresforindustrialparticulatesolids,suchashouseholdandpersonalcareproducts,chemicals,fertilizers,coal,cements,explo-sives,dyesandpigments.Thepackingbehaviourofapowderinacontainerisdeterminedbyitsinitialmicrostructureandtheensu-ingmechanicalprocessesincludingcompression,shear,vibrationandimpact,whichoccurduringtransportation,forexample.Forthemanufacturingofparticulatedetergents,bulkporosityisanimportantvariabletocontrolsincemostconsumerdosesaremea-suredbyvolumeandthesolubilityofdetergentpowdersnormallyincreasewithincreasingporosity.Inaddition,thecompressibilityofpowderscanin?uencetheirappearanceandvolumeincontain-ersoncetheyreachconsumers.Cakingisaphenomenonwhere

?Correspondingauthor.

E-mailaddress:j.ooi@ed.ac.uk(J.Y.Ooi).

free?owingpowdersaretransformedintolumps,aggregatesoreventuallyintoacoherentmass.Cakingofpowdercanhaveadverseeffectsonsolubility,mixing,anddispersionresultinginlossofproducts,delaysinlaunchandconsumercomplaints.Itcanalsocausestorageandhandlingrelatedproblemsincludinghopper/binarchingandratholing,resultinginno?ow.AccordingtoanestimatebyGrif?th(1991),thecostofunproductivecakeproductswasinanexcessof1billionUSDintheUSAalonein1985.Thepackingofporouspowderisgovernedbyinter-particleandintra-particleporosity.Severalfactorsincludingparticleshape,absolutesize,sizedistribution,andsurfaceproperties(stiffness,friction,andadhesion),affectinter-particleporosity.Inadditiontoparticlepropertiesinter-particleporositymayalsodependonsize,shape,androughnessofthecontaineraswellasthemethodandintensityofdeposition(Yu,1989).Itisgenerallyacceptedthatdeviationofparticleshapefromspheretendstoincreasetheinter-particleporosityofmono-sizedparticles(Yu&Standish,1993).Porosityisfoundtobeindependentofparticlesizeforparticlesizesabove100?m(Yang,Zou,&Yu,2000).Forparticle

http://dx.doi.org/10.1016/j.partic.2013.06.009

S.C.Thakuretal./Particuology12 (2014) 2–12

NomenclatureCucoef?cientofuniformity

D60diameterofparticleat60%passing(m)D10diameterofparticleat10%passing(m)eco-ef?cientofrestitutionf0constantadhesion(N)fncontactnormalforce(N)ftcontacttangentialforce(N)

fctcoulomblimitingtangentialforce(N)fndnormaldampingforce(N)ftstangentialspringforce(N)ftdtangentialdampingforce(N)fhys

hystereticspringforce(N)

fts(ntangentialspringforceatprevioustimestep(N)?1)k1loadingstiffnessparameter(N/m)

k2unloading/reloadingstiffnessparameter(N/m)kadhadhesivestiffnessparameter(N/m)kttangentialstiffness(N/m)

m*equivalentmassoftheparticles(kg)nnon-linearindexparameteráinterinterparticleporosityáintraintraparticleporosityápparticleporosity

distancefromthecontactpointtotheparticlecen-treofmass(m)

??n

relativenormalvelocity(m/s)

vpores

speci?cvolumeofmercurypenetratingtheparticlepores(L/kg)

??trelativetangentialvelocity(m/s)wmoisturecontent(%)

ˇnnormaldashpotco-ef?cientˇttangentialdashpotcoef?cient?angleofshearingresistance(?)??ftsIncrementaltangentialforce(N)?normaloverlap(m)

?maxmaximumnormaloverlap(m)?pplasticoverlap(m)

??sskeletaldensityorparticledensity(kg/m3)??bbulkdensity(kg/m3)ásamplebulkporosity??co-ef?cientoffriction

??rcoef?cientofrollingfriction??itotalappliedtorque(Nm)

ωi

unitangularvelocityvector(radian/s)

diameterssmallerthan100?m,theratioofinter-particleforcetotheweightofparticlescanbegreaterthanunity(Krupp,1967),resultingindifferentpackingbehaviour.Higherinter-particleforceratioscauseformationofchain-likestructureleadingtohighporosity(Yangetal.,2000).Forcohesionlesspowders,asthespreadoftheparticlesizedistribution(PSD)increases,theporositydecreasesbecausethesmallerparticles?lltheporesbetweenlargerparticles.TheeffectofPSDonporosityofcohesivematerialisnotverywellunderstoodandisin?uencedbythecomplexadhesiveforcesthatexist.Inaddition,theintra-particleporosityofapowdermaydependonchemicalcomposition,andshrinkageorpuf?ngeffectduetodrying(Hecht&King,2000a,2000b).

Thepowdercompressibilitymayresultfromparticlerearrangement,breakageoflooselybondedagglomeratesintoprimaryparticles,failureoftheparticleduringelasto-plasticdeformation,andfragmentationoftheprimaryparticles(Heckel,1961;Hersey&Rees,1970).Thesemechanismsdonothappen

insequenceandusuallyoverlapeachother(Hersey&Rees,1970).Foragglomeratedcohesivepowderssubjectedtoincreasingconsolidationstress,particlesarelikelytoundergorearrangementandlooselybondedagglomeratemaybreakwithoutexcessivedeformationattheparticlecontacts.Therearrangementoftheparticlewilldependontheparticleshape(Cho,Dodds,&Santamarina,2006;Güden,Celik,Hizal,Altindis?,&Cetiner,2008),sizeandsizedistribution(Hersey&Rees,1970),rollingandstaticfriction(Sheng,Lawrence,Briscoe,&Thornton,2004),andadhesion(Mehrotra,Chaudhuri,Faqih,Tomassone,&Muzzio,2009).Thebreakageofanagglomeratewillalsodependonbondstrength.Astheconsolidationstressisincreased,elasto-plasticdeformationoftheparticlesleadstosquashingandreductioninintra-andinter-particleporosity.Onfurtherapplicationofstress,fragmentationoftheprimaryparticlemayoccurandexcessivedeformationmayleadtoworkhardening.

Thecakestrengthofpowderatanappliedconsolidationstressisaffectedbyparticlesize,sizedistribution,friction,shape,humidity,moisturecontent,plasticdeformationandadhesionattheparti-clecontactetc.Severalexperimentsincludingshearcells(Jenike,annular,andPeschl),tensiletest,creeptest,penetrationtest,cak-ingindextest,blowtest,anduniaxialtesthavebeenusedforthemeasurementofcakingpropensity(Cleaver,2008).Eachtesterhasitsownadvantagesanddisadvantages,whichwereexplainedbySchwedes(2003).Uniaxialtesthaswidelybeenusedtostudythecakingorshearbehaviourofpowders(Bell,Catalano,Zhong,Ooi,&Rotter,2007;Enstad&Ose,2003;Freeman&Fu,2011;Parrella,Barletta,Boere?jn,&Poletto,2008;R?ck,Ostendorf,&Schwedes,2006;Williams,Birks,&Bhattacharya,1971;Zhong,Ooi,&Rotter,2005)inindustrialpracticebecauseofitssimplicityandrapidityinconductingatest.Repeatabilityofmeasurementisoneofthemajorconcernsforuniaxialtesters.Anextendeduniaxialtester,theEdin-burghPowderTester(EPT),hasbeendevelopedattheUniversityofEdinburgh,withafocusonrobustness,repeatabilityandspeedforindustrialsolidsmeasurement(Belletal.,2007).

Thediscreteelementmethod(DEM)hasincreasinglybeenusedtomodeldiscretephenomenaincludingpowderpacking(Dong,Yang,Zou,&Yu,2006;Yangetal.,2000;Yang,Zou,Dong,An,&Yu,2007;Yen&Chaki,1992),compaction(Morgeneyeretal.,2005;Redanz&Fleck,2001;Samimi,Hassanpour,&Ghadiri,2005;Shengetal.,2004),andpowder?ow(Baxter,Abouchakra,Tüzün,&MillsLamptey,2000;David,García-rojo,Herrmann,&Luding,2007;Ludingetal.,2004;Mehrotraetal.,2009;Moreno-Atanasio,Antony,&Ghadiri,2005).TodatetheDEMmodellingofcohesivepowdershasbeenlesssuccessfulinproducingquantitativepredic-tions.

Themajorobjectiveofthispaperistostudypacking,compres-sion,andcakingbehaviourofspraydrieddetergentpowdersusingtheEPT,andtomodelthefullspectrumoftheloadingregimesfromcompressiontoshearfailureusingDEM.TheEPTisusedtomeasurethemechanicalpropertiesincludingthestress–strainresponseandthecorrespondingporositychangeasafunctionofconsolidationstressinacon?nedcylinder.Inaddition,thestressstrainresponseduringuncon?nedshearingandthecakestrengthasafunctionofconsolidationstressisevaluated.Thephysicalpropertiesofthepowders,whichmayaffectthemechanicalproperties,arealsomeasured.Theseincludemoisturecontent,particlesize,sizedis-tribution,shape,inter-andintra-porosity.DEMmodellingisthenusedtosimulatethepacking,compressionandshearbehaviour,whichiscomparedwiththeexperimentsforoneexampledeter-gentpowder.Thesimulationsutilisedarecentlydevelopedcontactmodelthatuseshystereticnon-linearloadingandunloadingpathstomodeltheelasto-plasticpermanentcontactdeformationandanadhesionparameterwhichisafunctionofthemaximumcontactoverlap(Thakur,Morrissey,Sun,Chen,&Ooi,2011).

4S.C.Thakuretal./Particuology12 (2014) 2–12

Table1

Distributionofmoisturecontent(%)acrossdifferentsizefractions(n=3).

Sizefractions

SampleA

SampleB

RSD(%)

Bulk

2.292.394.742.70>500?m2.554.994.964.24500–250?m2.303.304.432.50<250?m

2.12

4.30

4.17

4.80

Notes:n=numberofsamples,M=mean,

RSD=relative

standard

devia-

tion=standarddeviation/mean.

2.Materialsandphysicalpropertiesmeasurement

2.1.Materials

Inthisstudy,spraydrieddetergent(SDD)powderswereinves-tigated,whichconstitute60–70%ofthecommerciallyavailabledetergentwashingpowdersandarethemostcommondetergentpowderssoldworldwidewithbillionsofdollarssales.TwoSDDpowdersproducedwithalowmoisturecontent(SampleA)andahighmoisturecontent(SampleB)wereselected,coveringarangeofuncon?nedyield(cake)strength.Thechemicalcompositionandmoisturecontentofspraydriedpowdersvaryacrossdifferentsizefractions.Therefore,thespraydriedpowderswereseparatedintothreedifferentsizefractions,<250?m(smallsize),250–500?m(mediumsize),and>500?m(largesize).Testswereconductedonbulksamplescoveringallparticlesizerangeaswellasdifferentsizefractions.

2.2.Measurementofpowderphysicalproperties

Beforeanymeasurementonthespecimenismade,itisvitalthatarepresentativesampleisobtained.Inthisstudythesamplesobtainedfromaspraydriedtowerwas?rstmixedinarotarymixertogetahomogenoussampleandalsotoreducethebulkpowderdowntoa5kgbatch.Thepowderisthenfurthersampleddowntothe1kgsizeusingasplitsampler.Finally,thepowderissampleddowntorequiredsizesusingaPascalturntablesampledivider,aspinningsampledivider.TherotationspeedandvibrationlevelsinaPascalturntablesampledividerwerechosentoprovideauniform?owofpowder.Sincespraydriedpowdersaresensitivetomoistureandhumidity,thepowderswerepackedandsealedinairtightcontainersforfurthertesting.

Thepowdermoisturecontent,particlesizeandsizedistribu-tion,inter-plusintra-particlepore,andshapewerecharacterised,usingmoisturebalance,mechanicalsieveanalysis,gaspycnome-try,mercuryporosimetry,andscanningelectronmicroscope(SEM).Moisturecontentbyweightwasmeasuredusinganoven-dryingmethod.Atemperatureof105?Candheatingtimeof24hwasused.ThemoisturecontentanditsdistributionacrossdifferentsizefractionsareshowninTable1.ThemoisturecontentsofSampleBwerehigherthanthoseofSampleAforallsizefractions.Addition-allyforbothsamples,thelargersizefractionshadhighermoisturecontentsthanthesmallersizefractions.Thiscouldbeduetotheagglomerationofprimaryparticlesintolargersizeswithhigherinternalmoisture.Itshouldbenotedthatthemoisturecontentisnotfreeandmobilesurfacemoisture;butrathermoistureafterthepowdershavegonethroughdryingprocessinaspraydryingtower.

ThesizedistributionsoftheSDDpowdersweremeasuredusingvibratingmechanicalsievesfollowingtheASTMD6913procedure.Theamplitudeandfrequencyofvibrationweresettominimisebreakageofagglomeratesandtoensurethoroughsievingofthesample.ThefullsizedistributionsofparticlesizeonweightbasisareshowninFig.1.ThemedianparticlesizesD50ofSampleAand

Fig.1.Particlesizedistributionofthespraydrieddetergentpowders.

SampleBwereapproximately480and390?mrespectively.Bothpowdershaveasimilarcoef?cientofuniformity,Cu,(D60/D10)of3.6.

Inter-andintra-particleporositywascharacterisedusingmea-surementsfromgaspycnometryandmercuryporosimetry.Agaspycnometer,AccupycII1340(Micromeritics,USA),wasusedtomeasureskeletaldensity(soliddensity),basedonagasdisplace-mentmethodtomeasurevolumeaccurately.Heliumgasisusedasitobeystheidealgaslawandisabletopenetratesmallpores(ASTMD5550,2006)duetoitssmallatomicnumber.HoweverHeliumdoesnotpermeateanyclosedpores.Theaveragevaluesofskeletaldensityfrom?verunsare1919and1910kg/m3forSampleAandSampleBrespectively.Therewasnosigni?cantdifferencebetweenskeletaldensitymeasurementsacrossdifferentsizefractions.

Poresizecharacterisationofthespraydriedsampleswascon-ductedusingmercuryporosimetry(AutoPoreIV,Micromeritics,USA).Theinstrumentprovidesawiderangeofinformation,e.g.theporesizedistribution,thetotalporevolume(inter-andintra-particlepores)orporosity,theskeletalandenvelopedensity.Theinstrumentcharacterisesamaterial’sporositybyapplyingvariouslevelsofpressuretoasampleimmersedinmercury.Thepressurerequiredtointrudemercuryintothesample’sporesisinverselyproportionaltothesizeofporesandgivenbytheWashburn’sequation(Washburn,1921).

AHitachiTM1000SEMwasusedinthisstudyforvisualinspec-tionofparticles.TheSEMphotographsofthreedifferentsizefractionsofSampleAandSampleBareshowninFigs.2and3,respectively.Asigni?cantamountofporeopeningscanbeseenonthesurfaceoftheparticles.NodiscernibledifferenceinshapeandtextureofrespectivesizefractionsofSampleAandSampleBwasfound.ItcanbeseenfromFigs.2and3thatthelargerparticlesarenotindividualbutagglomeratesofprimaryparticles.

2.3.Measurementofpowdermechanicalproperties

TheEPTwasemployedtomeasurethepacking,compression,andshearbehaviouroftheSDDpowders.ThemaindifferencesbetweenEPTandsomepreviousuniaxialtesterliesintheattentiontomechanicaldetails,thelevelofcaredirectedtotheconsolida-tionaswellasfailureloadapplication,andthestrategicintent(Belletal.,2007).ThediameteroftheEPTsamplemouldis40mmandtheheightcanbeupto80mm.Theheightofthespecimenismeasuredcontinuallywithabuilt-inlinearvariablevoltagetrans-former(LVDT)displacementtransducerofanaccuracyof0.1mmattachedtotheloadingpiston.Thepowdercompressibilitycanthenbeevaluatedfromthemeasurement.

ThephotographicillustrationoftheEPTtestprocedureisshowninFig.4.IntheEPT,thepowdersampleispouredintotheconsoli-dationcylinder.Thesampleisloadedbyapplyingaconstantweight

S.C.Thakuretal./Particuology12 (2014) 2–12

Fig.2.SEMphotographsofdifferentsizeSampleA:(a)passingthrough250?m,(b)between250and500?m,and(c)retainedon500?m.

Fig.3.SEMphotographsofdifferentsizeSampleB:(a)passingthrough250?m,(b)between250and500?m,and(c)retainedon500?m.

totheconsolidationcellandtheforceisrecordedbytheloadcellattachedtotheconsolidationplunger.Afterthesampleisloadedfor1min,theconsolidationplungerisautomaticallyliftedoffleav-ingtheconsolidatedsample.Themouldisthenmanuallysliddownthepedestal,exposingafreestandingcolumnofconsolidatedpowdersample.Thesampleisthenfailedbyamotordriventestpistonandthestress–strainresponseduringtheuncon?nedaxialloadingtofailurecanberecorded.Theloadingpistontravelswithaspeedof0.4mm/s.Thespeedofthepistonissochosenthatthetest

canbeconductedrapidly,andatthesametimeuncon?nedyieldstrengthisnotcompromised.WatanabeandGroves(1964)foundthatuncon?nedstrengthofdetergentsampleswasunaffectedifthepistonspeedwasvariedinarangeof0.084–0.43mm/s.

Thefrictionbetweentheparticlesandboundarymayaffectthecompressibilityofthepowdersinuniaxialtests(Enstad&Ose,2003).IntheEPT,boundaryeffectisminimisedbyallowingthepowdersampletocompressfromboththetopandbottom.Furthertominimiseanyeffectofboundaryfriction,thesample

Fig.4.(a)EdinburghPowderTester,(b)compression,(c)uncon?nedsample,and(d)crushedsample.

6S.C.Thakuretal./Particuology12 (2014) 2–12

aspectratio(sampleheightat1kPastresstodiameterratio)duringcon?nedcompressioniskeptinanarrowrangeof1.3–1.4.Duringuncon?nedcompression,thesampleaspectratioiskeptbetween1.2–1.4whichwasfoundtogiveverygoodtestreproducibilityinuncon?nedstrengthmeasurement.Previousstudieshavepro-posedanaspectratiooftan(45?+?/2)orlarger,where?=angleofshearingresistanceofthepowder,tominimisetheeffectofendplatefriction(Bishop&Green,1965;Rock&Schwedes,2005;Williamsetal.,1971).Williamsetal.(1971)arguedthatforlowervaluesofaspectratio,thefailureofthesamplecantakeplaceonlywhenpartofthespecimenslipsalongoneoftheendplatens,whichwouldrequireextraworktobedonecausinganincreaseinuncon?nedyieldstrength.However,thepresentstudyfoundthatevenwithaspectratiobetween1.2and1.4whichismuchsmallerthantan(45?+?/2),thefailedsampledidnotintersecttheendplaten(seeFig.4(d)foratypicalfailure).Ahigheraspectratiowouldalsoincreasetheeffectofwallfrictionandcauseagreaterdensityvariationacrosstheheightofthespecimenwhichcancompromisemeasurementreproducibility.

Itisfurtherproposedthatthesehighlyrepeatablebulkmea-surementscanbeusedforDEMmodelcalibration.Thesearethe(vertical)stress–strainandthestress–porosityresponsedur-ingcon?nedcompressionaswellasthe(vertical)stress–strainresponseduringuncon?nedcompressionincludingthepeakuncon?nedstrength.

3.Resultsanddiscussion

3.1.Experimentalresults

3.1.1.Packing

TheEPTwasusedtomeasurethebulkporosityofthepowderundercompression.Theinitialbulkporositywasmeasuredcor-respondingtoasmallappliedinitialstressof1kPa(approx).Thishelpstoreducethevariabilityofthe?llporositymeasurementandgiveastablemeasurementoftheinitialheightofthespecimenwithalevelsurface.Theheightandweightofthespecimenwereusedtocalculatetheaveragevalueofthebulkdensity(??b).Thesamplebulkporosity(á)canthenbecalculatedusing??b,moisturecontent(w),andtheparticledensity(??s)asfollows:

á??b

=1?

??.(1)

s(1+w)

However,inthisstudytheparticledensitywasmeasuredforthepowderwithmoisture,thereforethemoisturewasnotconsideredinporositycalculation,andporositywassimplycalculatedas:

á??b

=1?

??.s

(2)

Theporositycomprisesoftheinter-particleporesaswellastheopenandclosedintra-particlepores.However,theskeletalden-sitymeasurementoftheSDDsamplesbeforeandaftermillingwasfoundtobesimilar,indicatinginsigni?cantclosedporesinthesam-ples.TheaveragebulkporosityofSampleAandSampleBforfullsizefractionanddifferentsievecutfractionsareshowninTable2.Thebulkporositiesofthelargersievecutfractionsforbothsampleswerehighercomparedtothoseofthesmallersievecutfractions.AsitcanbeseenfromtheSEMimages(Figs.2and3)thelargerfractionsareagglomeratesoftheprimaryparticles.Inadditiontotheintraandinter-particleporosity,theinter-agglomerateporos-ityalsocontributestothetotalporosityleadingtoahigherporosityforthelargerfractions.

ThebulkporosityofthefullsizefractionofSampleAwasfoundtobehigherthanthatofSampleB(seeTable2).IndeedthebulkporositiesofdifferentsizefractionsofSampleAwereconsistently

Table2

Initialsampleporosity(%)measurementsforSampleAandSampleBpowders.

Sizefractions

SampleA

SampleB

RSD(%)

Allfractions(n=3)72.50.3669.60.35>500?m(n=1)77.7–75.2–500–250?m(n=1)75.4–72.8–<250?m(n=1)

72.2

–

69.8

–

NB:n=numberofmeasurements;initialporositytakenataconsolidationstressof1kPa.

higherthanthecorrespondingfractionsofSampleB.Thiswasdeemedcounterintuitiveconsideringthatbothsampleshavesim-ilarshape,morphologyandgradation,exceptahighermoisturecontentforSampleB.Onemightspeculatethatahighermois-turecontent(SampleB)couldleadtoamore-openstructureandahigherporosityresultingfromhigheradhesiveforcesattheparti-clecontacts(assumingthatmoistureisatthecontacts).Itshouldbenotedthatthemicrostructureofspraydriedpowdercomprisesporousprimaryparticlesandagglomeratesoftheseprimarypar-ticles.Suchamicrostructurecannotbeeasilyde?nedbyasinglevalueofbulkporosity.Therefore,acombinationofmeasurementsusingmercuryporosimetryandgaspycnometrywasusedtoesti-mateporositybetweentheparticles(inter-porosity)andporosityinsidetheparticles(intra-particleporosity).Inter-particleporositywascalculatedas:

áinter=1???b

??s(1?áp)

(3)whereáinteristheinter-particleporosity,andápistheparticleporositywhichwascalculatedas:

áp=

vpores

(v(4)

pores+,

(1/??s))

where,vpores=speci?cvolume(mL/g)ofmercurypenetratingtheparticlepores.

Thefractionoftotalvoidspaceinasamplecontributedbypar-ticleporosityistermedasintra-particleporosityandexpressedas:

áintra=áp(1?á).

(5)

Becauseofdif?cultyinseparatinginter-andintra-particlesforfullsizefractionsamples,inter-andintra-porositywasestimatedforthe250–500?mnarrowsizefractionsassumingthattheintra-porositymeasurementwillbevalidforothersizefractionsandfullsizefraction.Theassumptionisreasonablesinceintra-particleporosityrelatestoprimaryparticlesandshouldbeindependentofsizeofagglomerates(i.e.differentsizefractions).Table3showsthebreakdownofthetotalporosityfor250–500?mfortheSDDpowdersintermsofinter-andintra-particleporosity.Theinter-particleporosityofSampleBwas2.6%higherthanthatofSampleAwhichisindeedconsistentwiththepropositionofincreasinginter-particleporositywithincreasingmoisturecontent.However,theintra-particleporosityforSampleAwas5.2%higherthanthatofSampleBwhichmaskedthehigherinter-particleporosityin

Table3

Breakdownofbulkporosity(%)fortheSDDpowdersample(250–500?m).

Typesofporosity

SampleA

SampleB

RSD(%)

Bulkporosity

75.4–72.8–Intraparticleporosity21.380.8516.193.45Interparticleporosity

54.02

–

56.61

–

S.C.Thakuretal./Particuology12 (2014) 2–12

SampleBandledtoahigheroverallporosityfortheSampleA.Thehigheramountofintra-particleporosityforSampleAcanbeattributedtothewaythesampleswereprocessedinthespraydry-ingtower.SampleAwasexposedtoslightlyhighertemperatureinthespraydryingtowercausingpuf?ngorshrinkingandleadingtomoreporousprimaryparticles.

3.1.2.Con?nedcompressionanddecompression

Thecompressionprocesswasstudiedbyplottingtheaxialstress–strainmeasurementsandtheporosity-stressmeasure-ments.Fig.5(a)showstheaxialstrainforthreespecimensofSampleAandSampleBasafunctionoftheconsolidationstressandFig.5(b)showsthecorrespondingporosityvariationasafunctionofconsolidationstress.SampleBexhibitedahigheroverallcom-pressibilitythanSampleAdespitethefactthattheinitial(bulk)porosityofSampleBwaslower.InFig.5(b),thepowdercom-pressionprocesscanbedividedintotwostages;stageIrelatingtoparticlerearrangement(mostlycompressionofinter-porosity),andstageIIwhentheelasto-plasticdeformationcausingsquashingofbothinter-andintra-particleporositybegantodominate.Itcanbeseenthatattheonsetofconsolidationtheporositydecreasedsharply(stageI).DuringstageIIastheconsolidationprogressed,theporosityvariedlinearlywitha?atterslopecomparedtostageI.ThesteeperslopeoftheporositystresscurveforSampleBindicateslargerparticlerearrangementduringstageI,andlargerelasto-plasticdeformationforstageII.ThelargerparticlerearrangementofSampleBcanberesultingfromhigher(2.6%for250–500?msize)inter-particleporositycomparedtoSampleA(Table3).Thelargerelasto-plasticdeformationinstageIIforsampleBmaybearisingfromhighermoistureincreasingtheplasticityatcontacts(Okasanen&Zogra?,1990)andagglomeratebreakageduetoweak-eningofthesolidbridges(Yan&Barbosa-Canovas,1997,2001).Oncethedesiredconsolidationstresswasreached,thesamplewasunloadedandthesampleheightwasrecordedtocalculatetheconsolidatedporosity(denotedbypointsonX-axis,seeFig.5(b)).Noneofthepowdersreturnedtotheinitialporosityuponunloadingindicatingsubstantialplasticdeformationarisingfromtheparticlerearrangement,breakage,andplasticdeformationatthecontacts.AscanbeseenfromFig.5(b)themaximumdifferenceinporos-itymeasurementsforeachofthepowdersatanyspeci?cappliedstresswaslessthan0.5%(seeerrorbars)indicatingahighlevelofreproducibility.

Fig.6(a)showsaxialstress–strainbehaviourandFig.6(b)showscorrespondingporositychangeasafunctionofconsolidationstressfordifferentsieve-cutfractionsofSamplesAandB.Whilecom-paringdifferentsizefractionsofthesample,thelargersieve-cutfractioncompressesmore,whichcouldberelatedwithcompres-sionoflargerinter-agglomeratepore,breakageofthelargesizeagglomerates,andlargerplasticdeformation.Ithasbeenfoundinliteraturethatasthesizeoftheagglomerate(foodpowder)increasedahighervolumereductionforlargesizeagglomeratesduringcompressioninacylindricalmouldwasfound(Yan&Barbosa-Canovas,1997).Theparticlesizeeffectonbreakagewasexplainedbythelargerparticleshavingmoreedgesorcornersontheirsurfacethanthesmallerones,resultinginmoreabrasionandchipping.Whilecomparingcompressionbehaviourofcorrespond-ingsieve-cutsamplesoftwoSDDpowders,sampleAcompresseslessshowingasimilartrendtothefullsizefraction.

Inaddition,alargergradientinporosity-stresscurve(forbothstageIandstageII)isfoundforSampleB.Forexample,thedecreaseinbulkporosityfor250–500?msampleBwas0.2%and0.5%higherthanthesamesizefractionsampleAforstageIandstageII,respec-tively.ThisagainindicateslargerparticlerearrangementinstageIandlargerelasto-plasticdeformationinstageIIforSampleB.

3.1.3.Uncon?nedcompressionand?owfunction

Theuncon?nedstress–strainbehaviourforallsampleswasobtainedbuttheresultsarepresentedonlyforfullsizerangeSDDpowders.Fig.7showstypicalstress–strainbehaviourduringuncon?nedcompressionforfourdifferent(20–80kPa)consolida-tionstresses.Thepeakstressatwhichthesamplefails(denotedbydropdowninstress)isknownastheuncon?nedyieldstrength.Veryofteninliteratureonlytheuncon?nedyieldstrengthasafunc-tionofconsolidationstressisreported.However,theareaundertheuncon?nedstress–straincurveisrelatedtotheenergyrequiredtofailthesampleandneedstobecapturedintheDEMsimula-tions.Itcanbeseenthatboththeuncon?nedstrengthandtheareaunderthecurveincreasewithincreasingconsolidationstressforbothsamples.

Fig.8showstherelationshipbetweenuncon?nedstrengthandconsolidationstress,otherwiseknownas?owfunction.Therepro-ducibilityofEPTwastestedforfullsizerangeSDDbulksamples.Therelativestandarddeviation(RSD)at37kPaofconsolidationstressforSampleAandSampleB(3testseachonfreshsamples)werefoundtobe4.8%and2.8%,respectively.Whilstthreedatapointswouldnotusuallybeconsideredsuf?cientforrigorousstatisticalanalysis,thelowRSDindicatesthatthereproducibilityofEPTisveryhigh.

TheSampleBdisplayedhigheruncon?nedstrengthatthesameconsolidationstress.Themostplausibleexplanationisthatmois-tureincreasesstickinessandplasticityofthecontactleadingtohigheruncon?nedstrength.HigherplasticdeformationhasbeenobservedforSampleBduringcon?nedcompression(seeFig.5).Forthedifferentsieve-cutfractionsofSampleB,largersieve-cutfrac-tionsshowedhigheruncon?nedstrengthcomparedtosmallsievecutfractions(forthelargerthan500?mfractionconsolidatedat77kPa,theuncon?nedstrengthexceededthe45kPalimitoftheloadcell).Theplausibleexplanationforlowerstrengthassociatedwith?nerparticlesisthatthe?nefractionscontainadispropor-tionateamountofanticakingagentswhichreducestheadhesionbetweenparticlesandthat?nefractionshaveaslightlylowermois-turecontentcomparedtothecoarserfractions.Incontrast,thecoarserparticleshavehighermoisturecontentandhaveshownpreviouslytodeformmoreplastically(seeFig.6(a))comparedtosmallsizeparticles,whichmayprobablygiverisetohighercon-tactareaandthereforehigheradhesion.Thisisconsistentwithprevious?ndingsthatsmallincreaseinmoisturecontent(0.6%)producedsigni?cantincreaseincakestrength(64%)ofSDDpow-ders(Watanabe&Groves,1964).

3.2.DEMsimulation

3.2.1.Elasto-plasticadhesivecontactmodel

ADEMcontactmodelbasedonthephysicalphenomenaobservedinadhesivecontactexperimentshasbeenproposed(Jones,2003).Whentwoparticlesoragglomeratesarepressedtogether,theyundergoelasticandplasticdeformationsandthepull-off(adhesive)forceincreaseswithanincreaseoftheplasticcontactarea.Anon-linearcontactmodelthataccountsforboththeelasto-plasticcontactdeformationandthecontact-areadependentadhesionisproposed.However,thelinearversionofthecontactmodelisusedinthisstudy(Fig.9(b)).Theschematicdiagramofnormalforce-overlap(fn??)forthismodelisshowninFig.9.

ThiscontactmodelhasbeenimplementedthroughtheAPIinEDEM?v2.3,acommercialDEMcodedevelopedbyDEMSolutionsLtd(2010).Thetotalcontactnormalforceissumofhystereticspringforce,fhys,andnormaldampingforce,fnd,andisgivenbyEq.(6):

fn=(fhys+fnd)u,

(6)

8S.C.Thakuretal./Particuology12 (2014) 2–12

Fig.5.(a)Con?nedstress–strainand(b)porosity–stressbehaviouroffullsizerangeSampleAandSampleB.

Fig.6.(a)Con?nedstress–strainand(b)porosity–stressbehaviourofdifferentsievecutfractionsofSampleAandSampleB.

Fig.7.Uncon?nedstress–strainof(a)SampleAand(b)SampleB.

Fig.8.Flowfunctions(a)foruncutSampleBandSampleA,and(b)fordifferentsizefractionsofSampleBandSampleA.COVdenotescoef?cientofvariation,theabsolutevalueofwhichistheRSD.

S.C.Thakuretal./Particuology12 (2014) 2–12

Fig.9.Non-linear(a)andlinear(b)normalcontactforce–displacementfunction.

where,uistheunitnormalvectorpointingfromthecontactpointtotheparticlecentreandfhysisgivenbyEq.(7):

f+k?n??01

allowedbyshearslider,thetangentialforceissetequaltothe

maximumfrictionalvalue,fct:

nifk2(?n??np)≥k1?;

fct≤??|fhys+kadh?n|,

(15)

fhys=

f0+k2(?n??np)

nifk1?n>k2(?n??np)>?kadh?;

(7)

f0?kadh?n

ifkadh?n≥k2(?n??np);

wheref0isconstantadhesion,?isnormaltotaloverlap,?pisnormal

plasticoverlap,k1isthevirginloadingstiffnessparameter,k2istheunloading/reloadingstiffnessparameter,kadhistheadhesivestiffnessparameter,andnisthenon-linearindexparameter.ThedampingforceisgivenbyEq.(8):

where??isthecoef?cientoffriction.

Forthetorquecalculation,thedefaultEDEMrollingfrictionmodelisadoptedinthisstudy.Thetotalappliedtorque,??i,isgivenby:

??i=???r|fhys|Riωi,

(16)

fnd=?ˇnvn,

(8)

where??nisthemagnitudeoftherelativenormalvelocity,andˇnisthenormaldashpotcoef?cientexpressedas:

where??risthecoef?cientofrollingfriction,Riisthedistancefromthecontactpointtotheparticlecentreofmassandωiistheunitangularvelocityvectoroftheobjectatthecontactpoint.Fur-therdetailsaboutthecontactmodelcanbefoundinthepaperbyThakur,Morrissey,etal.(2013).

ˇn=

4m?k11+(??/lne)

(9)

withtheequivalentmassoftheparticlesm*,andthecoef?cientof

restitutionede?nedinthesimulation.

Thecontacttangentialforce,ft,issimilarlygivenbythesumoftangentialspringforce,fts,andtangentialdampingforce,ftd.,asgivenbyEq.(10):

ft=(fts+ftd).

(10)

Thetangentialspringforceisexpressedinincrementalterms:fts=fts(n?1)+??fts,

(11)

wherefts(n?1)isthetangentialspringforceattheprevioustimestep,and??ftsistheincrementofthetangentialforceandisgivenby:

??fts=?kt?t,

(12)

wherektisthetangentialstiffness,and?tistheincrementofthetangentialspring.Thetangentialdampingforceisproductoftan-gentialdashpotcoef?cient,ˇt,andtherelativetangentialvelocity,??t,asgivenbyEq.(13):

ftd=?ˇtvt.

(13)

Thedashpotcoef?cientˇtisgivenby:

ˇt=

4m?kt1+(??/lne)

(14)

ThetotaltangentialforceislimitedbyCoulombfrictionlaw.

Thatis,ifthefrictionforceisgreaterthanmaximumshearforce

3.2.2.Modelimplementation

Thereareseveralchallengesinmodellingcohesivepowderatindividualparticlelevel.First,itiscomputationallyprohibitivetomodeleachandeveryindividualparticleandthecohesionaris-ingfromseveraldifferentphenomenaincludingvanderWaals,capillarybridge,andelectrostaticforcesseparately.Second,realparticlesarenotsphericalandcanhavesurfaceasperitiesandcon-tactoccursnotatasinglepointbutthroughmultipleasperities.Finally,itisverydif?culttomeasureinputparametersinclud-ingadhesiveforce,contactstiffness,coef?cientofrestitutionetc.forcohesivepowders.Forexample,enormousscatterindatahasbeenreportedinmeasurementofadhesivepull-offforceusingAFMmeasurement(Heimetal.,2005;Tykhoniuketal.,2007).Inourapproach,thefocusisonanintermediatescalebetweenthemicro-andmacro-scales,aimingataphenomenologicalcontactmodelthatcanreproducethebulkcohesivestrength,stresshistorydependency,andotherbehaviourevidencedinbulkexperiments.

Asa?rststeptowardscalibrationofDEMmodelparameter,asimpli?edlinearversionofthecontactmodel,i.e.,parametern=1(Luding,2008;Walton&Braun,1986)isused(seeFig.9(b)).Thecohesivecontactmodelwasonlyappliedtoparticle-particleinter-actions.Theparticle-geometryinteractionsweremodelledusingtheHertz-Mindlin(no-slip)contactmodelandhencenoparticle-geometryadhesionwaspermitted.Forthisinvestigation,theDEMparameterswereestimatedtomatchprimarilythecompressionandtheuncon?nedstrengthofSampleBretainedon500?msieve.TheDEMinputparametersusedarepresentedinTable4.Anexten-siveparametricstudyisunderwaytodeveloparobustcalibrationmethodologywhichshouldpermitarigorousmodelcalibrationinthenearfuture.

Thegeometricsimilaritybetweentheexperimentsandsimula-tionswasmaintainedbyusingthesamediametermould.Inorderto

Table4

Simulationparameters.

S.C.Thakuretal./Particuology12 (2014) 2–12

Numberofparticles

Loadingspringstiffness,k1(N/m)Unloadingspringstiffness,k2(N/m)Adhesiveforce,f0(N)

Adhesiveparameterstiffness,kadh(N/m)Particlestaticfriction,??sfParticlerollingfriction,??rfWallfriction,??wf

TopandbottomplatenFriction,??PfCoef?cientofrestitution,eDEMtimestep,ts(s)

35001×1064×106–0.0042×1060.60.0010.40.40.4

4.6×10?6

(2)con?nedconsolidationtotherequiredstresslevelandsubse-quentunloading;and(3)uncon?nedcompressionofthesampletofailureaftertheremovalofthemould.TheprocessisvisualisedinFig.11.Therandomrainfallmethodwasadoptedtoprovidearandompackingofparticles.Toensurethatthesystemreachedaquasi-staticstate,loadingonlycommencedwhenthekinetictopotentialenergyratiowaslessthan10?5withaconstantcoordina-tionnumber.Thecon?nedconsolidationprocesswasconductedbymovingthetopplatendownwardataconstantspeedof10mm/s(strainrate≈0.14s?1)toapplyaverticalcompression.Aftercon-solidatingthesampletothedesiredstress,theloadontheassemblywasreleasedbymovingthetopplatenupwardatthesamecon-stantspeed.Thelateralcon?ningwallswerethenremovedandtheuncon?nedsamplewasallowedtorelaxforashortperiodoftime(0.1s).Thisallowedthekineticenergygeneratedfromtheremovalofthecon?ningwallandupwardretreatofthetopplatentodissipate.Thesamplewasthencrushedtofailurebymovingthetopplatendownwardagainataconstantrateof5mm/s(strainrate≈0.1s?1).

Fig.10.Pairedparticlewithaspectratioof1.5.

predictthemechanicalbehaviourofrealadhesivefrictionalmate-rialwhichisneithersphericalnorsmooth,itisimportantthatnon-sphericalshapeisconsideredtomimicthegeometricinter-lockingthatexists.Inthissimulation,thecylinderwas?lledwith3500non-sphericalparticles,eachconsistingoftwooverlappingspheresof2mmdiametergivingaparticleaspectratioof1.5(Fig.10).ItshouldbenotedthattheDEMparticlesinthisstudyaremesoscopicrepresentationofthedetergentpowders.AstudyonnumericalscalingofDEMparametersinuniaxialtesthasshownthatiftheDEMinputparametersarescaledproperly,sizeindepen-dentbulkstress–strainresultscanbeobtained(Thakur,Ahmadian,etal.,2013).Therefore,particlesizelargerthanrealisticsizepar-ticlesisused.Theparticlesizedistributioncanhaveaneffectonthebulkbehaviourbutisnotconsideredinthissimulationwhereadetergentpowderwithanarrowsizerangehasbeenchosenforcomparison.

Eachsimulationconsistsofthreestages:(1)?llingthecylin-dricalmouldtoformtheinitialpackingusedforallstresslevels;

3.2.3.Simulationresults

SampleBwithparticlesizerange500–2000?mischosenforDEMmodelcalibration.Thecompressionanddecompressionbehaviour(stress–strainandchangeinporosity–stress)isshowninFig.12.Thepredictedstress–strainresponsematchesverywellwiththeexperimentalstress–strainbehaviourofSampleBwithparticlesizerange500–2000?m.However,thereisadiscrepancyinporosity–stressbehaviourwiththeDEMpredictingalowerini-tialporosity.Thiscanbeattributedtothehighlyirregularshape,intra-particleporosity,andsurfaceasperitiesofSampleBasshownbytheSEMphotographs(seeFig.3(c)),whichhavenotbeenproperlyaccountedforintheDEMmodel.Thiswarrantsfurtherinvestigationintotheinteractionbetweeninter-andintra-particleporosityonpackingandcompressibilitybehaviourofcohesivepowder.However,whenchangeinporosityisplottedagainstappliedconsolidationstress,theresultsshowreasonableagree-mentbetweenthesimulationandtheexperiments(seeFig.12(b)).Fig.13(a)and(b)comparessimulationandexperimentalresultsfortheuncon?nedloadingresponse(tofailure)andthe?owfunction,respectively.Thecomputedpeakuncon?nedstrengthcomparesreasonablywellat37kPaconsolidationstress.How-ever,theinitialstiffnessinDEMsimulationwassteeperthantheexperiments.Furthermore,overconsolidationbehaviourwasnotobservedinthesimulations.ThiscouldbeduetothefragilenatureoftheSDDpowdersundergoingbreakageduringshearing.From

Fig.11.Snapshotsofuniaxialtestsimulations:(1)?lling,(2)con?nedconsolidation,and(3)uncon?nedcompression.

S.C.Thakuretal./Particuology12 (2014) 2–12

Fig.12.Con?nedstress–strain(a)andporosity–stressbehaviour(b)(simulationvs.experiments).

Fig.13.Uncon?nedstress–strainbehaviour(a)and?owfunction(b)forsimulationandexperiments.

Fig.13(b),the?owfunctionresultfromDEMsimulationscom-paresreasonablywelltoexperimentalresults,especiallyathigherconsolidationstresses(40–60kPa).

4.Conclusions

Thepacking,compressionand?owabilitybehaviouroftwospray-driedpowdersmanufacturedattwodifferentmoisturecontentshavebeenstudiedusingtheEPTuniaxialtester.TheEPTprovidedhighlyreproduciblemeasurementsofthecon?nedcom-pression(givingtheporosity-stressfunction)andtheuncon?nedcompressiontofailure(givingthe?owfunction)ofthepowders:thesecanbeveryusefulindescribingthehandlingcharacteris-ticsofthesepowderedproductsincludingscreeningnewproducts,studyingformulationchangesandtheeffectofanticakingagent.Comparingthetwomanufacturedpowders,thelowmoisturesamplehadhigherintra-particleporosityandlowerinter-particleporosity,resultinginahigheroverallporosity.Howeverthehigherintra-particleporositydidnotleadtoahighercompressibilityunderload.Forthehighmoisturesample,thehighermoisturegaverisetohigherinter-particleporosityandahigherplasticityatthecontactsunderload,resultinginahigheroverallcompressibility.Thehigherplasticityatthecontactseventuallyledtoahighercakestrengthforthehighmoisturesample.

Fordifferentsieve-cutsamples,itwasfoundthatmoisturecon-tentwasnotuniformlydistributed,withthelargersizefractionshavinghighermoisturecontents,mostprobablyduetotheagglom-erationofprimaryparticlesintolargersizesenclosinghigherinternalmoisture.Thelargersizefractionsshowedhighertotalporositycomparedtothesmallersizefractions.Itisnotedthatthelargerfractionsareagglomeratesoftheprimaryparticles.Thusthe

inter-agglomerateporosityalsocontributedtothetotalporosityleadingtoahigherporosityforthelargerfractions.Higherinitialporosity,andhighmoistureassociatedwithlargesizefractionsexplainswhylargesizefractionsalwaysshowedahighercom-pressibilitythanthesmallersizefractions.

Additionally,thelargersizefractionsalsoshowedhighercakestrengththanthefullsizerangeineachofthetwopowders.Thishasthepracticalimplicationthatifthedetergentpowdersegregatesduringthehandlingandtransportoperation,thecoarserfrac-tionmaydominatetheoverallcakingbehaviourofthedetergentpowders.Inaddition,thepowderswithhigherinherentmoisturecontentcanhaveahighercohesivityandmaythereforecausemore?owabilityproblemsespeciallywhensubjectedtosigni?cantcon-solidationstresses.

The?llingand,con?nedcompression/decompression,followedbytheuncon?nedloadingtofailure,inanEPTtesthavebeensimu-latedwithDEMusingarecentlydevelopedelasto-plasticadhesivecontactmodel.Thesimulationresultsareinreasonablygoodagree-mentwiththeexperimentalresultsforthe?owfunctionandcompressionbehaviourbutlesssoforotherobservedfeatures.Fur-therdevelopmentofcontactmodelisunderwaytoimprovethepredictivecapabilities.

Thisstudyisthe?rststeptowardsusingDEMtomodelcohe-sivepowdersforindustrialscaleapplications.MoresimulationsarerequiredtostudytheeffectsofseveralDEMinputparameterssuchasparticlesize,shape,particlesizedistribution,frictionetc.onthebulkresponse.However,this?rststepdemonstratedthemodel’scapabilitytopredictthepertinentmacroscopicbehaviourofacohesivepowderundercompressionandshearanditspotentialformodellingcomplexindustrialprocessesinvolvingtheseloadingregimes.

12S.C.Thakuretal./Particuology12 (2014) 2–12

Acknowledgements

ThesupportfromtheEUMarieCurieInitialTrainingNetworkisgratefullyacknowledged.TheauthorswouldalsoliketothankDrLuisMartindejuan,DrGrahamCalvert,MrSimonGreener,JohnPaulMorrissey,andProfJian-FeiChenformanyusefuldiscussionsandMissTaraAzizfortechnicalassistance.

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