StrainingofcolloidsattexturalinterfacesScottA.Bradford,JirkaSimunek,Me - PDF document

StrainingofcolloidsattexturalinterfacesScottA.Bradford,JirkaSimunek,MehdiBettahar,YadataF.Tadassa,MartinusT.vanGenuchten,andScottR.YatesReceived22September2004;revised22April2005;accepted23June2005;published11October2005.2005.1]Althoughnaturalsoilandaquifersystemsoftencontainlayersandlensesofcontrastingsoiltexture,relativelylittleresearchhasfocusedonthemechanismsofcolloiddepositionattexturalinterfaces.Saturatedcolumnstudieswereundertakentocharacterize GeorgeE.Brown,Jr.,SalinityLaboratory,ARS,USDA,Riverside,California,USA.DepartmentofEnvironmentalSciences,UniversityofCalifornia,Riverside,California,USA.Parsons,Pasadena,California,USA.Copyright2005bytheAmericanGeophysicalUnion.0043-1397/05/2004WR003675$09.00WATERRESOURCESRESEARCH,VOL.41,W10404,doi:10.1029/2004WR003675,20051of17 willdependonthesizeofthecolloidandtheporesizedistributionofthemedium[McDowell-Boyeretal.,1986;Bradfordetal.,2002,2003].MatthessandPekdeger[1985]presentedtheoreticalcriteriasuggestingthattheratioofthecolloid()tomediangraindiameter()needstobegreaterthan0.18forstrainingtooccurinuniformsand;increasingsandgradationwouldsomewhatlowerthisthreshold.Forthisreasonmostpreviousstudiesoncolloidtransporthaveneglectedstrainingasamechanismforretention[cf.SchijvenandHassanizadeh,2000;andHarms,2002;JinandFlury,2002;Ginnetal.,2002].Experimentalobservations,however,suggestthatstrainingmayoccurformuchlowervaluesof[1966,1969]reportedthatstrainingproducedapermeabilityreductionofbetween10and50%whenwasaround0.05.Bradfordetal.[2002,2003]observedsystematictrendsoflowereffluentconcentrationsandincreasingcolloidretentioninsandnearthecolumninletwithdecreasingsandgrainsizeorincreasingcolloidsize.Mathematicalmodelingindicatedthatstrainingalreadyoccurredfor�0.005.DatafromLietal.al.indicatesthatstrainingmayhaveoccurredfor0.002,butdecreasedwithincreasingporewatervelocity.ResultsfromTufenkjietal.[2004]suggestthatirregularityofthesandgrainshapesignificantlycontributestothestrainingpotentialofporousmedia.Foppenetal.al.foundthattherateoffillingofstrainingsiteswasdependentontheconcentrationofcolloids(bacteria)insuspension..6]Measuredcapillarypressurecurvesandresidualsat-urationscanberelatedtoporesizedistributionsaccordingtoLaplace’sequationofcapillarity.Thepercentageofporespacewherestrainingandsizeexclusionoccurscanbeinferredfromthisporesizedistributioninformation.andParrish[1988]presentaveragecapillarypressurecurveparametersforthe12majorsoiltexturalgroups.Dependingonsoiltexture,strainingispredictedin10.5to70.8%ofthesoilporespacefor0.1msizecolloids;largercolloidsproduceevengreaterpercentages.Conversely,mobilecol-loidsthatarenotstrainedmaybephysicallyexcluded(sizeexclusion)fromthissamefractionoftheporespace.space.7]Sizeexclusionaffectsthemobilityofcolloidsbyconstrainingthemtomoreconductiveflowdomainsandlargerporenetworksthatarephysicallyaccessible[RyanandElimelech,1996;,2002].Asaresult,colloidscanbetransportedfasterthanaconservativesolutetracertracerReimus,1995;CumbieandMcKay,1999;Harteretal.Bradfordetal.,2003].Differencesinthedispersivefluxforcolloidsandaconservativesolutetracerarealsoanticipatedasaresultofsizeexclusion[ScheibeandWoodBradfordetal.[2002]observedthatthedispersivityof3.2mcarboxyllatexcolloidswasupto7timesgreaterthanbromideinsaturatedaquifersand.Conversely,etal.[2000]foundinafieldmicrobialtransportexperimentthattheapparentcolloiddispersivitydecreasedwithincreasingparticlesize.size.8]Strainingandsizeexclusionhavesignificantimplica-tionsforcolloidtransportinthefield.Increasedstrainingnearthecolumninletisdeemedespeciallynoteworthysinceitmayhaveramificationsforlayeredsoilprofiles,hetero-geneoussubsurfaceformations,artificiallyconstructedmediasuchaslandfills,andwatertreatmenttechniquesthatarebasedonsoilpassage(riverbankfiltration,infiltrationbasinsandtrenches,andsandfilters).Muchofthetransportofcolloidswillthenoccurinthe‘‘hydraulically’’activenetworkofthelargerpores.Wepostulatethatstrainingismostpronouncedatthesoilsurfaceorattheboundaryofdifferentsoiltextureswherecolloidsareencounteringa(new)porenetwork.Atsuchboundaries,colloidsaremorelikelytoencounteraporesmallerthanthecriticalstrainingsizeoronelargerthanthecriticalsizethatsteerscolloidstoward‘‘dead-endregions’’oftheporespace.Oncecolloidshaveenteredthehydraulicallyactivenetwork,transportprocessessuchasadvection,dispersion,andsizeexclusionmakeitmorelikelyforthecolloidstoremainconfinedtothenetwork.network.9]Althoughnaturalsoilandaquifersystemsoftencontainlayersandlensesofcontrastingsoiltexture,relativelylittleresearchattentionhasfocusedonthemech-anismsofcolloidretentionattexturalinterfaces[Saierset,1994;,1995;Bradfordetal.,2004].Saierset[1994]foundthatcolloidtransportanddepositioncouldbeadequatelydescribedwithanadvection-dispersiontrans-portmodelthataccountedforfirst-orderkineticattachment/detachment.Incontrast,[1995]foundsignificantcolloidretentionattexturalinterfaceswherewatermovedfromlargertosmallerdiametersands.Thisobservationwasattributedtostraininginitiatedbycolloidattachment.Bradfordetal.[2004]foundthatcolloidtransportinheterogeneoussystemswascontrolledprimarilybystrain-ingwhen�0.005,butthatattachmentandtheaqueousphaseflowfield(flowbypassing)alsoplayedimportantroles.roles.10]Theobjectiveofthisworkistoinvestigatethemainprocessescontrollingthetransportandfateofcolloidsacrosstexturalinterfaces.Whilesuchinformationisneededtoaccuratelyassesscolloidtransportinheterogeneousaquiferformations,fewstudieshavethusfarsystematicallyfocusedonthistopic.Itseemslogicaltoanticipatethatstrainingwillbemostpronouncedatlocationswherecolloidsencounteranewporenetwork(e.g.,texturalinterfaces).Colloidtransportexperimentswereconductedusinghomogeneousandlayeredsandsystems(usingbothcolumnsandmicromodels).Transportandretentionwereassessedbymeasuringtemporalchangesincolloideffluentconcentrationsandbystudyingthefinalspatialdistributionofcolloidsremaininginthesandcolumns,aswellasbymicroscopicallystudyinglocationsofcolloiddepositioninhomogeneousandlayeredsandexperimentsconductedinaglassmicromodel(0.2cm2.0cm7.0cm).Thecolumntransportdataweredescribedandanalyzedusingatransportmodelthataccountsforadvective,dispersive,anddiffusivecolloidfluxes,andtwo-sitekineticdeposition.Onedeposi-tionsiteisusedtoaccountforconventionalfirst-orderattachmentanddetachment,whiletheseconddepositionsiteincludesaformulationforaccessibilitystrainingsites.2.MaterialsandMethods2.1.ColloidsColloids11]Yellow-greenfluorescentlatexmicrospheres(InterfacialDynamicsCompany,Portland,OR)wereusedasmodelcolloidparticlesintheexperimentalstudies(excitationat490nm,andemissionat515nm).Twosizesofmicrosphereswereusedinthetransportexperiments,1.12of17BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES and3.0m.TheuniformityofthecolloidsizedistributionswasverifiedusingwithaHoribaLA930(HoribaInstru-mentsInc.,Irvine,California)laserscatteringparticlesizeanddistributionanalyzer.Thesemicrosphereshadsulfatesurfacefunctionalgroups,adensityof1.055gcm(providedbythemanufacturer),andanequilibriumcontactangle(air-water-lawnofcolloids)of101(measuredwithaTantecContactAngleMeter,TantecInc.,Schaumburg,Illinois).The1.1and3.0mcolloidshadasurfacechargedensityof5.2and14.3Ccm(providedbymanufacturer)andazetapotentialof66.5and75.5mV(measuredwithaZetaPALsInstrument),respectively.Theinitialinfluentconcentration()forthe1.1and3.0mcolloidsfortheexperimentswas3.3and1.5denotesnumberofcolloids),respectively.Oneexperimentwasconductedusing1.1mparticlesat=1.652.2.SandSand12]AquifermaterialusedforthecolumnexperimentsconsistedofvarioussievesizesofOttawa(quartz)sand(U.S.Silica,Ottawa,IL).Theporousmediawereselectedtoencompassarangeingrainsizes,andaredesignatedbytheirmediangrainsize()as:710,360,240,and150Specificpropertiesofthe710,360,240,and150msandsinclude:thecoefficientofuniformity(;here%ofthemassisfinerthan)of1.21,1.88,3.06,and2.25;andintrinsicpermeabilitiesof4.08,6.37,and4.68,respectively.Ottawasandstypicallyconsistof99.8%SiO(quartz)andtraceamountsofmetaloxides,havespheroidalshapes,andcontainrelativelyroughsurfaces.ThevastmajorityofthesandspossessanetnegativechargeataneutralpH.pH.13]BradfordandAbriola[2001]presentedcapillarypressure–saturationcurvesforthe710,360,240,andmsands.Anestimateoftheporesizedistributionofdrainedpores(thatmayproducestraining)canbeobtainedfromcapillarypressure–saturationcurvesusingLaplace’sequationofcapillarity.Unfortunately,itisrelativelydifficulttousethismethodtocharacterizethesmallporesizesofsandsbecauseofthepresenceofresidualwater(duetodiscontinuitiesinthewettingfilms).Alternatively,Herziget[1970]calculatedthevolumeofsphericalcolloidsthatcouldberetainedinporesbasedongeometricconsidera-tions.Thepercentageofthetotalcolumnvolumeretainedbystrainingwascalculated(assumingacoordinationnum-berof7,aporosityof0.35,acolloiddiameterof1.1m,andagraindiameterequalto)tobe0.0002%forthe710sands,0.0020%forthe360msands,0.0129%forthemsands,and0.0225%forthe150msands.Althoughthesestrainingvolumesarequitesmall,significantnumbersofcolloidsarerequiredtofillthesites[Foppenetal.,2005].Forexample,6.3colloids(1.1m)wouldberequiredtofullysaturate(fill)allthestrainingsitesinuniform150msandpackedinacolumnthatis10cmlongandhasaninsidediameterof5cm.Thiscorrespondstocompleteretentionof1.1mcolloidsin27.9porevolumes(PV)ofsuspensionataconcentrationof3.32.3.AqueousPhasePhase14]Theaqueousphasechemistry(pH,ionicstrength,andcomposition)oftheexperimentalsolutionsutilizedinthecolumnstudiesconsistedofdeionizedwaterwithitspHbufferedto6.98using5MNaHCO(ionicstrengthequalto5M).Thissolutionwaschosentocreateastabilizedmonodispersedsuspensionwiththeselectedcol-loids,andtominimizeelectrostaticinteractionsbetweenthecolloidsandporousmedia(highlyunfavorableattachmentconditions).Thecolloidtracersolutionconsistedofthissamesolutionbutwiththepreviouslyindicatedinitialcolloidconcentration.2.4.ColumnExperimentsExperiments15]ProceduresandprotocolsforthepackedcolumnexperimentswerepreviouslydiscussedindetailbyBradfordetal.[2002].Onlyanabbreviateddiscussionisprovidedbelow.KontesChromaflexchromatographycolumns(Kimble/Kontes,Vineland,NewJersey)madeofborosili-categlass(15cmlongand4.8insidediameterwereequippedwithanadjustableadapteratthetop)wereusedinthetransportstudies.Thecolumnswerewetpacked(waterlevelkeptabovethesandsurface)withthevariousporousmedia.Forthelayeredexperiments,equalmassfractionsofthetwosandtypesweresuccessivelypackedintoacolumn,takingcaretominimizethedisturbanceatthetexturalinterface.Table1providesporosity()valuessDanielsonandSutherland,1986]andcolumnlength(foreachexperimentalsystem.Thecolloidsuspensionwaspumpedupwardthroughtheverticallyorientedcolumnsatasteadyflowratefor77.5(forexperiments)or150(0.5*experiment)min,afterwhichathree-wayvalvewasusedtoswitchtothebackgroundsolutionforatotalexperimentaltimeof250min.TheaverageDarcianfluxdensities()forthevariousexperimentsaregiveninTable1.EffluentsampleswerecollectedandanalyzedforcolloidconcentrationusingaTurnerQuantechfluorometer(Barnstead/Thermolyne,Dubuque,Iowa).Theaverageofthreemeasurementswereusedtodetermineeachcolloidconcentration(reproducibilitywastypicallywithin1%ofof16]Followingcompletionofthecolloidtransportexperi-ments,thespatialdistributionsofcolloidsinthepackedcolumnsweredetermined.Thesaturatedsandwascarefullyexcavatedinto50mLFalconcentrifugetubescontainingexcessdeionizedwater.Thetubeswereslowlyshakenfor15minusingaEberbachshaker(EberbachCorporation,AnnArbor,Michigan)toliberateretainedcolloids.TheconcentrationofthecolloidsintheexcessaqueoussolutionwasmeasuredwithaTurnerQuantechfluorometerusingthesameexperimentalprotocolasfollowedfortheeffluentsamples.Theseconcentrationswerecorrectedforcolloidreleaseefficiencydeterminedfrombatchexperiments.Thereleaseefficienciesfor1.1mcolloidswere0.78inthemsand,0.75inthe360msand,0.71inthe240sand,and0.68inthe150msand,whilethe3.0colloidshadreleaseefficienciesof0.80inthe710msandand0.78inthe150msand.sand.17]Acolloidmassbalancewasconductedattheendofeachcolumnexperimentusingeffluentconcentrationdataandthefinalspatialdistributionofretainedcolloidsinthesands.Thecalculatednumberofeffluentandcolloidsretainedinthesandwasnormalizedbythetotalnumberofinjectedparticlesintoacolumn.Table1presentsthecalculatedeffluent(),sand(),andthetotal()colloidmassfractionsrecoveredforthevariousexperiments.BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES3of17 2.5.MicromodelExperimentsExperiments18]Severaltransportexperimentswereconductedinaspeciallydesignedmicromodeltoexaminethedepositionbehaviorofthe1.1and3.0msulfatecolloidsinhomoge-neous(150msand)andlayered(710/150)sandsystems.Themicromodelconsistedofa0.2cmthickby2.0cmwideby7cmlongglasschamber(insidedimensions),withaglasstube(0.5cminsidediameter)andseptumassemblyjoinedatbothendsofthechamber.Thetubingwasconnectedtothechamberbyaglassbloweratanangleofabout45,sothatthemicromodelcouldlayflatonahorizontalsurface.Duringpackingthemicromodelchamberwasorientedverticallywithoutthetopseptum.Thedesiredsandswerethenwetpackedinthechamber(homogeneousorlayeredconfigurations).HypodermicneedlesandTeflontubingwereusedtoconnecttheinletsideofthechambertoaLabAlliancechromatographypump(StateCollege,Penn-sylvania)andareservoirontheoutletsideofthechamber.Tobecomparabletothecolumnexperiments,thecolloidsuspensionwaspumpedatasteadyrateof0.04mlmin(Darcyvelocityof0.1cmmin)forabout60min(around2.5porevolumes),followedbydeionizedwaterforanadditional60min.Aftercompletionofatransportexperi-ment,thehypodermicneedleswereremovedandthefinaldepositionbehaviorofthefluorescentcolloidswasmicro-scopicallyexaminedatseverallocationsusingaLeicaDMIRBepifluorescentmicroscope(LeicaMicrosystemsInc.,Bannockburn,Illinois).Imageswerecapturedbyconnect-ingthemicroscopetoavideomonitorandcomputersystem.Photographs(600timesmagnification)weretakenusingvariousintensitiesofbothUVandvisiblelightsothatsandgrainsandfluorescentcolloidscouldbevisualizedsimultaneously.2.6.TheoryandModelModel19]Theaqueousphasecolloidmassbalanceequationiswrittenas NcL3]isthecolloidconcentrationintheaqueous[T]istime,(dimensionless)isthevolumetricwatercontent,content,cL2T1]isthetotalcolloidflux(sumoftheadvective,dispersive,anddiffusivefluxes),andandcL3T1]andandcL3T1]arethecolloidmasstransfertermsbetweentheaqueousandsolidphasesduetocolloidattachment/detachmentandstraining,respectively.Anexpressionforcanbewrittenas Here[ML]isthesoilbulkdensity,,cM1]isthesolidphaseconcentrationofattachedcolloids,sionless)isadimensionlesscolloidattachmentfunction,andand1]andd1]arethefirst-ordercolloidattachmentanddetachmentcoefficients,respectively.When=1and=0,cleanbedattachmentisassumed(leadingtoanexponentialspatialdistribution),whiletraditionalfiltrationtheory[Loganetal.,1995]canbeusedasneededforforBradfordetal.,2003].Incontrast,toaccountforcolloidblocking(fillingoffavorableattachmentsites)thevalueofdecreaseswithincreasingAccordingtotheLangmuirianapproach[e.g.,andShonnard,1999],;wherewherecM1]isthemaximumsolidphaseconcentrationofattachedcolloids.Forgivenvaluesof,adecreasingtendstoproducehighereffluentconcentrationsandlowervaluesofof20]StrainingismodeledaccordingtoaslightlymodifiedformoftheapproachdescribedbyBradfordetal.l.Themassbalanceequationforstrainedcolloidsisgivenas 1]isthestrainingcoefficient,less)isadimensionlesscolloidstrainingfunction,andandcM1]isthesolidphaseconcentrationofstrainedcolloids.Thevalueofforeachlayerisafunctionofdistanceanddescribedas SstrS )istheHeavisidefunction,z[L]isdepth,[L]denotesthedepthofthecolumninletortexturalinterface,rface,cM1]isthemaximumsolidphaseconcentrationofstrainedcolloids,and(dimensionless)isaparameterthatcontrolstheshapeofthecolloidspatialdistribution.TheHeavisidefunctionisequalto0forand1forgreaterthanorequaltoz.Inhomogeneoussystems,thevalueofequalsthezcoordinateofthesandsurface.Inlayeredsystems,thevalueofequalsthezcoordinateofthesandsurfaceforthefirstlayer,andthezcoordinateoftheinterfaceforthesecondlayer..21]Thesecondtermontherighthandsideofequation(4)isincludedtoaccountforfillingandaccessi-bilityofstrainingsitesinamannersimilartotheLangmuirianblockingapproach.Forgivenvaluesof,decreasingtendstoproducehighereffluentconcentrationsandlowervaluesofstr.Theremaining Table1.PackedColumnProperties(Porosity,,DarcyWaterVelocity,,andColumnLength,)andtheRecoveredEffluent),Sand(),andtheTotalColloidMassFraction(,cmmin,cm7101.10.3500.09412.80.7750.0790.8547103.00.3480.09612.80.7820.1240.9063601.10.3330.10812.50.6410.2470.8882401.10.3090.11712.10.5340.3690.9031501.10.3380.10512.60.5660.4341.0001.10.3450.10612.70.5720.4631.0351503.00.3440.10312.70.0390.9781.017150/7101.10.3350.11312.50.6500.3591.009150/7103.00.3560.11613.00.0620.5300.592150/3601.10.3420.12312.70.6220.3200.942150/2401.10.3260.13312.40.5490.4330.982710/3601.10.3450.08512.70.7030.2330.936710/2401.10.3450.09712.70.6690.2700.939710/1501.10.3530.10112.90.6760.2860.962710/1503.00.3560.09813.00.3840.6341.018360/2401.10.3230.10812.30.4850.5941.079360/1501.10.3270.10212.40.5160.5681.084240/1501.10.3280.09212.40.3860.6791.065Inputconcentrationequalto0.5C4of17BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES termsontheright-handsideofequation(4)assumethatcolloidmassretentionbystrainingoccursprimarilyatthecolumninletortexturalinterfacebecauseofretentionofcolloidsindeadendporesand/oratgrainjunctionsthataresmallerthansomecriticalsize.Theapparentnumberofdead-endporesishypothesizedtodecreasewithincreasingdistancesinceadvection,dispersion,andsizeexclusiontendtokeepmobilecolloidswithinthelargernetworks,thusbypassingsmallerpores.Thepotentialrolesofsizeexclu-sionanddispersiononcolloidtransporttosmallporesisrelativelyeasytounderstand.Waterrelativepermeabilityfunctionsforsandysoils[e.g.,vanGenuchtenetal.,1991]alsosuggeststhatwaterflowtothesmallerregionsoftheporespaceaccountsforonlyasmallfractionofthetotalpermeability(saturatedflow)oncetheflowfieldhasbeenestablished.ablished.22]TheHYDRUS-1Dcomputercode[Simuneketal.1998]simulatesthemovementofwater,heat,andmultiplesolutesinone-dimensionalvariablysaturatedporousmedia.Thiscodewasmodified[Bradfordetal.,2003]toaccountforcolloidattachment,detachment,straining,andblockingasoutlinedabove.Althoughattachmentandstrainingarelikelytooccursimultaneouslyinnaturalsystems,theseprocesseswereconsideredseparatelyinthisworktofacil- Figure1.(a)Effluentconcentrationcurvesand(b)spatialdistributionsfor1.1msulfatecolloidsin710,360,240,and150msand.InFigure1a,relativeeffluentconcentrations(C/C)areplottedasafunctionofporevolumes,whereasinFigure1bthenormalizedconcentration(numberofcolloids,dividedbythetotalnumberaddedtothecolumn,)pergramofdrysandisplottedasafunctionofdimensionlessdistance(distancefromthecolumninletdividedbythecolumnlength).BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES5of17 itatethedeterminationofuniqueparameterestimatesforthelayeredsystems.Bradfordetal.[2003]andBradfordand[2005]discussseveralwaystoestimatethemag-nitudeofattachmentandstraininginhomogeneouscolumnexperiments.HYDRUS-1DiscoupledtoanonlinearleastsquaresoptimizationroutinebasedupontheMarquardt-Levenbergalgorithm[Marquardt,1963]tofacilitatetheestimationofsolutetransportparametersfromexperimental3.ResultsandDiscussion3.1.Transportof1.1mColloidsinHomogeneousSystemsSystems23]Figures1aand1bpresenteffluentconcentrationcurvesandspatialdistributions,respectively,for1.1sulfatecolloidsin710,360,240,and150msands.InFigure1atherelativeeffluentconcentrations()areplottedasafunctionofporevolumes,whereasinFigure1bthenormalizedconcentration(numberofcolloids,dividedbythetotalnumberaddedtothecolumn,)pergramofdrysandisplottedasafunctionofdimensionlessdistance(distancefromthecolumninletdividedbythecolumnlength).Therecoveredcolloidmassfractionsintheeffluentandthesandcolumn,aswellasthetotalrecoveredmassfractionareshowninTable1.Highrecoveryrateswereobtainedusingtheoutlinedexperimentalmaterialsandprotocols.ls.24]Figures1aand1bindicatethatdecreasingthemediangrainsizeofthesandtendedtoproduceslightlylowereffluentconcentrations,andgreaterretentionofcolloidsinthesandnearthecolumninlet.SlightdifferencesineffluentconcentrationcurvesalsooccurredasaresultofvariationsinthecolumnporosityandDarcyvelocity Figure2.(a)Effluentconcentrationcurvesand(b)spatialdistributionsfor1.1msulfatecolloidsinmsandatinputconcentrationsofand0.5*6of17BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES (Table1).ThetransportresultswereconsistentwiththebehaviorofsimilarlysizedcarboxylcolloidsinthesesameOttawasandsasshownbyBradfordetal.[2002].Simu-lationspresentedbyBradfordetal.[2003]suggeststhatstrainingwasthedominantmechanismofcolloidretentioninthesesystems.Strainingoccurredprimarilyatthecolumninlet,presumablyduetothehighaccessibilityofpotentialstrainingsites(smallpores)toflowingcolloidsuspensionsatthislocation.Sizeexclusionandadvectionwerehypoth-esizedtoincreasinglyrestricttheflowofcolloidstolargeporenetworks(bypassingsmall,low-permeabilitystrainingsites)asthetransportdistanceincreased.d.25]Aftertheinitialcolloidbreakthrough,Figure1ashowsthateffluentconcentrationscontinuedtoslowlyincreasewithcontinuedcolloidaddition.Thisbehaviorhaspreviouslybeenreportedinmanystudies[Tanetal.1994;Liuetal.,1995;JohnsonandElimelech,1995;Rijnaartsetal.,1996;CamesanoandLogan,1998;Camesanoetal.,1999],andisreferredtoasblocking.Blockingimpliesthatasfavorableattachmentsitesbecomefilled,attachmentdecreasesandcolloidtransportisenhanced.Thissameexplanationcanalsobeappliedtofillingofstrainingsites.Asstrainingsitesbecomefilled,enhancedtransportoccurs. Figure3.(a)Observedandsimulatedeffluentconcentrationcurvesand(b)spatialdistributionsformsulfatecolloidsin150msand.OneofthesimulationsconsideredattachmentandLangmuirianblocking(=0and=0)accordingtoequations(1)and(2).Theothersimulationconsideredstraining(=0and=0)accordingtoequations(1),(3),and(4).FittedmodelparametersarepresentedinTables2and3.BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES7of17 26]TherateoffillingofstrainingsiteswasanticipatedtodependontheconcentrationofcolloidsinsuspensionnsionFoppenetal.,2005].Tofurtherexaminethishypothesis,anadditionaltransportexperimentwasconductedataninputconcentrationof0.5*.Figure2presentseffluentconcentrationcurves(Figure2a)andspatialdistributions(Figure2b)for1.1msulfatecolloidsin150msandatinputconcentrationsofand0.5*.Noticethattheeffluentconcentrationcurveforthe0.5*systemexhibitsamoregradualincreaseinrelativeconcentrationthanthesystem.Similarrelativeeffluentconcentrationsoccurred,however,afteraddingequalcolloidmasses(twicethenumberofporevolumesfor0.5systems).Slightdifferenceswerealsoobservedbetweentheand0.5*spatialdistributions.The0.5*systemexhibitedslightlylowerretainedconcentrationsnearthecolumninletthenthesystem,whilefurtherinthecolumn(dimensionlessdistance�0.25)thistrendwasreversed.Theseobservationscanbeexplainedbythehigherdepositionratethatoccurredinthe0.5*system(ittakeslongertofillthestrainingsites).Forthecolloidsusedinthisstudy,thetotalretentioncapacitywasindependentoftheinputconcentration(similarvaluesofinTable1afteradditionofequalcolloidmass).mass).27]Figures3aand3bpresentobservedandsimulatedeffluentconcentrationcurvesandspatialdistributions,re-spectively,for1.1msulfatecolloidsin150msand.Oneofthesimulations(dottedline)consideredattachmentandLangmuirianblocking(weresetequaltozero)accordingtoequations(1)and(2).Table2presentsattach-mentandblockingmodelparameters(hydrodynamicdis-persivity,;attachmentcoefficient,;andmaximumsolidphaseconcentrationofattachedcolloids,)thatwerefittedtothetransportdataforthevarioushomogeneoussystems,alongwithstatisticalparameters(SEisstandarderror,risthecoefficientoflinearregressionfortheeffluentdata,andristhecoefficientoflinearregressionforthespatialdistributiondata)reflectingthegoodnessoffit.TheothersimulationinFigure3consideredonlystraining(termsweresetequaltozero)accord-ingtoequations(1),(3),and(4).Table3presentsstrainingmodelparameters(werefitted,isthesameasinTable2,whereaswasobtainedbyfittingtotransportdataforthe150msystem)andstatisticalinformationforthevarioushomogeneoussystems.InFigure3thestrainingmodelprovidedamuchbetterdescriptionoftheeffluentandspatialdistributiondatathantheattachmentmodel(seerandrvaluesinTables2and3).Thestrainingmodelalsogaveimproveddescriptionsofthecolloidtransportbehaviorforthecoarser710,360,andmsandsystems(seeTables2and3).Othernumericalsimulations(notshown)revealedthatdifferencesinthepredictedcolloidmigrationandfatefortheattachmentandstrainingmodelswillincreasewithincreasingtransportdistance.nce.28]Asbrieflymentionedintheintroduction,variousexplanationsfornonexponentialcolloiddepositionhavebeenproposedintheliterature.Sincethefocusofthisstudywasoncolloidstraining,theexperimentalconditionsweredesignedtominimizethepotentialforcolloidattachment(i.e.,usinguniformlysizedandchargedcolloids,negativelychargedcolloidsandporousmedia,andsimpleaqueouschemistryhavingaverylowionicstrength).Themecha-nismsofcolloiddepositionwerefurtherdeducedbymeansofamicromodelexperiment.Figure4apresentsaphotoofmcolloiddepositionnearthemicromodelchamberinletin150msand.Thisphotodemonstratesthatmanyfluorescentcolloidscanbedepositedatagivengrainjunctionduetostraining.Theshapeandsurfaceroughness Table2.Fitted(HydrodynamicDispersivity,;AttachmentCoefficient,,andMaximumSolidPhaseConcentrationofAttachedColloids,)ParametersfortheAttachment(Equations(1)and(2))ModelinHomogeneousSystems(1.1mColloids),cm,min7101.10.26(0.04)0.0047(0.0007)0.014(0.023)1.000.693601.10.49(0.23)0.0110(0.0028)0.031(0.117)0.990.512401.10.20(0.15)0.0231(0.0042)0.004(0.004)0.990.431501.10.28(0.18)0.0156(0.0011)0.005(0.003)0.980.401.10.280.0246(0.0051)0.003(0.002)0.920.42Standarderrorvaluesfortheparameterfitsareprovidedwithintheparentheses.Inputconcentrationequalto0.5*.Thevalueofwastakenfromtheexperiment. Table3.Fitted(StrainingCoefficient,,andMaximumSolidPhaseConcentrationofStrainedColloids,)andEstimated(HydrodynamicDispersivity,,and)ParametersfortheStraining(Equations(1),(3),and(4))ModelinHomogeneousSystems(1.1mColloids),cm,min7101.10.2641.311.065(0.303)0.001(0.001)0.990.653601.10.4901.312.561(0.317)0.020(0.009)0.980.842401.10.2031.3110.99(0.970)0.011(0.002)0.980.971501.10.2831.3113.86(6.080)0.014(0.005)0.960.971.10.2831.3120.29(0.001)0.0130.920.95Standarderrorvaluesfortheparameterfitsareprovidedwithintheparentheses.HereisfromTable2;isobtainedfromfittingtotransportdataforthe150msystem.Inputconcentrationequalto0.5*.Thevalueofwastakenfromthe8of17BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES ofthesandgrainsarealsoapparentinthisphoto.Thelargenumberofcolloidsretainedatthislocationsupportsourhypothesisthatfillingofstrainingsitescanoccurduringthecourseofourtransportexperiments.Aggregationofcolloidsinsuspensioncannotexplainthisbehaviorsincetheuni-formityofthecolloidsizedistributionwasexperimentallyverifiedwithalaserscatteringparticlesizeanddistributionanalyzer.3.2.Transportof1.1mColloidsinLayeredSystems:FinetoCoarseCoarse29]Thissectiondiscussesthetransportbehaviorofmsulfatecolloidsinlayeredsandsystemswhenwaterflowsfromafiner-textured(150msand)toacoarser-textured(710,360,or240msand)medium.Figures5aand5bpresentrelativeeffluentconcentrationcurves(Figure5a)andspatialdistributions(Figure5b)for1.1sulfatecolloidsinsystemsconsistingof150/710,150/360,and150/240msandlayers.Theeffluentconcentrationcurvesandspatialdistributionswerequitesimilarforthevariouslayeredsystems.Decreasingthemediangrainsizeofthecoarser-texturedlayerresultedinaslightdecreaseinthepeakeffluentconcentration(Figure5a).Figure5bindicatesthatcolloidretentionwascontrolledbythefinermfirstlayer.Littlecolloidretentionoccurredatthetexturalinterfacewhenflowoccursfromthefinertothecoarser-texturedsand.Possibleexplanationswillbedis-cussedbelow..30]Figures5aand5balsoshowsimulatedeffluentconcentrationsandspatialdistributions,respectively,forthe1.1msulfatecolloidtransportexperiment(150/710,150/360,and150/240msandlayers)assumingstrainingweresetequaltozero)inaccordancewithequations(1),(3),and(4).Strainingmodelparameters,includingthespatialdistributionmodelparameter,weretakenfromthecorrespondinghomogeneoussystemspre-sentedinTable3,withtheoneexceptionofthecoarser-texturedlayer,whichwasfitteddirectlytothelayeredtransportdata(Table4).Asforthehomogeneoussystems,thestrainingmodelprovidedagooddescriptionofboththeeffluent(Figure5a)anddeposition(Figure5b)5b)31]Foragivensand,thevalueof(Table4)wasalwayssignificantlysmallerforthelayeredsystemthanforthecorrespondinghomogeneoussystem(Table3).Wehypothesizethatthevalueofforthelayeredsystemshouldbelowerbecauseofdiminishedcolloidaccessibilitytostrainingsitesasaresultoftransportprocessessuchassizeexclusion,advection,anddispersionthattendtoconfinecolloidstothehydraulicallyactiveporenetworkandthelargerporesspaces.Similarprocesseswerethoughttooccurinthehomogeneoussystemsawayfromthecolumninlet(Figure1b).Strainingsitesatthetexturalinterfacescouldalsobepartiallyfilledwithnaturalcolloidsthatmayhavebeenmobilizedduringthesandcleaningprocess.Incontrast,concentration-dependentcolloidtrans-port(Figure2)couldnotaccountforthedepositionbehav-iorinthelayeredsystems(Figure5b)becauseofhigherratesofcolloiddepositionatthelowerinputconcentration(seeTable3).Wewillshowlaterthatstrainingwasmuchmorepronouncedforsystemsinvolvingflowfromcoarsetofiner-texturedlayers. Figure4.Photos(magnified600times)ofcolloiddepositioninthemicromodelexperiments.(a)The1.1depositionin150msandnearthechamberinlet.(b)Themdepositionin150msandnearthe710/150texturalinterface.(c)The3.0mdepositionin150msandnearthe710/150texturalinterface.Seecolorversionofthisfigureatbackofthisissue.BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES9of17 32]Whenstrainingandattachmentbothoccurinporousmediaitisdifficulttoseparatelyestimatethemagnitudesofthesedepositionprocesses.Colloidattachmentisthereforeprobablybestestimatedinsystemswithlittlestraining.Figures5aand5bsuggestthatverylittlestrainingoccurredinthesecondlayerwhenwaterflowedfromafinertoacoarser-texturedsand.Thisprovidesanopportunitytobetterestimatethemagnitudeofattachmentinthesecondlayersand.Forthispurpose,strainingwasmodeledonlyinthefirstlayer(=0and=0)usingparameterstakenfromthecorrespondinghomogeneoussystems(Table3).Inthesecondlayeronlyattachmentwasmodeled(=0and=0)byfittingavalueoftothespatialdistributiondatainthislayer.Toestimatethemagnitudeofinthefinest150msand,thehomogeneoustransportdatawasanalyzedasalayeredsystem(firsthalfonlystraining,thesecondhalfonlyattachment).Simulatedbehaviorforthefiner-tocoarser-texturedlayeredsystemsusingthisapproachwasquitesimilartothatpresentedinFigures5aand5bandisthereforenotshownhere.Thefittedvaluesofattusingthisapproachwere0.002,0.002,0.004,and0.005minforthe710,360,240,and150msandsystems,respectively.Thervaluesinthesesystemswereallgreaterthan0.97,suggestingaccuratecharacterizationofthedepositionbehavior.Valuesofinthehomogeneoussystems(Table2)were2.9–5.9timesgreaterthaninthese Figure5.(a)Observedandsimulatedeffluentconcentrationcurvesand(b)spatialdistributionsformsulfatecolloidsinsystemsconsistingof150/710,150/360,and150/240msandlayers.Heresimulationsconsideredonlystraining(equations(1),(3),and(4)).10of17BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES ‘‘layered’’systems,thusindicatingthatsignificantlylessdepositionoccurredinthe‘‘layered’’systems.3.3.Transportof1.1mColloidsinLayeredSystems:CoarsetoFineFine33]Thissectiondiscussesthetransportbehaviorofmsulfatecolloidsinlayeredsandswhenwaterflowedfromacoarsertoafiner-texturedmedium.Figures6aand6bpresentrelativeeffluentconcentrationcurves(Figure6a)andspatialdistributions(Figure6b)formsulfatecolloidsinsystemsconsistingof710/360,710/240,and710/150msandlayers.Effluentconcentra-tioncurveswerequitesimilarforthevariouslayeredsystems.Thepeakeffluentconcentrationforthelayeredsystemsapproachedthatofthehomogeneous710msand(around0.77).Incontrasttothefinerhomogeneoussandsystems(360,240,and150mdatainFigure1a),theeffluentconcentrationsforthelayeredsystemsexhibitedafasterrateofconcentrationincreasewithincreasingcolloidaddition(i.e.,PV).Thisobservationsuggestsamorerapidfillingofaccessibledepositionsitesforthelayeredsystems.systems.34]InspectionofFigure6brevealedsimilarretentionofthe1.1msulfatecolloidsinthefirst710mlayer.Incontrast,theretentionbehaviorinthesecondlayerdependedonthesandtexture.Thefiner-textured150andmlayersexhibitedgreaterretentionattheinterfacethanthe360mlayer.Asforthehomogeneoussystems,adecreaseinthemediangrainsizeofthefiner-texturedlayerwashypothesizedtoproducemorestrainingandthereforegreaterretention.Incontrast,thelayeredsystemsexhibitedsignificantlylessretentionatthetexturalinterfacethanatthecolumninletforthecorrespondinghomogeneoussys-tems(seeFigure1b).Asdiscussedintheprevioussection,feweraccessiblestrainingsiteswerehypothesizedtoexistwithinthelayeredthaninhomogeneoussystems.Thismayoccurasaresultoftransportprocesses(sizeexclusionandlimitedadvection)aswellaspartialfilling(depositionofnaturalcolloidsduringcleaning)ofstrainingsitesattexturalextural35]Anadditionalmicromodelexperimentwascon-ductedtofurthersupportourhypothesisthatstrainingoccurredattexturalinterfaces.Figure4bpresentsaphotoof1.1mcolloiddepositionin150msandadjacenttoa710/150texturalinterface.SimilartoFigure4a,thisphotodemonstratesthatmanyfluorescentcolloidscanbedepos-itedatgrainjunctionsduetostraining.Verylittledepositionwasobservedinthe710msandontheothersideofthisinterface.rface.36]Tofurtherillustratetheroleofstrainingattexturalinterfaces,considerFigure7,whichshowsrelativeeffluentconcentrationcurves(Figure7a)andspatialdistributions(Figure7b)for1.1msulfatecolloidsinsystemsconsistingof710/150,360/150,and240/150msandlayers.Inspec-tionofFigure7revealsadistincttrendofdecreasingeffluentconcentrationandincreasingcolloidretentionnearthecolumninletwithdecreasingmediangrainsizeofthecoarser-texturedlayer.Theseresultsareconsistentwiththoseforthehomogeneoussystems.Figure7bindicatesthatcolloidretentioniscontrolledbythe(first)coarser-texturedlayerinthe360/150and240/150layeredsystems.Colloidretentioninthe710/150layeredsystem,however,wasdominatedbythefiner-texturedlayerduetothegreatertextural(permeability)contrastatthisinterface.Henceincreasingthetextural(permeability)contrastinthesandlayersleadstoatransitioninthelocationofpredominantstrainingfromthecolumninlettothetexturalinterface.interface.37]Figures7aand7balsopresentsimulatedeffluentconcentrationcurvesandspatialdistributions,respectively,for1.1msulfatecolloidsin710/150,360/150,and240/150msandlayers.Thesimulationsagainconsideredstraining(=0and=0)accordingtoequations(1),(3),and(4).Thevalueoftheforthe(second)finer-texturedlayerwasfitteddirectlytothetransportdata(Table4),whereasothermodelparameterswereobtainedfromthehomogeneoussystems(Table3).Thestrainingmodeldidareasonablejobofdescribingboththeeffluent(Figure7a)andspatialdistribution(Figure7b)data.Table4indicatesthatthevalueofincreasedwithdecreasingsizeofthefiner-texturedsand(morestrainingsites),andtendedtoincreasewithincreasingcontrastinsandtexture(increasedaccessibilitytoavailablestrainingsites).sites).38]Theabilityoftheattachmentmodeltodescribecolloidtransportanddepositioninthelayeredsystemswasalsoinvestigated.Figures8aand8bpresentobservedandsimulatedeffluentconcentrationcurvesandspatialdistributions,respectively,for1.1msulfatecolloidsin710/150,360/150,and240/150layeredsystems.Inthiscase,valuesofweretakenfromTable2.Theattachmentmodelsignificantlyunderestimatedcolloidde-positionatthecolumninletandtendedtooverestimateddepositioninthesecondlayer.Thesimulatedeffluentconcentrationstendedtooverestimatethetransportpoten-tial.Thevaluesofrandrforthe710/150,360/150,and240/150systemswere0.97and0.18,0.99and0.11,and0.89and0.47,respectively.Recallthatvaluesofinthehomogeneoussystems(Table2)were2.9–5.9timesgreaterthaninthefinertocoarser‘‘layered’’systems.Henceutilizationofvaluesdeterminedinthefinertocoarser‘‘layered’’systemswouldhavepredictedsignificantlylessdepositionatthecolumninletandtexturalinterfacethanshowninFigure8b.Similarly,thepredictedeffluentcon-centrationswouldhavebeenmuchhigherthanthatshowninFigure8a.3.4.Transportof3.0mColloidsinHomogeneousandLayeredSystemsSystems39]Thissectiondiscussesseveraladditionalexperimentsthatwerecarriedoutwith3.0msulfatecolloidsusingboth Table4.FittedValuesof(forSecondSandLayer)fortheLayeredSystems(1.1mColloids)150/7101.10.000(0.001)1.31.000.97150/3601.10.000(0.000)0.10.980.98150/2401.10.001(0.000)6.00.990.97710/3601.10.001(0.000)5.80.970.86710/2401.10.002(0.001)15.40.950.87710/1501.10.002(0.000)16.40.940.96360/2401.10.002(0.001)15.20.930.63360/1501.10.001(0.000)10.50.970.74240/1501.10.001(0.001)8.70.790.97Thequantity‘‘Percent’’isusedtodenotethepercentageofinthesecondsandlayerrelativetothecorrespondinghomogeneoussandsystem(seeTable3).Standarderrorvaluesfortheparameterfitsareprovidedwithintheparentheses.BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES11of17 homogeneous(150and710msand)andlayered(150/710and710/150msand)systems.OnthebasisofresultsbyBradfordetal.[2002,2003],greaterstrainingwasantici-patedfor3.0than1.1mcolloidsinaparticularsand.Transportanddepositionbehavioracrosstexturalinterfaceswasthereforeexpectedtobemorepronouncedusing3.0than1.1mcolloids.colloids.40]Figures9aand9bpresentobservedeffluentcon-centrationcurvesandspatialdistributions,respectively,for3.0mcolloidsinsystemsconsistingofhomoge-neous150and710msands,aswellas150/710andmlayeredsystems.Asanticipatedforstrainingbehaviorinthehomogeneoussands,significantlymoreretentionoccurredinthe150thanthe710msand.Consistentwiththisobservation,transportanddepositioninthelayeredsystemswascontrolledbythe150msandlayer.Theeffluentandspatialdistributionsdataforthelayeredsystems,however,dependedstronglyonthetexturalorder(150/710comparedto710/150).Transportinthe150/710layeredsystemwassimilar(intermsofpeakeffluentconcentrations,withcolloiddepositionoccurringprimarilynearthecolumninlet)tothehomo-geneous150msandsystem.Incontrast,highereffluentconcentrationsandsignificantlylessdepositionoccurredforthe710/150layeredsystemcomparedtothehomo-geneous150msandorthe150/710system.Asforthe Figure6.(a)Effluentconcentrationcurvesand(b)spatialdistributionsfor1.1msulfatecolloidsinsystemsconsistingof710/360,710/240,and710/150msandlayers.12of17BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES mcolloids,thisbehaviorcanbeexplainedbytransportprocesses(sizeexclusionandlimitedadvection)orpartialfilling(depositionofnaturalcolloidsduringcleaning)thatlimitaccessibilityofstrainingsitesattexturalinterfaces.Significantlymoredepositionoccurredatthetexturalinterfaceinthe710/150systemforthem(Figure9b)thanthe1.1m(Figure7b)colloids,suggestingincreasedaccessibilityofstrainingsitesattexturalinterfaceswithincreasingcolloidsize.Tofurthersupportourhypothesisthatstrainingoccurredatthe710/150texturalinterface,Figure4cpresentsaphotoof3.0mcolloiddepositionin150msandadjacenttoa710/150texturalinterfaceinamicromodelexperiment.SimilartoFigures4aand4b,thisphotodemonstratesthatfluorescentcolloidscanbedepositedatagrainjunctionduetostraining.4.SummaryandConclusionsConclusions41]Naturalsoilandaquifersystemsfrequentlycontainlayersandlensesofcontrastingsoiltexture.Incomparisontohomogeneoussystems,relativelyfewstudieshaveex-aminedcolloidtransportanddepositionattexturalinter-faces.Saturatedpackedcolumnstudieswereundertakentocharacterizecolloidtransportprocessesinlayeredsandsystems.Specialattentionwasgiventotherolesofcolloid Figure7.(a)Observedandsimulatedeffluentconcentrationcurvesand(b)spatialdistributionsformsulfatecolloidsinsystemsconsistingof710/150,360/150,and240/150msandlayers.Heresimulationsconsideredonlystraining(equations(1),(3),and(4)).BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES13of17 strainingandsizeexclusion.Mechanismsofcolloidtrans-portandretentionwerededucedfrommeasuredeffluentconcentrationcurves,finalspatialdistributionsinthecol-umns,massbalanceinformation,microscopicexaminationofdepositionbehaviorinmicromodelexperiments,andnumericalmodeling.modeling.42]Foragivensandandcolloid,depositionwasalwaysmostpronouncedatthesandsurfacethanatatexturalinterface.Colloidsenteranewporenetworkatthesandsurfaceandarethereforemorelikelytoencountersmallerporesordead-endregionsoftheporespacethatcontributetostraining.Incontrast,wehypothesizethattransportprocessessuchasadvection,dispersionandsizeexclusiontendtoconfinecolloidtransporttothelargerporenetworksattexturalinterfaces,andthuslimitaccessibilitytostrainingsites.Increasingthetexturalcontrastataninterface,how-ever,producedgreatercolloiddepositionwhenwaterflowedfromcoarsertofiner-texturedsands,suggestinganincreasedaccessibilitytostrainingsitesinthese(new)porenetworks.Conversely,whenwaterflowedfromfinertocoarser-texturedsands,littledepositionoccurred.Hencecolloideffluentandspatialdistributiondataforlayeredsystemsdependedstronglyonthetexturalorder,especiallyforlargercolloidsandgreatertexturalcontrasts.contrasts.43]Simulationofthe1.1mcolloidtransportdatausingaconventionalattachment/detachmentandblocking(Lang- Figure8.(a)Observedandsimulatedeffluentconcentrationcurvesand(b)spatialdistributionsformsulfatecolloidsinsystemsconsistingof710/150,360/150,and240/150msandlayers.Heresimulationsconsideredonlyattachment(equations(1)and(2)).14of17BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES muirian)modelprovidedapoordescriptionofthespatialdistributiondata.Apreviouslydevelopedstrainingmodelwasthereforemodifiedtoaccountforblocking(filling)andaccessibilityofstrainingsites.Thismodelprovidedasatisfactorycharacterizationofcolloideffluentandspatialdistributiondatainbothhomogeneousandlayeredsystems.systems.44]Findingsfromthisstudyhaveimportantimplicationsformanycolloidtransportscenariossuchasthedesignofefficientwatertreatmenttechniquesbaseduponsoilpassage(riverbankfiltration,infiltrationbasinsandtrenches,andsandfilters),aswellasthetransportandfateofmicro-organismsandcontaminants(colloid-facilitatedtransport)inheterogeneoussystems.Knowledgeofcolloidtransportprocessesacrosstexturalinterfacesinunsaturatedsystemsis,however,verylimited.Inthiscase,thetopologyandgeometryofthehydraulicallyactivenetworkwillgreatlydependonthedegreeofsaturation.Additionalresearchisneededtoquantifytheinfluenceofmanyphysical(watervelocity,flowbypassing,watersaturation,anddimension-ality),chemical(aqueousphasesolutioncomposition,sur-facechargeofcolloidandporousmedia),andbiologicalfactorsoncolloidtransportandtoincorporatethesepro-cessesintomathematicalmodels.models.45]Acknowledgments.Thisresearchwassupportedbythe206ManureandByproductUtilizationProjectoftheUSDA-ARS.MentionoftradenamesandcompanynamesinthismanuscriptdoesnotimplyanyendorsementorpreferentialtreatmentbytheUSDA. Figure9.(a)Observedeffluentconcentrationcurvesand(b)spatialdistributionsfor3.0msulfatecolloidsinsystemsconsistingofhomogeneous150and710msandsaswellas150/710and710/150sandlayers.BRADFORDETAL.:STRAININGOFCOLLOIDSATINTERFACES15of17 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