CoIC0S.s ana Su. ;&es, 1 CE980) 313-334 Q Eketier Scierdfk PuhlFshing Company, Amsterdam - Ptinted ia Belgium

313

(Received August 14th, IS’rs’; accepted in final form January Zbth, 1980)

ABSTRACT

The deprxitian of sub-micron latex particles during flow tEtrough beds of fine aImnina Ehers has been studied as a function of pH and ionic strength in the vicinity 0P the fiber isoetectrie point (ie-p-I_ Conditions were chasen so that the predominant capture rr,echa- nism was diffusion Rests have heen compared with the ‘%lassical” theory of convective diffizsion to cyiinders and with modern theory, which takes into account coEloZdaL and fiydrodyoamic interactions between particles and cobctor,

&titial fiber collectioon efficbncies, determined at the iep_ where the fibers hear no surface charge, are considerably Lower than those predicted h;t classical theory and are insensitive to ionk streng& This lack of dependence on ionic strength suggests that neither constant potent&I r~or constant charge conditions are maintained during particle- Gber encounters and that some interme&ate condition is more appropriate- ParticIe capture results obtained at pH values ahove and heEow tixe fiber LP-p_ agree qua@itativeLy witi the predictions of the Spielman and Friedlander ‘Surface reaction” modeb although this is not strictly valid Mow the Lep_ whae the fibers ate positively charged and there is no reptiion barrier, Under these conditiors a sig&Ecant enhancement of captm-e effi- ciency is observed at low ionic strength, as a result of double Eayer attraction Above the itzp., where the fibers and particles are hoth negativeIy charged, double Eayer repulsion causes a IaTge reduction in capture efficiency, ahough the predicted reduction is even larger_

The s&~&on coverage of the fibers hy deposited garticles was found to decrease strongly as the ionic strength was decreased. indicating the importance of lateral inter- actions heteen particles.

The deposition of cOHoidal parfkks on to solid surfaces is of direct practical concern id such E&is as detergency, water treatment and mherd processi& md aTso of fimdame~~tal iM&st as IL means of investigating the interaction ,forces involved. These forces are of essentiaII~. the same type as those acting between identitial partickss ie- van der WaaIs and eIectricaI double Iayer fori+ which form the basis of the weIl-known DLV43 the&y of coEc$d st%biIitg; (Der&.in aud Landau, 1941; Vemrey ana3 Overbeek, l948)_ Additional forcks may arise from s&r& inkra~tions {‘e-g- Napper, 19771 and possiblym kom effects due to sofvation hyers~

314

~~ilethereis~~~edoub~abouttheessen~qu~~~ecorr~~essof DLVOtheory,thereare~conside~Ieq~anti~ti~eunc~tiesinap~~y- ingee theory,especiaEyfor -_ * 'Tar ~aces,asinthedeposi~onprobIem_ Forinstance,~evanderWaaIs~~~ctionmayundercertaincon~tionsgive arepursion,ratherthan~emo~~ a~c~on~vanOsse~aL.1978)_ Furtherraore,~hesimple~~aker (1937) approach,b~edontheassump~on 0fpaFruPSsead~~i~~oflrrtermolecuEar forces,isknowntobeanover- simpLification~~~~canleadtoappreci~le~or,p~cl~ly~ aqueous media(Parsegian, 1975)-

In~~ula~gelec~~~doublelayer~~~~tion,~aresultcandepend greatlyon the assumedb~undarycon~tions,whetficrcons~~surface poten~i~,cons~~slrrfilcecharge densi~orsomein~edia~con&tion_ Between~dentica2p~~lesa~close approa~h,theco~~pof~rrtial and constantcharge ~~mp~ionsLead~overydIfferentcalculatedr~~~ions,the latter~vlngmuch~ea~errepursion andhencea Izigherpre&ckd colloid stability. ForunIikeparticles,the~wo assumptionsIeadtostillgrea~rdiffer_ encesandeven~e~~of~he~~eraction(ie_repulsionora~~ction)can ~~r_Thecons~~potentiaZassumptionpre~e~ana~cti~nbe~~een xzr'aces atclose approach.eventhoughtheymay havepote&iak oflike sign_ Conversety,theconstantcharEIeassrrmption~eeads~o~hecon~~~ion~hat opposielychargedp~e~eswo~drepeleacho~hera~~c~entLycZose approach_

ItisgeneraByaccepted(e_g_ Gregory,1973)tha~thecons~~po~entid andcons~~chargecondi~ionsrepresenth~othe~~~~emesgivIng, respectively,lowerandupperbounds~otieintirac~ionenergy andthatsome In~nne~ateconditionsm~~themoreappropria~_Formany~aces,having oneormo~~p~ofionizabIe~oups,~es~~e potentid dependsonthe densityandio~a~ionconstants of thesegroupsandontheeoncenfzations of potential-determIgions~e_g_ H')insoIution_ Whenko suchsurfaces approa~heachother,theconcen~tionsofpofentia_-deferminingionsc~ose tothesurface~changeandtheionizationeq.&ibriaPviZLheaffec~d_ CaIculationsbasedontiisreguIa~dsurfacechargemodeLgivein%ra&ion.s intermediatebetween~heconstantchargeandco~~~potentiaZconditions (NlnhamandP~~an,197f).~eveand Rucken&eiufl978)baveshown howsuchbehaviourc-anhave aprofoundeffectoncaIeulateddepositZonrates_ Theyconsideredcasesin whichapproaehingsurfaceshadeihers%rongLy ionicgroups,such th;r~th8chargeden~~remainedessentiaLIycon~~or equdR=JmbersofwealcIyac~Iic and basicsF~s~vi,lganphoterie~a~~ wFtfranearlyco~~~~acepotentiaZexcep~a~verysmallseparations_ Thesemode~surfacesarenotverydifferen~*~~mth~~~p~c~e and al~a~bersurfaceselrrploy~din~hepresent~dy-fnp~~~cases of deposition,encountersbe~een~a&i&sandtiesurf~cemaybeofsuch Sho~d~tiontha~ior~ation~quilibrZaarenotm~~edandtheinter- actionwouldthenbemoreli?ce~heconstantchargecas~~E'rensandOverbeek, 1972)_

~p~en~studiesonp~c~edepositionusinga~e~oftechnlques havebeenrepo~butsof~~eres~~~~avenotenabEeaanyEirmcon- ~Eusionstobe~~co~lcemingthe n&ureoftheco~oidalforcesinvoEveb, ~ero~t~gdisctechnique(Marsh~and~~ener.~966;~uZLandKitchener. 1969;~~tetak,1913)hasbeenusedtome~eratesofdepositionontoa fiatsurfaeeunderweU-defined hydradynamicconditions,When~~eroisno repulsion betweenp~c~~ancF~ediscsurface,depositionratesare~ene~y ingoodagreement~t~thosepr~c~~by~~~B1962)theory,In~e presenceofrepulsFon,depositIon~esarereduced,ssexpec~~,bEmt~e reduced de_oo&ionrate observedexperimentaEycanstiNbeordersofmag- nr~de~ea~thantha~c~c~~theoreticatEJr_Apossiblee~p~anationis thatthedisc surface maynotbeentireLyurriform~dtha~depos~tioncan CJCCZV atcertain&es ~herethein~~c~onismorefavourabIa However, Ruckensteti arzd Frieve (1973) have pointed out the extreme sensifSv%tg of predic~ddeposition~~sto thevaluesofsurfacepotentialusedin the calculations- achargeofonLy5mVcan,u11dercertainconditions,aEerthe depositionratebysix ordersof magnitude_ThismaybeespeciaNysignifIcan~ s~ceeEectroIdneticprope~sof~ediscs~acecannotheconveniefieLy measuredandhaveEobeestimatedin&ecLJy_

Another~perimental depositiontecbnique(ClayfieId and Smith,1970) istoflowsuspensions ofpertidesthrougtrpackedbedsof substrateinasuit+ ali\Ieform{usuallyeitherfibers or sphericalbeads),measuretheconcentration ofp~clesirrthe~~e~dL_rencecaIcula~thenrrmherofp~cles deposited_ThemainadvantagesofthisflIfxationtechniquearethatarange of well-characterized materials can be used as the filter medium and tbati the measurementsaremoresfxaightforwardthaninthero~tingdiscmethod_ One~vantageistha~frhehydrod~amicsoffEowtErrougfrpororrsmedia are~~ts~~eLLe~b~hedasforthero~ETng~e,sothat~eoret~cal~~s carmotbecalcuIatedsoeastiy_ Anobherproblemisthattheparticleshaveto besufEcientlysmaPLso tha~sfmkingisrzof asignificantremovalmechanism. SinceGErationisawidely used solid-liquid separationtechnique, the resuXs ofsuchstudiesmay&obeofsomepracticalvaEue_

Ea~epresentworka~~tionf;ec~que has beenusedwith aIuminaEihers as thehEtermedium and suspensionsofpoLyst~?neIa~_Th~sys~mis especi&yusefuLfordepositionstu&essinceahnnina., likemanyotheroxides, hasa pH-dependentsurfacepotential,xv-itha weliLdeEiiedisoe~ectic point, enabIlngthe~ectricalinteractionbe~eenfibers and partic~estobeconv~ nien~pcorr~o~edbypHadiustmen~ Eisintheregionof theisoeEe&ricpoint wher, .,e c~c~tedelectricaZin~~c~orzismostsensi~vetotheass~e~ boundaryconditIons~d~h~ec~tic~testsofcurrenttheoriessho~dbe possible-Depositionhasbeenstudiedasafmction ofpHand ionicstrength underconditions where~ionis~pectedtobe~epredomin~tcapture mechanism,

Thep~blemofcouvectivediffusionofparticles~ocyllndricaI.coUec~ors ha:beensoLvedinanumberofwiays(seee_g. Friediander,~977).TheresuIt isusuaHyexpressedas a dimensionlesssinglecolliectare~c~ency,p, v&&is definedastheftaction ofparticksco~ectedfkomth~ ffuidvohrueswept by thecyEnde_r

PD = 3,64A~'~Pe-+'3 (2)

~h~ePeis~ePecletn~ber(=zaF~/R,w~;ere Dis thediff&sioneaefficient ofthep&cles)_ AF isaffow fieldparameterwhichdependsonthepacking ofthefibersin~hefili;erbedandcanbe~culatedfrolllan~ber of tieoreticalmcdelsof packedheds_TheHapp~cellntode~rETappd,1959) hasbeenchoseninthe present ~orksince~~sgiveslresta~ee~en~~~hthe measuredpermeab~tiesoffhefIberbe~.Tfia~apprdresrrlf;forA~ is-

AF = 1/~-ha-I+ot?~(l+a*)]

vzl-tereock thevalumeftactionofSbersinthebed_(ThemoreusuaLversion ofeqn(Z)isforisoIated cylinderswhenthe factorA~ hkesaratherdifferent f&lL)

Fi&er performance

Aspa.&iclesarecapfmredbyfihers_ theconcentrationC,of~articEesinthe ~o~gsuspension~suc~and.a~.anyiEl~~thezoncen~~ionvaries w%bdepthLinthefiMerbed accordingto the following e9pressian(seee_g_ Eves, 1975):

ac -= --XC aL

C - = exp(--h&) CO

3x7

Aa = =V/J=F (6)

Thusitispossib~etocakuIatep fromtheinitiaZvah~eofC~C~ andfrom measurabfep~ope~esof~e~~rbed

OnceparticIesaredepositedonfibers,theymayinfIuencesubsequen~ depositioninseveraLTAays,eF~herincreasingordecreasing~hef~~~coef~c~en~ IngeneralthefiMercoefEcientwiirv~assomefuncf3onoftheamo~ntof deposited particles,o,(usuaEy expressedasavolumefractionandc~ed the specific deposit):

h = h,ffo) (7)

Thesimplest assumptionis that deposi~p~c~esoccupysites of ace&aim areaonthefiibersurface

model assumestiat particIescannot

form:

f(a) = (I-rrlo,) (8)

fortheE.Itration processcanbewritten:

acfaL = -(l/u)(&T/3f) (9)

~For&mmsiorudconsiskncyC andamusthavethesametits-usually vo~/voL)

Itis~er,possible,usingeQns~4),(5),~7~9)~oob~asoI~tionfor C/C, asafunction oftime~ie_thebreakthxcughcurue). TheresuIt%:

31%

Othersolutions,fordifferent~ormsoffjo)havebeengivenbyEXetiget aL(1970),

The"classicaL"resuEtfordiffu~onalcap~byfibers,eqn(2)isbasedon theassumption thateveryeneo~~Leadstopermanenta~~~ent,all interaction forcesbeingignored. Infact,asaparticleapproachesafiber surface,severaltrpesofin~c~oncancomeintoplay,w~ch mayhavea profoundinfluenceonthecapturer&x

ColIoidal forces, arkingfkomvan derWaalsandelectri4xldoubleIayer in~tior~,usuallyactoveravergshortrange,muchsmallerth~theehi~k- ness ofthe concen~tionboundaryIayer,~~atcase,i~hasbeen shown (RuckensteinandPrieve,^r973;SpiehnanandFriedIander,1974)t5at the depositionproblemcanbe treatedasoneofconvectivedZ!Z&iontotheco~- k&or surfacefollowedby a first-ordersurfacereaction_Theratecon&mt fort&issurface reaction,K',dependson~e~~~ctionpo~n~~(#)

ofSpielmanandFriedlander(l974)gives:

wherekisBo~tzmann'sconstant andTtheabsolute temperature- Themadifiedcapti.eeffi&ncybecomes:

QD

ie.the"c~~*'efficien~~venby by

0_7375Ar"3Pez'~U-'~

andC(8)isaslowlyvaryingfunction of~withvaIuesrangingtioml-34for #3=ltQUni~for~=~J, SomevaluesofC@)aretabnIated byspiehanand EYriedlander(1974),

~en~e~~tion,#,ispo~~eovertheimpo~~regionofseparatian (Le.ifthereis apotential energybarrkrhinde&g deposition),thenK'is positiveandthecapturera~ereduced,ase;+pected. InordertocalcuIateQ appropriateexpressionsforvan der WaaLs andekcfxical doublelayerinter- actionmustbechosen.Formanycasesofcapture ofsm&partic~es by much 13~gereoFlecto~.itissufficientto~~the~~ctionasonebe~~na sphere~da~tsurface,Also,since~einteractionisofrathershortrange. itisoftena~cep~letouseapprogima~clrrpressio~~vaIldforver~rclase approach,&houghthesecanbecomeveryinaccux&eatIargerdistances(of the order of~ep~~eradius)_~o~dedt~~theInteractionisnegligibleat suchsep~~ons,theinaccuracyisofIi~e consequence_

3L9

ForvanderWaaIsattraction,#~,~tisusualtoempIoytheexpressionsof Hamaker(1937),inspiteoftheirknownsho~o~~_~deposi~ionstud~es the retardation e~~fectcambeimportamt bu~~here~dedHarnakere_upr~sions c~b~omera~herunwieIdy((=lay~e~detaE.,f97k;V~cen~ P973)- An empiricalexpressionforecpcaIspheres(Gregory,to bepubIished)whichgives goodagreemen~withtheeompu~~onsofC~ayfieIdefat_(197Lj,can be written for thesphereptatecaseass

whereA isthe Hamakerc~nstant~a~ isthe particleradiusand 6 = 5_32/X',X' beingthecharacteristicwavelen~hof~evarrder ?Vaabinteraction,often assumedtobeabot&100r,m.

Equaticn (13)shouldbeanacceptabIeapproximationformostpurposes atseparationdistancesx~ ~~~/2,A~grea~~dis~~~*for~eralvaluesofehe Hamakerconstant~theattractionenergybecomesverysmaEB-

FortheeIectricafinteraction,~E,variousexpressionsareavailabIe_The simpIe linearsuperpositionapproximation(LSA)givesresuIts intermediate be~~een~econs~~po~n~~Ldcons~~~cch~eeondrtionsand for the spher~-pIatecaseinasymmetrical(z-z)eIectroIytecan he written:

oE(LSA) = 64a,a~(~T/ze)*rrrzexp(--Kx') (141

where E is tke permitfSvity of the dispersion medium, z the valence of the ionsinsoIutionandetheeIement.aryebarge.y~ and 7= are functionsofthe surfacepo~ntiaT~ofthep~cI~s~dcollector,9~,and gZ:yI= tlmh(ze@Xf&T)etc_ K is&e Debye-HiZcke~reciprocaaLen~parame~r givenbyK Z=2e2nzZ/kT,wh~nis~henumberofca~ioons(orarrio~)per unitvoIume.Ineqn,(14) amodified separationdisbnce,x',isincIuded to allow for thefaei~ha~~ec~o~etic(zeta)po~ntiaIs~viEllbeusedf~rthe S~acepo~n~and~a~~esepo~ntiaIsaremeasure d aha plane;rtsome distancefromthetruesurface_Thus theelectricdiuteraction opera+&over asomewhat.shorterdistancethan~evan der Waalsattraction (Bijsterbosch, 1978)and~eeffectivedistanceisx'=w-_6,~hereS isthesumofthetwo Sternlayerthicknesses andwillbeassumedtobe about0_5nm_

Thepresenttsys~mofIakxparticIeswithstronglyionCzedsurfacegroups titeractingwithamphoteri~aIumina surfacescorres~ondsdoseIywiththe T'ypeAmB sy.c'eminvestigated theoreticaUybyPrieve and Ruckenstein (1978),AI~orrgh~~xein~ction~such acaseis Iike that betweenconstant po&ntiaI audconstzntchaqgesurfaces,the computedde_aositionrateswere onlyslightiylessthanthose betweensurfaces ofconstantpo~ntialu~der simiTarconditions,Sincethe assumptionofconstantpotentialsurfacesIeads tuthehighes%predicted deposiionraresi&givesan upperboundwithwhich tocomp~egperimzntaPresu2ts,For~eeaseofunli~ surfacesatconstant po~n~aconve~e~~approxFmationwasderivedhyHogg,Efealyand

rvherey, andyZ arereducedsurfacepo~ntials,y~=~e9~lkTetc, TheLSA andHHF egpressionsglvesim~arre~~a~largesepas~tions,bu~

becomeverydifferene whenthesep~~iondistanceissmallin comparison wIth~eciou~lelayertIrickness(i.e.mhen RX* <I). Whenone surfacehasa potentialofzero~heLSA~pressionpredictsno~~~ction,whereas~he EiE3FresuI~givesasign&xntafAractionatcLoseapproach~Sincetherangeof ~einte~~~icrldependson~onic~n~(via~heDeby~~~ckelp~e~r, tc),thedependence of CaptureeBciency onionicstrengthfor uncharged fihersandchargedparti&sshouIdprovideinformationonthenatu.reofthe doublelayer-5tteraction,

~ydradyn~~corviscousin~ractionsareno~ recognizedas playingan Fmpo~~p~in~e~p~eofp~~esbycoIlectors(e.g_ SpieIrnan, 1977) andfordiff&ionaLcapturethe effectismanifestedasa reduceddtffusionco- ef&ientforparticIesclosetoaco&ctorsurface. Inthelimttofzerosepara- tionthediffusion caefficient approacheszero andso,in the abseneeofany euternalforce, nocaptureshouldaccur, Howevertheuniversalvander GVaaLs forcesof a~c~~o~usualLyovercometheviscousresis~ceso~at capture canuccur, ~~houghof:tenaeasignrtrc~~yreduced~~-The diffhsionco-

efficient ofasphere~thevicinityofawaltnascalc~tedbyBrenner(1961) andaverysFmpleempiri~represen~tionofhIsre~~hasbeengFv~by Dahneke(1974):

D(x) = !I(-)/(1 WY&) 616)

where D(;c)is thediffusioncoefflcientofasphereseparat&byadistancex ~oma-~~andD(~)is~ebulkv~u~(i,e-atinfiniteseparatibn),

Thisresul~isneverinerrorbymoretha.~about6%andenabIeseqn(lI) toheeasiLymadifiedtogive thesurfacerateconstantincorporatinghydro- d~amicresistance:

Theincorporation ofhydrodynamic resistancecausestheintegndin eqn(l7) todiverge,sothattheupperKmi~cannotsticfJybetakenasi&nity(Prieve and Ruckemtein,1976),whentheinfzractionpotentidispositive(giving a repuIsion)the predominan t contributiontotheintegralcomesl2omvery smallsep~tion~~#s~d~heeffectofthehydrodynamiceffec~a~farger separationscanbeignored,When#iszeroornegative,aBniteupperlitnit hastobechosen(seeMer)_

Equation(17)wiZLbeused,toge~zr~~heqn(rZ),~calcuIafe~eeffe~

321

of coHoidal forces and hydrodynamic resistance on deposition rates, for comparison with experimental results_

Polystyrene law particles were prepared by emulsion polymerization of styrene withorrt added surfactant and using potassium pert&fate as initiator. The method of Kotera et al_ (X970) was employed but witi a Low @AM) monomer concentration (Bijsterhosc& X978), resulting in smash particles having a mean diameter of 0.112 pm w&h a coefficient of variation of 4,655 ~determined from ekctron micrographs). Afti preparation tie Iatex was neutralized with NaOH and extinsively diaLyzed against distilled water in a Bia-Rad hoIIow-fiber beaker dialyzer.

Alumina fibers with mean diameter 2_0 pm, with a coef&ient of variation of 15%, were supplied by ICI Mond Division (similar fibers with a small proportion of silica are avaZtabIe under the trade name “Saffd”)_

Eecause of the necessity of maintaining constant pE-I during -tended filter runs, alI soWions weal buffered with tris (hydroxymethyl) methylamine- HCL Solutions of varying pH could be conveniently prepared at constanc ionic stren&h_ Even at the lowest ionic strength employed (lW4M) this sys- tem gives reasonable buffer capaciJr,

Au water was tripIy distilled, the firtal distillation being from alkaline permangan2&e soIution_

Techniques

Electrophoretic mobilities of both latex p&cIes and fibers were deter- mined in a Rank microelectrophoresis apparati (Rank Bras- Eotiisham, Cambridge, Engkmd), Particle mobilities were measured in the cylindrical cell and fiber mobiities in the ffat cell_ Fiber beds which had undergone a similar preparation and equi.Iibration procedure to those used in filtration expe& ments (see below) were suspended irt the appropriate buffer soIntion and allowed to stand for a few minutes prior to intiaduction into the flat ceL The remaInin gfiberswere fllfficienffysho~(5-~~0~m)~se~eq~~

so their couId determined fiber were to PO-&& the Smoluchowski tion, of much size the particles cor-

are and potentials obtained the computafions O’Brien White

The apparatus pmcedure been previou@y and X979), the involved

of fibers WV) 0_005M (PI-Z with aid a bIender_ by settling the &om long

322

col~~formauniform,reprc;ducibIemat42cmindiameter,TypicaELy 0.05gfiberaset&dto&e abed deptiofl25mmand a porosityofO.965 (Le_ac =O_OS5),

ImmediafeLyprior~~~tion,the~~wereequiLib~~bypassing 300cm30fb~~soLutiona~~esamepHandionics~~asthe suspcnsiontobefiLtered,Particle~pensions(Co=6_45 X IO9 particIescm-3) werethenflowedthroughthefiberbedatthe requiredffowrate (2,Ocm3 min+,U=8,77X 10~5ms~'),~~~~~samplesco~~~~~anau~omati~ fractioncolIector,ThefiErate qualitywas determinedturbidimetricaIlyby measuringtheabsorbanceat350nmwith aUnicam SP6-5OOspectrophoto- meter.

REXXJLTS AND DISCUSSION

Zetapoten~ofiheaZuminafibers~sho~inFi~las ahnctionof pH andronic~ngth,Theresults:;howacleatLyd~n~ isoelectric point (Le.p.)atpEZ7.8,which ~independentofionic~en~,indi~~gtha~~he bufferionsarenotspec~c~yadsorbe~Thishasfieenconfirmedforsimirar fibersby -gout po~ntiometricti~tions~oobtain avahxe forthepoint of zero charge (p.z_c.), The p_z_c. and &e-p. were very close, again indicating a lackofspecificadsorption_

ThezetapotenialsoftheIatexpartic&s aZ oneion.5cstrengthare*o showzxinFig.las afunction of pH,fncl;hiscase~e~isp~ctic~y~ovarIa- tion,asexpectedfromthefactthat the surface chargearisesfromsulfate groups_The~issome~tionofp~c~eze~po~nti~wi~ianics~n~h an~val~esa.tlO-flO-~ and10-2Mionicstrengthwerefoundtobe-59,-64 and -54 mV respectivdy~

Breakfkrough curues

323

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325

curues,Thena~eof~discrepancyimp~~~atthesImpIemode~ greatly underestirnatestheeffect ~fdepo~~partic~esonsubsequen~depo~tion. Depositedparticiesmustaffect theflow fieldaroundthefibers,aIthough, even atsafxratiorr,thereis nomeasurabIechangeinthehydrauIicpermeabi& ityoftheGberbeds_NevertheIess,thefIowcIosetothefibersurfacemustbe modified anditislikely thatfbiscouldh.inderthecaptureoffurtherparti&zs, quiteapartfromtheeffectofsurfacesiteb!ackage_

~eranaIysisoftheformoftheb~~u~c~~willnotbegiven here, Atten~onwillb4~ec~~ow~~he~~ fi.EerperSormance and thecapaei~ofthe~~~rsfcrp~c~eremovaLatdifferentvaIuesofpHand ioEdcstn?ngtk

AusefulfeatureofthebreakthroughcurvesinFig_2isthatthey showan initial linear rise of C/c, wi”Jr fibaf~ voIcu.~e which enabies a simple exti- polationtobemadetogive theinitiri!vaiue, correspondingtoacleanmter b~d,TbiseztrapoIationcanbemadewithsomeconfidencesince~hevohune of thefiRerbedandtheassociateddeadvoIumetogetheramaunttoonLy ahout cm3.

TheextrapoIatedvaIues ofC/CO showa pronounceddepende~~eonpE4 atlW"Mionicstrength_ At ~heis~el~~cpo;nt(pHa_8)the~~aP~~ performanceisfzood -about85~ofthePa~~particPesbelngr~ov~.~ performancedeterioratesmarkecIlyasthepHisr&xzdabove theie.p.and ~efibersbecomeincreasingIyne~~e_B~ow~eie,p. whenthefihersare positiveIycharged,thereisameaswra b~eIncreasein~~rperformance_~ese e~~~canbequ~~tiv~y~d~odintermsofelec~~~doubIelayer ~~ctionbetweenthefibersand~en~t~ela~particles,

Athigher ianic&rengtb,doubIelayerinteractionisofshorterrangeand thee~~tofpKonfiIterperformancesho~d~Lsspronounced_T~~is indeedtheease,as shown bythe~~in~g_2,which~ethe~ti~ parts oftiebreakthro ugbcurvesforionicstrengfS1~of10'~ and10-2&I_Itc~be so,enthatinitial particIeremovaZdecreasesressmarkedIy~~incre~gpH atthehi~~ionic~ngths,~hermore,theenhancementof~t~per- formancebeIow~ei~p.is~Iessmarke~becomiagInsignificantat~O-*M.

Theseeffec~oninitiaZfilterperformancecan~more~adiIyappreciated ifthe~~~~conve~~sing~efiberefflciencies~,Theproced~is~ calcuIace~he~~~~c~cien~Xa,homeq~(5)us~g~heini~vaIue ofC/C~~d~hemessuedbeddep~~qua~~~~6)can~renbeused~ caIcula~~~FinaEy~thisisexp~~~~Ias a fractionofthecaIcuIated'%Eassica.P capture efficiency~D.cahx&&edtiomeqn~2) and theknown propstksof thefiherbed, VaIuesofq/qD can thenbeusefully compar&befmeendiffi?r- entmnqeven thoughthere may besIi~tchangesInffowrate,porosr~and ~p~~fromoneexperimentto~o~er,sin~e~~cIrangeswill~ ~~intoaccountincalc~~g~e~~~ticalefficiency,gD_PPo~of q/CD vS-pHfOrfhreed%&rent iOnfCSb?Y@hS~e shownhxFig, 3-

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At UlehigheA ionicstrengthth~isnomeas~lrabIeIncrease incoUe&ion efficiency on the positivesideofthe i~p_indkatingthat doublekyer attractionis oft00 shortararlgeto infIuencethedepositionprocess_The captureefkiencyshouldthenb eC~ermineden~IybyhydrodynamFc factorsandtiefktthattheobs.=rvedefGc~encyisonIyabout40%ofthat predictedbystandarddifCasiontheory~eqn(2),maybeexplainedbyhydro- dynamic~~~tance,discussedearFier,DiffUsion-eontrclfledco~ationof latex particles tiknowntobeslowedbyafactorofabouttwoasaresuItof hy~odynamic~~ce(LIch~nbeItetaI.,1974).Astheionic~en~his decreasedatlowpH,captureeffkiencyincreasesandattheIowestionic stre~~gth(IO-~M)q/q~ can reachvaIuesah~~ostdoubIethosefoundatthehe_p. In~c~~doubleIayera~ctionextendsoverarangewherehydrodynareie res~~ceissignificantarrdcanp~~yco~~~ctit,

At~~herpn,as~hetibersbecomeprogressiveIymorenegative,EiEtration performance declines andthiseffixtisakodependentonionicstrengthheing mo~apparentat~owsaLtconcentratIon,wh~edoubZe~yerrepulsionis of

gcmkrange, Whenthe~s~~inFig,3arere_castLRtheformof~~~D vs-fiberzeta

potentiaI~using the dataof~g_I)thecurvessfrown~FIg,4areob~~_ Theseindkatethatfora givenuegative~iberzetapotentiaZthedecreasein captureeBiciencyismorepronouncedat10-*Mionicstrengththanatthe twolowervaIues.ThisisjustthereverseofthebehaviourexpectedquaIi~- tivelyonthebasisofDLVOtheorywhererepukion shouldbe greaterat Iowerionicstrength~ThereasonforthishehaviourisnotcIear~butmayhave todowiththeconversionofmobiIitiestozeta~otentiaIsandthesignificanee of~ela~indoubPeLayerIn~~ctio=r,Atall~onic~n~hsthemo~sig- nificantdecreaseincaptureeffic?encyoccursoverpHrangeswherethezeta potenfGIshavereachedneatlyconstantvaIues,whicharestiUquitetow_On thepositivesideoftheie-p,thereIationship between captuxeefficiencyand ze~po~n~see=nstobe~~~tiv~yco~~

InaIl casess~far~vestigated,p~cIedepositionon~theaEluninaEibers appears~bee~scln~yineversrble, RemovalofdeposiedparticIescan

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onlybeacfiievedbya~~er~ticchangeInchemicarlcondltions-by flowing10-3MNaOHtErrough~hefi~rbed, Eventhen,onIyasmaIIpro- porEionofp~cI~caraberemovedTheseobservationssuggesf;~atparEicIes arenotcapturedin asecondary minimum, but are in very cIose contact tith thefibersurfaces,

k order~ocalculatetheefZectsofccELoidaZ forcesonpartSecapture,the smfacerateconstantcanbe ob~edfromeqn(l?),usingapprop~a~~- pre~~ionsforvanderWaaIsanddoubIeIayerinteraction~ThecoIIectionef- ficiencycan~enbecaIcuLatedfrom~~(12),Thispro~~ehasbeen carriedou~usingeqp(l3)fortheretardedvanderWaaLsinteractionancI eqns(14)and(l5)fordoubIeIayerinteraction~Whenconditionsare~uch tha~arepulsionbarrier~~=~dednRcap~,~en~proced~eisq~~ s~~o~~However,in~e~senceofrepulsion,the~~~tio~~eqn (l?)pre~~~prob!emssince~ehydrod~~c~causes~e~~~tu diverge,~mentionedprevious2y=so~at~zenpper~tcannotbetakenas irxfhCt$.In the pr~en~c~~~onstheupper~~hasbeentahen~bi~y as5Q0nm,correspondingrou~y~~~e~cknessof~econcen~tion boundarylayer, Choice ofanyo~~v~uein~erangelO~lOQORm praduceso~yaverysIigh~sItif%~thecalcuIatedcurves~ A fi.wtherdiffkuI~ istbatintheca~e ofanattractive potentiaIbetweenparticIesandfibers(ie. on~epasitivesideof~efiberie_p_)theconcep~ofaflIlrfacereactiianrate constantbecomes dubious-K'takesne~~ev~u~~_~ev~~e~,for~e sakeofcomparkon,cakuIationshavebee=rperformedforbothrepulsion and atfzaction and thezsubam showninFig_5,as afuuctionof fiberzeta PO&-&al andionicstreqth~ TheHznnakerconskmtfortheaIumina-wa~ poIystyrenesystemh~beentakenas2XlO~2oJ,basedonopti~prop~es ofthematerbkand foIlowingthe method ofGrego~(l969)_ThevaIueof6 in the double layer computations was assumedtobe 0,5nm.BoththeIinear ~uperposition,eqn(l4) andconstant potentiaI,eqn(15)expreSsionswere usedtithexperimentalzetapotenf&k

These~c~t4xiV~?%?sOf~~~D bearSOme reSernbIancetotheexpert- menta~resuBsinJ3g.4, bu~~erearesubs~~~~nc9s-Thec~c~tions basedonthe LSA expressioncorrecffypr&ictthe insensitivityofcapture rate to ionic stn2ngth at the fiber i-e-p., whereas the eonstad potential assumption leads to an enhanced capture rate at low ionic zdrength, However thepredictedvaIueofo~~~ at~ei~~-isabou~0_~4whe~~eobserved valueis0_42_TheresuItobtained~d~~~conditionsdependson~e rekxtiveimportanceofvander WaaIsa~tionandhydrodgnamic~~~~~ and onewayofbringing ~etheoreticaLvalueFntoline~~~eexperimeff~ ~~istochooseamu~lowervaluefor the HamakercubkAnun- reasonablyIow due wouId havetobechosentogiveagreement Amore pIat&bIereaSon forthediscrepmcybehmentheo~ and experhnentistha~

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331

the assumptions regarding the packed fiber bed, such as uniforrniQ and enhEy transverse fibers may not hoI& In that case the cakxzI&ion of single fiber efficiencies fiomfi&rcoefficientsfor the packedbedwould be subjech ko erroIL

Onthenegative side oftheie.p.thec~c~tionspredictadrasticdec~e ofcollecfioneffi~e~cyasthe6hffze~po~ntialIs~c~~~beyonda ~tic~uaIue~~chdependsonio~c~en~andontheconditionsass~ed_ For the ISA case and PW4M ionic strength this critical value can be as iow as -2mV. The exp-imental restits in Fig_ 4 aIso show a rather sharp decline in capture efficiency with fiber zeta potentiaE, especially at Low ionic strength, but the cr%ical zeta potentials are considerably higher than those predicted Agreement between theory and experiment could be achieved by assuming a lower electrical repulsion or a greater atfzaction between particles and fibers. TheconstantpotentiaI madelgivesasma&rrepuIsionthanthe LSA expres- sion~d~vesresul~cLosertotheexperlmen~curves,bu~s~predicts essentiaHyzeroremovaLforfiberzetapotentiaLsof-10 mVorgreate& where- as, attheIowerionicstrengths~theobservedremovaIisnotreducednotic~ abLyuntiithefibersaremore negativetbn about-2U mV_Theuseof acon- stantchargembdeLoranyoftheregcdat~EsurfacecbargemodeIswouldgive greater repuIsionthantheconstar&potentialexpressionandhencepoorer agreemen~,PLgreementbe~een~eory andexperimentcouldbeimprovedin tbisrespect bytbechoice ofa dif%rentvaIuefortheHamakerconstant, but thevaIuewouldhavetobesubstantiaHyincreas~togivetherequiredvaIue ofthecriticaZzetapotential,andthiswouPdIeadtostiHpaoreragreement withtbeoryattheie.p,

On the positive side of the i.e.p., the caIcuIated capture efficiency shows no enhancement at IWz M ionic strength, a modest increase at IW3 M and a more pronounced increase at 10V4 M, in qutitative agreement tith experi- mentaI observations, The lack of any better quantitative agreement is not surprising in view of the sho~%~oruings of the model under these conditions,

Bycarryhqoutfiltrationrunsuntithe fiberbediscompleteIysaturated (C/C,, =I) the total number of particles removed can be caIculat.ed from the breakthrough curves, as mentioned ear&r_ This has been done and the results expressedas afkactionalcoverag~8,basedon themaximum number of partich~thatcanbe acconmxadatedonthecakuIatedfibersurfacearea, c=Wng hexagonal close packin& The results are shove-n in Fig-6 as a func- tion of pH and ionic strength,

332

The e2cperiments reported here were desigued to enable critical tests of current particle capture and deposition theories to be made, in a system whereslrrfacech~c~ancCby~dynamFcparameterscouldbecarefrrlLy controHedInsp%eof thenear-idealie oftheexperimental system,thzreare serious discrepancies beEween the observed cap- efficiencies and those eakuhtidfrom modexntheoriesincorporatingco~oidalandbydrodyzwnic in~c~ons,Q~~tiv~yffie~~~ofp~c~esbyaluminafiEerswas found to be appreciably enhanced in the presence of strong doubie layer amtion and very much reduced in the case of repulsion. At the fiber iso- eI~~cpoint~ereisgoodevFdence#at~ereis~~eornoeIectric~~ter- actionbetweentheunch~edfibersandthenegativela~p~c~es,sug- g~~g~atne~~~~econstantpoten~nor~eco~tchargemodeIs applies under these conditions. The observed deposition on to negative fibers is much greater than expected from theory and may possibly be explained by a heterogeneity of fiber surface charge.

ACKNOWLEDGEPAEXTS

This work was supported by a grant from the Science Ressrch Council Theauthors ~ivo~dliketoexpEess~e~grati~detoIcTMond Divisionfor supplying the alumina fibers used izx these studies and for maEdng avaSabIe relevant information.

BBFBBBNCBS

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