Application of microstructured membranes for increasing retention, selectivity and resolution in asymmetrical flow field-flow fractionation

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ContentslistsavailableatScienceDirect

Journal

of

Chromatography

A

jou rn al h om ep a g e : w w w . e l s e v i e r . c o m / l o c a t e / c h r o m a

Application

of

microstructured

membranes

for

increasing

retention,

selectivity

and

resolution

in

asymmetrical

ﬂow

ﬁeld-ﬂow

fractionation

Maria

Marioli

a,∗

_,

_Ü.

_Bade

_Kavurt

b

_,

_Dimitrios

_Stamatialis

b

_,

_Wim

_Th.

_Kok

a

a_Analytical_Chemistry_Group,_van’t_Hoff_Institute_for_Molecular_Sciences,_University_of_Amsterdam,_P.O._Box_94157,₁₀₉₀_GD_Amsterdam,_the_Netherlands b_{(Bio)artiﬁcial}_Organs,_Department_of_Biomaterials_Science_and_Technology,_TechMed_Institute,_University_of_Twente,_P.O._Box_217,₇₅₀₀_AE_Enschede,_the Netherlands

a

r

t

i

c

l

e

i

n

f

o

Articlehistory: Received10April2019

Receivedinrevisedform25June2019 Accepted2July2019

Availableonline3July2019 Keywords:

Field-ﬂowfractionation Flowovergrooves AF4

Computationalﬂuiddynamics Microstructuredmembranes Proteinseparation

a

b

s

t

r

a

c

t

Inthepresentproof-of-conceptstudy,wedemonstratethatretentiontime,selectivityandresolution canbeincreasedinasymmetricalflowfield-flowfractionation(AF4)byintroducingmicrostructured ultrafiltrationmembranes.Evenlyspacedmicron-sizedgrooves,thatareplacedperpendiculartothe channelflowontheaccumulationwallofafield-flowfractionationsystem,causeadecreaseinthe zonevelocitywhichisstrongerforlargersolutes.Thishasbeendemonstratedinthermalfield-flow fractionation,andweprovethatthisisalsothecaseinAF4.Weexaminethehypothesistheoretically andexperimentally,bybothcomputationalandphysicalexperiments.Bymeansofmomentanalysis,we derivetheoreticallyasetofequationswhich,undercertainconditions,describethemasstransportand relateretentiontime,selectivityandplateheighttothedimensionsofthegrooves.Physicalexperiments arecarriedoutusingmicrostructuredpolyethersulfonemembranesfabricatedbyhotembossing,andthe experimentalresultsarecomparedwithcomputationalfluiddynamicsexperiments.

(http://creativecommons.org/licenses/by/4.0/).

1. Introduction

Asymmetrical flow field-flow fractionation (AF4), the most appliedsubtechniqueofthefield-flowfractionation(FFF)family, isanestablishedanalyticalmethodtoseparatemacromolecules andnanoparticlesaccordingtotheirhydrodynamicsizeundermild conditions[1–3].Thecouplingwithvariousphysicalandchemical detectorshascontributedsignificantlytoitspopularityasitcan providevaluableinformationsuchasmolecularweight distribu-tion,sizedistribution,conformationandchemicalcompositionin asinglerun[4].Considering therapidgrowthinbiotechnology, nanotechnologyandpolymerengineering,itisevidentthatAF4is goingtowitnessafurthergrowthinapplicationsinthecoming years.Inthisregard,itisworthwhiletoproposeandinvestigate possiblenewtechnicaldevelopmentsthat mayimprove perfor-mance.

Inthisstudyweinvestigatethepossibilityofincreasing reten-tion time, selectivity and resolution by using microstructured ultraﬁltration(UF)membraneswithparallelgroovesontheir

sur-∗ Correspondingauthor.

E-mailaddress:M.Marioli@uva.nl(M.Marioli).

face (Fig. 1). However, considering that AF4 is a very flexible techniquewhere severalparameterscanbealtered tooptimize separation,firstajustificationshouldbegivenfortheusefulness ofsuchadevelopment.

AccordingtotherigorousFFFtheory,theretentiontimeof well-retained(withretentionratio<0.1)componentsinAF4isequal to[5], tR= w 2 6Dln

1+ V˙c ˙Vout B

(1)

where wisthechannelthickness, ˙Vcthecross-ﬂowrate, ˙Voutthe

channeloutletﬂow rateandBthefractionoftheaccumulation areaafterthefocusingpoint.Therefore,theselectivityofapairof well-retainedsolutesequalstheratiooftheirdiffusioncoefﬁcients,

˛=tR,2 tR,1 =

D1

D2

(2)

andconsequently,itcannotbealteredbychangingthe experimen-talparameters.Resolutioncanbeimprovedbyreducingtheplate https://doi.org/10.1016/j.chroma.2019.07.001

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Fig.1.AF4withmicrostructuredmembranes.

heightwhich,basedonthenonequilibriumtheory(for<0.1),is equalto[6],

H= 24D2

v

0

u3crw

(3) whereucr isthecross-ﬂowvelocitythoughtthemembrane and

v

0 is thecross-sectional mean carrier velocity. Hence, a high

cross-flowvelocitydecreasesplateheight.However,itmaylead toadsorptiononthemembrane and massoverloading for sen-sitivemacromolecules.Inaddition,highflowratesarehindered bythetransmembranepressurewhenultrafiltration(UF) mem-braneswithverylowmolecularweightcut-off(MWCO)areused toseparatesmallmacromolecules.

Thesolutescanberesolvedatlowercross-flowratesby increas-ingtheretentiontime,sinceaminimumtimeisrequiredtoachieve separation [7], which couldbe accomplished by increasingthe cross-flowtooutlet flowratioor thespacerthickness[8].Very highcross-flowtooutletflowratiosareimpractical,particularly forUFmembraneswithlowMWCO,andmaydistorttheparabolic flowprofile[9].Inaddition,theuseofathickerspacerresultsin higherrequiredfocusingtimesand moredilutionwitha subse-quentdecreaseinsensitivity[7].Moreover,alowaspectratiob/w (<30),wherebis thechannel breadth,mayaggravateedge and endeffectsincreasingplateheightandreducingrecovery[10,11]. Therefore,itcouldbebeneficialtoinvestigateamethodthatcould increase retention and resolution without altering the optimal cross-flow,spacerthicknessandcross-flowtooutletflowratio.

Theconceptofanaccumulationwallwithmicron-sizedgrooves inFFFhasbeenintroducedin1978byGiddingsetal.[12]asan attempttoincreaseretentionforsmallanalytesinthermal field-flowfractionation(ThFFF).Inaddition,groovedsurfaceshavebeen incorporatedinmicrofluidicchannelsforvariousotherapplications suchastoenablemixing[13]andtoseparatecellsand micropar-ticles[14].Navierhasdescribed thatmacroscopicallytherough surfaceisequivalenttoasmoothsurfacewithpartialslip[15–17]. Infact,forthisreason,asmallslipmightexistontheflatmembrane oftheAF4channel,asa resulttotheporosity,but itis negligi-bleforUFmembranes[18].NanostructuredUFmembraneshave beenfabricatedbynano-imprintinglithography[19–21], where membraneswerehot-embossed,andmicrostructuredpolymeric materialshave been developed withphase separation [22–24], whereapolymersolutioniscastoverapatternedmold.

Thescopeofthisstudyistoconductaproof-ofconcept inves-tigationtoassesstheeffectofmicrostructuredmembranesonthe retentiontime,selectivityandresolutioninAF4.Ahotembossing methodwaschosenforthefabricationofthesemembranes.We sharefundamentaltheoryandexperimentalﬁndingsthat comple-mentandexpandthepreviousstudywithperpendiculargrooves inThFFF[12].

Fig.2. Left-handfigure:displayofthetheoreticalmodel.Right-handfigure:velocity profile(a)overaflatmembraneand(b)overagroovedmembranewherethevelocity zero-planeistakenontheedgeoftheridge(x=h).

2. Theory

2.1. Transportequationsandmomentanalysis

Here,wedescribeasimplifiedmodelthatenablesustoderivean analyticalsolutiontotheproblemofmassmigrationovergrooves inanAF4channel.Inthismodelthegroovesareformedby zero-widthridgeswithauniformheighthonthemembranesurface, perpendiculartotheflowdirection.Slipflowthroughthegrooves isneglected;thezero-velocityplanefortheaxialflow(

v

)istaken atthetopoftheridges(Fig.2).

Thefollowingsimpliﬁcationshavebeenmade:

(1)Moleculardiffusionintheaxial(z-)directionisneglected. (2)Thedevelopmentoftheconcentrationproﬁleinthe

perpen-dicular(x-)directioniscompletebeforeelutionisstarted,bya precedingfocusingstepintheprocedure.

(3)Onlywell-retainedcompoundsareconsidered(withretention ratio <0.1). Such compounds are present predominantly closetotheaccumulationwall,wherethelinearpartoftheflow profileprevailsandthecross-flowvelocityucrmaybe

consid-eredasbeingequaltothefluidvelocitythroughthemembrane. For well-retainedcompounds,themathematicscanbe sim-plifiedsinceintegralsover theheightofthechannelcanbe takenfromx=0toinfinityinsteadoftotheupperwallposition (x=w),withgoodaccuracy.

(4)Therearenointeractionsbetweentheproteinandthe mem-brane.

(5)Flowconditionsarelaminar.Thisassumptionshouldholdtrue sincethepresenceofperpendiculargrooves,whicharesmall compared tothechannelthickness,reduceslocallytheflow velocity and decreasestheReynolds number [16]. Although eddiesmayexistinthecornersofthegrooves,theflowvelocity isverylowthereandthefluidisalmoststagnant.

Thetransportofacompoundi,withalocalconcentrationci=

ci(x,z,t),isgivenbythesimpliﬁedgeneraltransportequation

∂

ci

∂

t =Di

∂

2ci

∂

x2 +ucr

∂

ci

∂

x −

v

(x)

∂

ci

∂

z (4)

whereDiisthediffusioncoefﬁcientofthecompoundofinterest,

and

v

(x)thelocalaxialﬂowvelocity.Themoleculardiffusionterm alongthez-directionisneglectedintheRHSofEq.(4).Theplus signfor thesecondtermoftheRHSappearsbecausea positive valueistakenforucr,evenwhenthecrossﬂowisinthenegative

x-direction.Theassumptionthattheanalytehasbeenintroduced inthechannelasaﬁniteplugleadstotheboundaryconditions

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andtheassumptionthatthewallsofthechannelareimpermeable forthecompoundto

Di

∂

ci

∂

x +ucrci=0 for x=0,w (4b) Twosetsofmomentsaredefined.Localmoments,thatdescribe themassdistributionofacompoundiinafluidlayeratacertain distancexfromthemembrane,aredefinedas

mn,i(x,t)=

+∞ −∞

zn_c

i(x,z,t) dz (5)

andoverallmoments,thatdescribethemassdistributioninthe axialdirectionintegratedovertheheightofthechannel,as

Mn,i(t) =

w 0 mn,i(x,t) dx≈

∞ 0 mn,i(x,t) dx (6)

MomentsexistwhentheintegralsconvergeinEq.(6),i.e.,whenit canbeassumedthattheconcentrationofacompoundiapproaches zerofastenoughwhenzgoestoplusorminusinﬁnity.Thiswillbe thecasewhenthecompoundwasintroducedinthechannelasa plugorpeakofﬁnitewidth.

WhenbothsidesofthegeneraltransportEq.(4)aremultiplied withzn_and_integrated_over_z_from_minus_to_plus_inﬁnity,

expres-sionsareobtainedforthelocalmomentsofi

∂

mn,i

∂

t =Di

∂

2mn,i

∂

x2 +ucr

∂

mn,i

∂

x +n

v

(x)mn−1,i (7) ThethirdtermoftheRHSinthisequationisobtainedbypartial inte-grationwiththeassumptionthatzn_c

i(x,z,t)vanishesforz→±∞.

Whenalocalmoment(n−1)isknown,thisequationcanbeusedto evaluatethenextlocalmoment(n).IntegrationofEq.(7)overthe heightofthechannel,consideringboundarycondition(4b),gives anexpressionfortheoverallmomentMn,i

∂

Mn,i

∂

t =n

w

0

v

(x)mn−1,idx (8)

2.2. Thezerothmoment(massdistribution)

IntegratingbothsidesofEq.(4)overzfromminustoplusinﬁnity givesanexpressionforthelocalzerothmomentofi,

∂

m0,i

∂

t =Di

∂

2m0,i

∂

x2 +ucr

∂

m0,i

∂

x (9)

Undertheassumptionthatfocusingwascomplete,andasteady statewasreachedbeforetheexperimentwasstarted,bothsidesof Eq.(9)mustbezero,andthemassdistributionovertheheightof thechannelcanbefoundas

m0,i=m∗0,i·exp

−ucr

Dix

(10) wherem∗_0,iisthezerothmomentonthemembranesurface(with x=0).Theexp.concentrationproﬁleextendsoutfromtheupper wall(x=w)here. Eq. (10)describesthewell-known exponen-tialconcentrationproﬁleontheaccumulationwallinFFF,witha characteristiclayerthickness

equaltoDi/ucr.Whenthe

con-centrationoftheanalyteisscaledsoas m*

0,i=

ucr

Di

(11) theoverallzerothmomentM0,ibecomes1,andthehigheroverall

momentsareautomaticallynormalized.

2.3. Theﬁrstmoment(meanretentiontime)

Themodelforthegroovedsurfaceusedhere(Fig.2),witha stagnantlayerof fluid determinedby thegrooveheight h,and approximatelylinearlyincreasingchannelflowratefromtheslip planeatthetopoftheridges,givesforthelocalaxialflowvelocity

v

(x)=0 for 0≤x≤h (12a)

v

(x)=6(x−h)

w

v

for x≥h (12b)

WhenEqs.(10)–(12)aresubstitutedintoEq.(8),

∂

M1,i

∂

t =

w h 6(x−h) w

v

ucr Di exp

−ucr Dix

dx (13)

theaxialvelocity

v

_iofthecompoundisobtained(withforsimplicity integrationtoinﬁnityinsteadoftox=w),

v

_i=

∂

M1,i

∂

t = 6Di ucrw

v

exp

−ucrh Di

(14) Eq.(14)withh=0givesthewell-knownexpressionforthezone velocity over a ﬂatmembrane. With a groovedmembrane, the velocitydecreasesexponentiallywiththeratiooftheridgeheight overthecharacteristiclayerthickness.Fortheretentiontimethe oppositecanbewritten

tR,i=tR,iFLexp

+ucrh Di

(15) wheretFL

R,iistheretentiontimewithaﬂatmembrane,under

oth-erwise thesameconditions. Theretention time increasesmore stronglybythepresenceofthegroovesforcompoundswithasmall layerthickness,i.e.,formorestronglyretainedcompounds.

In the separation of two components, the selectivity ˛ is increasedwithincreasingridgeheightanditcanbewrittenas ˛=tR,2 tR,1 = D1 D2 exp

ucrh

₁ D2 − 1 D1

=˛FLexp

h 1

˛FL−1

(16) where˛FL_is_the_selectivity_with_a_ﬂat_membrane,_and

1the

char-acteristiclayerthicknessoftheﬁrst,leastretainedcompound.In Fig.3a,thecalculatedeffectofthe(relative)heightofthegrooveson theretentiontimesandtheselectivityisshownfortwocompounds withdiffusioncoefﬁcientsthatdifferbyafactorof√2.

2.4. Thesecondmoment(peakvariance)

Toevaluatetheinfluenceofthegroovedsurfaceonpeak broad-ening,first anexpressionfor thedevelopmentofthelocalfirst momentshastobederived.Inthis,wefollowtheapproachtaken byTaylorandArisintheirtreatmentofpeakbroadeningin cylin-dricalchannels,andinearlyworkofGiddingsondispersioninFFF [25].TheyfoundsolutionsforthegeneraltransportEq.(4)inthe formofasumoftransientfunctionsandastationaryfunction.The transientfunctionsdescribetheconcentrationchangesintimeand spacedirectlyafterthestartofthe’elution’andtheydependonthe initialconditions.Itwasshownthatthesetransientfunctionsdie outrapidly,andthatastationarysituationdevelopsinwhichthe localcentersofgravityatdifferentdistancesfromthewallare situ-atedinasteadyprofilearoundtheoverall(mean)centerofgravity ofthetransportedplugofthecompoundofinterest.Here,a solu-tionissoughtforEq.(4)describingonlythestationarysituation, i.e.,asolutionthatobliges

1 m0,i(x)

∂

m1,i(x)

∂

t =

∂

M1,i

∂

t =

v

i for all x (17)

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Fig.3.Theoreticalestimationofvariablesasafunctionoftherelativeridgeheight:a) increaseinselectivityandretentiontimefortwosoluteswithdiffusioncoefﬁcients thatdifferbyafactorof√2(e.g.,monomeranddimer);retentiontimeshereare normalizedwiththeretentiontimeofthesmallersoluteforaﬂatmembranetFL

R,1b) increaseinplateheightc)increaseinresolution.

Asetofparticulatesolutionsform1,i(x)canbefoundthatsatisfyall

boundaryconditions. For0≤x<h, mA_1,i(x,t) = 6

v

w

t− Di u2 cr − x ucr

exp

−ucrh Di

exp

−ucrx Di

(18a) andforx≥h, mB_1,i(x,t) = 6

v

w { (x−h)2 2Di + x−h u +

t− Di u2 cr − x ucr

exp

−ucrh Di

}exp

−ucrx Di

(18b)

Theincreaseintimeoftheoverallsecondmomentcannowbe foundbysubstitutingEqs.(12b)and(18b)intoEq.(8)

∂

M2,i

∂

t =2

w h 6

v

0 w (x−h)m B 1,idx (19)

Sincetheﬂuidvelocityiszerofor0<x<h,Eq.(18a)doesnothave tobeincludedintheintegration.Centralizingoftheoverallsecond momentgivestheincreaseofthespatialvarianceintime

∂

2 z

∂

t =

∂

M2,i

∂

t −2M1,i(t)

∂

M1,i

∂

t (20)

andﬁnally,theplateheightHcanbeobtainedas H=

∂

z2/

∂

t

∂

M1,i/

∂

t

(21) TheﬁnalresultforHis

H=24D 2 i

v

0 u3 crw

₅ 2exp

+ucr Dih

−3₂− ucr 2Dih

exp

−ucr Dih

(22) Foraﬂatmembrane,withh=0,thesecondandthirdfactorsinthe RHSofEq.(22)areequalto1,andthewell-knownexpressionfor H(HFL₎_is_obtained_(Eq.₍₃₎_).

InFig.3btheincreaseoftheplateheightwiththerelativeridge heightisshown,andinFig.3ctheincreaseinresolutionoftwo soluteswithratioofdiffusioncoefﬁcients√2isshown.Weobserve thatforgrooveheighth=1.51,thereisatwo-foldincreasein

res-olutionandafour-foldincreaseintheretentiontimeoftheless retainedcomponent.Forcomparison,thesameincreasein reso-lutioncouldbeachieved (withoutaltering thecross flow)by a two-foldincreaseofthespacerthicknessorapproximatelyten-fold increaseofthecross-flowtooutletflowratio.

3. Materialsandmethods 3.1. Samplesandcarriereluent

Bovineserumalbumin(BSA),␥-globulin,apoferritin, thyroglob-ulinandhemoglobinwerepurchasedbySigma–Aldrich(MO,USA). PBS0.15M(20mMduetosodiumphosphatesalts)withapHof 7.2wasusedasacarriereluentfortheAF4experimentsandas adiluentfortheproteins.Allproteinsampleswerepreparedata concentrationof1mg/mL.

3.2. Fabricationandcharacterizationofthemicrostructured(MS) membranes

Twosiliconmolddesignswithparallelgrooveswereusedfor preparationofthemicrostructuredmembranes.MoldI(LioniXBV, TheNetherlands)hadapatternedareaofdiameter15.1cmwith groovesof cavity widthc=50␮m,ridge width r=50␮m, ridge heighth=12␮mwhereasMoldII(MESA+cleanroom,Universityof Twente,TheNetherlands)hadapatternedareaofdiameter6.8cm withgroovesofc=30␮m,r=20␮mandh=25␮m. Polyethersul-fone(PES)membraneswith10kDaand30kDamolecularweight cut-off(MWCO)(Sartorius,Germany)wereusedforthemembrane patterningwithoutanypretreatment.

Microstructured (MS) membranes were prepared via hot embossing which was performed with an imprinter (Obducat, Sweden)inMESA+cleanroom(UniversityofTwente).The emboss-ingtemperature,pressureandtimewere120◦C,40barand180s, respectively and demoldingoccurredat 40◦C [20]. Surface and cross-section images of the microstructured membranes were takenby scanningelectron microscopy(SEM) equipment,XL30 ESEM-FEG(Philips,TheNetherlands)orJEOLJSM-6010LA(JEOL, Japan).MSmembraneI(Fig.4a)wasfabricatedbyhot-embossing a PES 10kDa membrane with the Mold I, and MS membrane II(Fig.4b)byhot embossinga PES30kDa membrane withthe MoldII.Membrane sampleswerewashed,dried,broken in liq-uidnitrogenforcrosssectionimagesandgold-sputteredforSEM imaging.

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Fig.4.MicrostructuredmembranesandAF4channels:a)MSmembraneI(hotembossedwithMoldI)andChannelIb)MSmembraneII(hotembossedwithMoldII)and ChannelII.

Cleanwaterﬂux(Jw)valuesofthemembranesweremeasured

withdead-endAmiconStirredCell(Model8050,MerckMillipore, MA,USA)andultrapurewater(MilliQsystem,MerckMillipore). Measurementswereperformedatfourdifferenttransmembrane pressures(P)in therange of0.5–2bar,afterremoving ofthe membrane preservativesby immersingin water and after pre-compactionat2bar.Theweightofpermeatedwaterversustime wasmeasuredandthecleanwaterﬂux(JwinL/m2/h)was

calcu-latedforeachpressureconsideringtheeffectivemembranesurface area,whichwas13.4cm2 _(The_area_is_assumed_as_constant_after

preparationofamicrostructuredsurface).Thecleanwater perme-ance(CWP,inL/m2_/h/bar)_of_the_membrane_was_determined_from

theslopeofJwversusPrelationship.

3.3. AF4experiments

TheAF4systemwasanEclipseDualTecsystem(Wyatt Technol-ogyEurope,Germany)connectedtoanAgilentHPLC1200system (AgilentTechnologies,Germany)thatconsistedofadegasser,an isocraticpump,aUVdetectorandanautosamplerequippedwith athermostat.Thetemperatureoftheautosamplerwassetat5◦C. TwoAF4trapezoidalchannelswereused,designatedasChannel IandII,oneforeachmembrane/moldsize(Fig.4).TheMS mem-braneswerecutwiththegroovesperpendicularandintheshape oftheporousfritwithsurgicalscissors.

ChannelIwasacommercialAF4channel(WyattTechnology Europe) which was used with the largerpatterned membrane (d=15.1cm).Ithadtip-to-tiplength13.3cmandaccumulationarea 15.6cm2₍_Fig.₄_a)._The_nominal_spacer_thickness_was₂₅₀_or₃₅₀_␮m.

Thefocus-ﬂowwas1.5mL/minfor3minandthefocusingpointwas setat18%ofthechannellength.Theinjectedvolumewas10␮L (10␮ginjectedmass)andtheUVdetectionwasat280nm.

ChannelIIwasaminiaturizedchannelcreatedtotestthesmaller patternedmembrane(d=6.8cm).It hadtip-to-tiplength6.3cm andaccumulationarea7.24cm2 ₍_Fig.₄_b)._It_was_created_using_a

commercialchannelmodifyingitsupperinlayandspacer.Inthe upperinlaytwointernalthreadsweremilledtoconnectthetubing ﬁttingsfortheinletandoutlet.Thespacerwasfabricatedcutting

MylarA4sheetsofnominalthickness250and350␮m.The focus-ﬂowwas0.8mL/minappliedfor3minandthefocusingpointwas setat18%.Theinjectedvolumewas5␮L(5␮ginjectedmass)and UVdetectionwasat220nm.

3.4. Computationalﬂuiddynamics(CFD)

Afiniteelementsolver,COMSOLMultiphysics5.2(COMSOLInc., MA,USA),wasusedtomodeltheAF4channelandsimulatethe proteinmigrationovertheflatandthepatternedmembrane.To reducethemodelintotwo dimensionsforlowercomputational cost,asymmetricalchannelwasmodelledinsteadofan asymmet-rical.Forthispurpose,asimplerectangulardomainwascreated, withaflatorgroovedbottomboundary.Ameshoffreetriangular elementswascreatedwithveryfineelements(<1␮m)inthe prox-imitytothebottomboundarytosimulateproteinmigrationwith highaccuracy.

Todescribetheflow,laminarflowofanincompressiblefluid wasusedand theboundaryconditions(inlets,outlets)wereset todefinechannel flowandcross-flowvelocities(itwasverified laterfromtheresultsthattheassumptionofthelaminarflowwas validbythecellReynoldsnumber).Thecross-flowvelocitywas dis-tributedhomogeneouslyalongthebottomboundary(membrane). Theoption“transportofdilutedspecies”(includingconvectionand diffusion)wasusedtosimulateproteinmonomeranddimer.The studyoftheflowprofilewassolvedasasteadystateproblemand theoutput(velocityfield)wasusedtosolvethetimedependent problemoftheproteinmigrationwithaBDF(Backwards Differen-tialFormula)solver.Therelativeandtheabsolutetoleranceswere setat10−4.Theinitialandthemaximumtimestepswereset0.001s and0.5s,respectively.

4. Resultsanddiscussion

4.1. Characterizationofthemicrostructuredmembranes

Themicrostructuredmembranes,designatedasMSmembrane Iand IIhadsimilarridgeheight,h∼12␮m,anddifferent

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peri-Table1

ProteinrecoveryinAF4beforeandafterhotembossingoftheUFmembranes.AF4conditions: ˙Vc= ˙Vout=1mL/min. Recovery(%)±s.d.

BSA(66.5kDa) ␥-Globulin(150kDa) Apoferritin(443kDa) Thyroglobulin(669kDa)

Flatmembrane(10kDa) 89±2 86±2 87±3 78±4

MSmembraneI 22±4 35±5 86±1 76±3

Flatmembrane(30kDa) 20±3 60±5 82±4 71±2

MSmembraneII 9±1 11±3 84±2 72±3

odicity(i.e.,thesumofcavityandridgewidth),100and 50_␮m respectively (Fig. 4). The shape of the patterns was rectangu-lar with round corners (MS membrane I) or ellipsoidal (MS membrane II)as therectangularcavities of themoldwere not completely ﬁlled during embossing. Although the polymer is heatedaboveits glasstransitiontemperaturein hot embossing processes,embossing wasperformed belowtheglasstransition temperature, since collapse of the pores and loss of perme-ance are reported in the literature for a PES membrane [20]. TheCWPs ofthe non-patterned membraneswereestimated as 150±20L/m2_/h/bar _(for _membranes _with ₁₀_kDa _MWCO) _and

271±113L/m2_/h/bar _(for_membranes_with₃₀_kDa_MWCO). _The

CWPsofbothmembranesdecreasedafterhotembossing;MS mem-braneIhadCWPof74_±1L/m2_/h/bar_and_MS_membrane_II_had_CWP

of130±18L/m2_/h/bar.

ProteinrejectionoftheMSmembraneswasevaluatedwiththe AF4system;therecoveryoffourproteinsofdifferentmolecular weight(66.5–669kDa)wasestimatedfromtheratioofthepeak areaof thefractionatedsampletothepeak areaofthe unfrac-tionatedsample.Thepeakareaoftheunfractionatedsamplewas estimatedfromthefractogramobtainedbyinjectingandeluting thesameamountoftheproteinwiththesamechanneloutletflow rate,withouttheapplicationof focusflow orcross-flowexcept forapoferritin.Thesolutionofapoferritincontainedlow molec-ularweightcomponentswhichwereUV-activeatthedetection wavelength,andthereforefocusflowwasappliedfortheirremoval. Forthisreason,therecoveryvaluesofapoferritinmaybeslightly overestimatedforallmeasurements(bothwithflatandwithMS membranes).TheexperimentalresultsaregiveninTable1;the recoveryofthesmallerproteins(BSAand␥-globulin)was signifi-cantlylowerfortheMSmembranes.

Thedecreaseinrecoveryafterhotembossingshouldindicate anincreaseintheactualMWCOratherthanproteinadsorption sincethePESmembranesusedinthisstudyarehydrophilicwith lowfoulingpropertiesforproteinsolutions.Thiswasconfirmedby injectingandfocusingforseveralminutesahighvolume(100␮L) ofaconcentratedsolution(30mg/mL)ofhemoglobin(∼65kDa) whichhasaredcolor.Itwasobservedthatthesamplewasfocused asanarrowbandwithaflatmembranewhileitwaspassingthrough thecross-flowwithanMSmembrane.Whenthemembranewas removedandvisuallyinspected,itwasnotstainedwhichwould indicateadsorption.

Theaforementionedresults(increaseinMWCOanddecrease inCWP)seemcontradictingsincelowerCWPisoftencorrelated withadecreaseinthesizeornumberoftheporesoftheselective (patterned)side.ApossibleexplanationisthattheCWPdecreases becauseof the membrane compaction (particularly in thearea ofthegrooves’valleyswhichexperiencethehigheststress dur-inghotembossing).Inaddition,theincreaseintheactualMWCO mightberelatedtoanincreaseoftheporesizeof thegrooves’ ridgesbecause of themembrane deformation or toother local defectsthatoccurduringimprinting/demoldingwhichare, how-ever, small enough to affect only the recovery of the smaller proteins.

Incontrastwithourobservations,Marufetal.[20]showedthat hotembossingcouldleadtosimilarCWPand lowerMWCOfor

anotherPESmembraneandamoldpatternedwithsmallergrooves (inthesub-micronrange).Perhapstheporedeformationtherewas minimalbecauseofthesmallersizeofthegrooves.However,the effectofthemembranecompactionontheCWPandthedifference inthestressdistributiononthevalleysandontheridgesduring hotembossinghavebeendiscussedinthesestudies[21].Overall ourresultsindicatethathot-embossingneedstobeoptimizedto avoidchangesoftheMWCOsincetheconceptwouldbe beneﬁ-cialparticularlyforlowmolecularweightanalytes,andingeneral UF membraneswithhighsolventpermeability are preferredin AF4.

Using BSA as thecalibrant withknown diffusioncoefﬁcient (6.21·10−11_m2_/s_[₂₆_]),_the_actual_channel_thickness_for_the

Chan-nel I and the Channel II witha ﬂat membrane was estimated 305±6␮mand294±8␮mrespectively,andthediffusion coef-ﬁcientofapoferritinwasestimated3.38·10−11_m2_/s_from_Eq.₍₁₎_.

Thesevalueswereusedinthesimulations.However,MS mem-branesarealreadycompressedduetohotembossing,andhence anyadditionalcompressioncausedbythespacerisexpectedto besmall.Thiswouldresultinlargeractualchannelthicknessand consequentlyin longerretention times. Thedifference in com-pressionbetweentheﬂatandtheMSmembraneswasevidentby visualinspectionwhenthemembraneswereremovedfromthe channelandinspected.Unfortunately,themethodwithaprotein ofknowndiffusivitycannotbeappliedfortheMSmembranesas theretentiontime increasesbythepresenceofthegroovesfor well-retainedcompounds.However,inorder toassesscorrectly theeffectofgrooves,theactualchannelthicknessoftheMS mem-branes needs tobe measuredand we attempted this by other means.

First,themembranecompressibilitywasestimatedfromthe dif-ferenceinthethicknessofthecompressedandnon-compressed partofthemembranes,measuredbySEMandamicrometerscrew gaugewhentheywereremovedfromthechannel.The compres-sionthatoccurredwithaflatandaMSmembranewas∼50␮m and∼20␮mrespectively.Thiscorrespondsto11%largerchannel thicknesswiththeMSmembranes.However,thesemethodshave lowprecisionsincetheymeasureonlyaverysmallpartofthetotal membraneareawhenthemembranesaredry.Second,weapplied therapidbreakthroughmethod[27]inthefractogramsobtained fortherecoveryexperimentswithinjectionand elutionof thy-roglobulin(withouttheapplicationoffocusorcross-flow).Thevoid volumewasmeasured13%largerwiththeMSmembranewhich correspondstoa13%thickerchannel.Thisresultisinclose agree-mentwiththefirstmethod.However,bothmethodsdonotuse cross-flowwhichmightslightlyaffectthemembranecompression and/orswelling.

4.2. AF4experiments

Apoferritinandthyroglobulinwerechosenasthemodel pro-teinstoassesstheeffectofthegroovesonretentiontime,selectivity andplateheight,sincetheyexhibitedhighrecoverieswiththe pat-ternedmembranes(Table1).InFig.5thefractogramsofapoferritin, obtainedusingﬂatandMSmembranes,areoverlaidafter subtrac-tionofthetimethatwasrequiredforthefocusingstep.Forboth

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Fig.5. ComparisonofﬂatandMSmembranesanalyzedwithﬂowrates ˙Vc= ˙Vout=1.0mL/minfora)ChannelIandMSmembraneIandb)ChannelIIandMSmembraneII.

Fig.6.CFDmodelfortheChannelII/MSmembraneIIsystem:a)Meshofthemodelinthebeginningofthechannel,b)velocityproﬁleoverthegrooves,c)concentration proﬁleofapoferritinoverthegroovesandd)derivedconcentrationattheoutlet(rightboundary)foreverytimepointforthemonomeranddimer.

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Table2

ComparisonofﬂatandMSmembranesforbothchannelswithrespecttotheplateheightofthemonomerH,theretentiontimeofthemonomertR,1andtheselectivitya betweenthemonomerandthedimer.Theerrorbarsaregivenat1␴levelandreﬂectthemembrane-to-membranereproducibility.

ChannelI

Apoferritin Thyroglobulin

˙Vc/ ˙Vout(mL/min) H(mm) tR,1(min) a H(mm) tR,1(min) a

Flatmembrane, w=350␮m 0.8/0.8 0.88±0.02 4.66±0.17 1.35±0.02 0.69±0.01 6.32±0.30 1.35±0.01 1.0/1.0 0.66±0.02 4.62±0.25 1.36±0.01 0.54±0.02 6.26±0.33 1.36±0.00 1.5/1.5 0.43±0.01 4.51±0.16 1.37±0.02 0.42±0.01 6.33±0.31 1.36±0.02 MSmembraneI, w=350␮m 0.8/0.8 1.03±0.01 7.78±0.04 1.42±0.01 0.87±0.02 11.15±0.24 1.46±0.01 1.0/1.0 0.78±0.03 8.09±0.08 1.45±0.00 0.69±0.01 11.45±0.18 1.51±0.01 1.5/1.5 0.65±0.04 8.25±0.23 1.49±0.01 – – – MSmembraneI, w=250␮m 0.8/0.8 1.27±0.02 4.59±0.04 1.44±0.01 0.91±0.04 6.57±0.15 1.45±0.02 1.0/1.0 0.93±0.05 4.92±0.37 1.46±0.02 0.79±0.02 6.63±0.10 1.48±0.01 1.5/1.5 0.64±0.00 5.00±0.04 1.51±0.01 0.54±0.01 7.39±0.04 1.53±0.02 ChannelII Apoferritin Thyroglobulin

˙Vc/ ˙Vout(mL/min) H(mm) tR,1(min) a H(mm) tR,1(min) a

Flatmembrane, w=350␮m 0.5/0.5 0.27±0.01 4.25±0.23 1.34±0.01 0.21±0.00 5.90±0.48 1.33±0.00 0.8/0.8 0.16±0.00 4.26±0.32 1.35±0.02 0.16±0.02 5.92±0.46 1.33±0.01 1.0/1.0 0.13±0.00 4.33±0.17 1.35±0.01 0.15±0.00 5.89±0.47 1.34±0.01 MSmembraneII, w=350␮m 0.5/0.5 0.43±0.01 8.88±0.14 1.49±0.01 0.39±0.02 13.16±0.13 1.50±0.01 0.8/0.8 0.33±0.01 9.90±0.08 1.55±0.01 0.36±0.01 14.56±0.09 1.57±0.02 1.0/1.0 0.29±0.00 12.22±0.05 1.59±0.01 – – – MSmembraneII, w=250␮m 0.5/0.5 0.53±0.01 4.61±0.03 1.48±0.00 0.47±0.00 6.80±0.14 1.53±0.02 0.8/0.8 0.34±0.02 5.47±0.08 1.56±0.02 0.32±0.01 8.28±0.18 1.63±0.00 1.0/1.0 0.29±0.01 5.74±0.02 1.62±0.01 0.30±0.00 8.88±0.20 1.68±0.01

channels/MSmembranesystemsandthesamespacerthicknessof 350␮m(Fig.5left-handfigures),thereisaconsiderableincrease inretentiontime,selectivityandresolutionbetweenmonomerand dimer.Althoughthereismorepeakbroadeningwiththepresence ofthegrooves,resolutionishigherbecauseofthehigherselectivity (asexpectedbythetheory,Fig.3).Consequently,thesame resolu-tioncouldbeachievedwiththeMSmembranesand applyinga lowercross-flowrate,oralternativelyusingathinnerspacer(Fig.5 right-handfigures).

Therefore,theMSmembranescouldbebeneficialasthesame retentionandresolutioncouldbeachievedwithlowercross-flow rates without the need to increase spacer thickness or to use impracticalcross-flowtooutletflowratios.Inpracticethatwould beparticularlyusefulforrelativelysmallsolutes(suchasBSAor evensmaller)sincelargersolutescanbeanalyzedwithoptimal spacerthicknessandflowrates,andthereforethereisaneedto fabricateMSmembraneswithlowerMWCO.Thechallengesand theprocedurestooptimizeAF4methodsforsmallsoluteswitha 300DaMWCOmembranehavebeenreported[28].Smaller macro-moleculesaretypicallyanalyzedbysizeexclusionchromatography (SEC)wheretheyexhibitverygoodresolution,butinsomecases, SECisnotsuitable,forinstance,whenthereisstrongnon-specific adsorptioninthechromatographicsupportandwhenlarge macro-moleculesco-existinthesamplethatneedtobeanalyzed.Inthe lastcase,across-flowprogramwithexponentialdecayshouldbe usedasthegrooveswouldcauseverystrongretentionforthelarge components.

Aseriesofexperimentswerecarriedoutusingdifferent cross-ﬂowrateswhileretainingtheratio( ˙Vc/ ˙Vout=1);theresultsare

displayedinTable2.Theplateheightofthemonomerwas esti-matedfromthewidthathalfpeakheight.Anumberofconclusions maybedrawnfromtheseexperimentalresults.Althoughthereis alargedepartureoftheengineeredgroovesfromthetheoretical model(i.e.,noslip,inﬁnitesimalridgeandrectangularshape),the underlyingconclusionswerefoundsimilar.

First,fromTable2,itcanbeseenthatforhigher ˙Vcandsame

˙Vc/ ˙Vout the retention time of the monomer and theselectivity

betweenmonomeranddimerweresimilarfortheﬂatmembranes asexpectedbythetheory(Eqs.(1)and(2))butincreasedfortheMS membranes.Thisisinlinewiththetheoreticalequationsderived bymomentanalysis(Eqs.(15)and(16)).Secondly,forthesame experimentalconditions,theincreaseinselectivitywashigherfor thyroglobulin(lower)anditwasindependentofthespacer thick-ness,aspredictedbythetheory.Lastly,theincreaseinretention timeandselectivityforthesamecross-ﬂowvelocitywashigherfor theMSmembraneII,probablyduetothesmallerslipbecauseof thesmallerperiodicityofthegrooves.

It is howeverimportant tonotethat partof theincrease in retentiontime isa resultofthelargeractualchannelthickness withtheMSmembranes.Asitwasmentionedabove,thechannel thicknesswasestimated∼12%largerwithMSmembranes,which correspondsto∼25%longerretentiontimescausedbytheeffectof themembranecompression,astheretentiontimeisproportional tow2_(Eq.₍₁₎_)._Even_so,_in_the_experimental_results₍_Table₂₎_we

observeamuchhigherincreaseintheretentiontimes,namelyfrom 67%(forChannelIandacrossﬂowrateof0.8mL/min)to180%(for ChannelIIandacross-ﬂowrateof1.0mL/min)forthemonomerof apoferritin,whichindicatesthattheeffectofthegrooveshasthe largestcontributiontotheincreaseintheretentiontime.Moreover, overloadingwasinvestigatedbyinjectingdifferentsamplemass, namely2␮g,10␮g,and20␮g,intheChannelI/MSmembraneI system;nooverloadingeffectwasobservedasretentiontime,plate heightandselectivitywerepracticallythesameforeveryexamined injectedmass.

4.3. Computationalﬂuiddynamics

FortheCFDexperiments,theminiaturized channel(Channel IIin Fig. 4)wasmodelled and themigration ofthe apoferritin monomeranddimerwassimulated.Thediffusioncoefficientsfor themonomerandfor thedimer ofapoferritinweretakenfrom theAF4experiments(wheretheratioofthediffusioncoefficients, andtherefore theselectivitywas1.34).Themodelwasverified byreducingsignificantlythesizeofthemeshelements,thetime

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Table3

CFDexperimentsandcomparisonwiththeexperimentalresultsforapoferritin, ChannelIIandcross-ﬂowrate0.5mL/min.

tR,1(s) tR,2(s) a

Flatmembrane-Exper. 255 342 1.34

Flatmembrane-CFD 261(SE=2%) 350(SE=2%) 1.34(SE<1%)

MSIImembrane-Exper. 533 794 1.49

MSmembraneII-CFD 720 1310 1.82

stepandthetolerances;allthesechangesdidnotalterthe reten-tiontimes(within0.2%).TheCFDmodelwasvalidatedcomparing theresults(retentiontimeandselectivity)withtheexperimental resultsobtainedforthenonpatternedmembrane.Goodagreement wasfound,thestandarderror(SE)was2%fortheretentiontime ofapoferritin (monomeror dimer)and<1%for theirselectivity (Table3).Theassumptionofthelaminarﬂowconditions,which wasusedforthemodel,wasjustiﬁedbytheresults;theReynolds numberwaslessthan0.05acrossthewholechannel(maximum inthemiddleofthechannelthickness)andlessthan2·10−4_inside

thegrooves.

For the patterned membrane (MS membrane II) and ˙Vc=0.5mL/min, the ﬂow and concentration proﬁles, and the

derived concentration at the outlet for each time point are depictedinFig.6.Itwasrevealedthattheexperimentalretention time and selectivity are much lower compared to the values predicted by the simulation (Table 3). This may be due to a non-uniform cross-ﬂow velocity as a result of differences in themembranecompactionand/orintheporesizebetweenthe ridgesandthecavitiesofthemembrane’sselectivelayerasitwas discussedabove.

5. Conclusions

Todateonlyflat(non-patterned)UFmembraneshavebeenused inAF4asmicron-sizedfeaturesareconsideredharmfulforthe sep-aration.Wehavedemonstratedthatmicron-sizedgroovescouldin factimproveperformanceinAF4.Thiswasshownbyseveralmeans includingmomentanalysis,physicalexperiments,andCFD simu-lations.Ourresultsshowthatperpendiculargroovescanincrease retention,selectivityandresolution.Thissystemcouldbeusefulas macromoleculesandnanoparticlescouldbeanalyzedwithlower cross-flowrateswithouttheneedtousehigherspacerthickness orhigher cross-flowtooutletflow ratio.Thisconcept couldbe appliedonanyFFFsystemasithasbeenoriginallydemonstrated byGiddingsetal.forThFFF[12].

Thephysical experimentswerecarried outwith microstruc-turedUFmembranesfabricatedbyhot-embossing.Thisfabrication processcausedanincreaseintheactualMWCOofthemembrane (asindicatedbytheAF4experiments)buttheeffectofthegrooves couldbeshownwiththelargerproteinstandardsusedinthisstudy (apoferritin 443kDa and thyroglobulin 669kDa). However, this conceptcouldbeparticularlyusefulforsmallermacromolecules, andthereforefutureworkshouldbefocusedonthefabricationof microstructuredmembraneswithlowerMWCOandhighwater permeability. This couldbe achieved,for instance, by methods otherthanhotembossingsuchasphaseseparationoradditive tech-nologies(e.g.,3Dprintingofanon-porousorporousmaterialover anUFmembrane).AdditionalresearchwithCFDexperimentsof differentgrooveshapesanddimensionsisunderwaytoinvestigate theoptimalgroovestructure.

Acknowledgements

Thisworkwas partof theresearchprogram SmartSep with projectnumber 11400 which wasﬁnanced by theNetherlands

OrganizationforScientiﬁcResearch(NWO).Authorsalso acknowl-edgeLydiaBolhuis-Versteeg(UniversityofTwente)forherhelpon SEMimagingandWyattTechnologyEuropeforprovidingtechnical assistance.

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