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Journal of Contaminant Hydrology 181 (2015) 141–152
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Journal of Contaminant Hydrology
j ourna l homepage: www.e lsev ie r .com/ locate / jconhyd
Equilibrium and kinetic models for colloid release under
transient solution chemistry conditionsScott A. Bradford a,⁎, Saeed Torkzaban b, Feike Leij c, Jiri Simunek d
a US Salinity Laboratory, USDA, ARS, Riverside, CA, United Statesb CSIRO Land and Water, Glen Osmond, SA 5064, Australiac Department of Civil Engineering and Construction Engineering Management, California State University, Long Beach, CA 90840-5101, United Statesd Department of Environmental Sciences, University of California, Riverside, CA 92521, United States
a r t i c l e i n f o a b s t r a c t
nsientase to
Article history:Received 3 December 2014
5
E-mail address: [email protected]
http://dx.doi.org/10.1016/j.jconhyd.2015.04.000169-7722/Published by Elsevier B.V.
We present continuum models to describe colloid release in the subsurface during traphysicochemical conditions. Our modeling approach relates the amount of colloid rele
inetic,ates ofatasetsid size,odels
Received in revised form 26 March 201Accepted 8 April 2015Available online 17 April 2015
Keywords:Colloid
colloidease inemical(NPs)entions onlyndingscolloidc, and/ity didsitivityse thenalysiscolloidemical
ier B.V.
changes in the fraction of the solid surface area that contributes to retention. Equilibrium, kequilibrium and kinetic, and two-site kinetic models were developed to describe various rcolloid release. These models were subsequently applied to experimental colloid release dto investigate the influence of variations in ionic strength (IS), pH, cation exchange, colloand water velocity on release. Various combinations of equilibrium and/or kinetic release mwere needed to describe the experimental data depending on the transient conditions andtype. Release of Escherichia coliD21gwas promoted by a decrease in solution IS and an incrpH, similar to expected trends for a reduction in the secondary minimum and nanoscale chheterogeneity. The retention and release of 20 nm carboxyl modified latex nanoparticleswere demonstrated to bemore sensitive to the presence of Ca2+ thanD21g. Specifically, retof NPs was greater than D21g in the presence of 2 mM CaCl2 solution, and release of NPoccurred after exchange of Ca2+ by Na+ and then a reduction in the solution IS. These fihighlight the limitations of conventional interaction energy calculations to describeretention and release, and point to the need to consider other interactions (e.g., Born, sterior hydration forces) and/or nanoscale heterogeneity. Temporal changes in the water velocnot have a large influence on the release of D21g for the examined conditions. This insenwas likely due to factors that reduce the applied hydrodynamic torque and/or increaresisting adhesive torque; e.g., macroscopic roughness and grain–grain contacts. Our aand models improve our understanding and ability to describe the amounts and rates ofrelease and indicate that episodic colloid transport is expected under transient physicochconditions.
Published by Elsev
MicroorganismModelTransientsChemistry
lution
1. Introduction industrial applications. Under steady-state flow and soict thculatoroul, and
chemistry conditions low amounts of colloids are slowlygy ofnergyShen
eleasets) inmbak,
An understanding of and an ability to accurately predrelease of colloids (including microorganisms, partiorganic matter, clay, metal oxides, and nanoparticles) in pmedia are needed for many agricultural, environmenta
⁎ Corresponding author. Tel.:+1 951 369 4857.
1998,v (S.A. Bradford).3
ees
released from the solid phase when the kinetic enerdiffusing colloids exceeds the adhesive interaction e(Ryan and Elimelech, 1996; Ryan and Gschwend, 1994;et al., 2007). Conversely, significant amounts of colloid rmay rapidly occur during temporal changes (i.e., transiensolution chemistry (Grolimund et al., 2001; Roy and Dzo1996) and/or water velocity (Bergendahl and Grasso,
2000). These observations indicate that different mechanismscontrol colloid release during steady-state and transient
occuhargend/o
catioistinnamihesivfusinnts its o000)of thistracroknes96). Iioni
oscalnessDavissoligeneorphiroupsrticle2005abilitatio
nitiate thaof thation
simuistr
munet alto thentioIS, pHns fod anep. Ainetisomultiplcy ovariels cants iet al
ase iysicoan bs. Th(Smax
-stat
conditions, the value of Smax can be determined by directmicroscopic observations in simplified systems (Adamczyk
reak-czyk
ticallyet al.,e thatnamic2013;ysico-olloid2011;ax onolloidlloidsrsibledencen andce ofolloidbeene full
olloidribingn at awith aact inpatialn dis-ion ofrfaces.odelsc ions002).been
apidlymundt andToscorium,o-siteundernuumed to
e ourunderlishednts toinetic,odelsavior.ed tonsientcationalysisactorsmicalations
142 S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
conditions. Transient physicochemical conditions mayin the subsurface as a result of infiltration and recgroundwater and surface water interactions, injection aextraction wells, and contamination events.
Colloid immobilization and release at a particular loon the collector surface depend on the strength of the resadhesive torque in comparison to the applied hydrodytorque (Bergendahl and Grasso, 1998, 2000), and the adinteraction energy relative to the kinetic energy of difcolloids (Shen et al., 2007; Simoni et al., 1998). Transiewater velocity alter the hydrodynamic force that acimmobilized colloids (Bergendahl and Grasso, 1998, 2and is spatially variable because of the complex geometrypore space (Bradford et al., 2011). Transient solution chemconditions impact the adhesive force by altering the mscopic zeta potentials and the electric double layer thic(Grolimund and Borkovec, 2006; Ryan and Elimelech, 19addition, the dependence of the adhesive force on solutionstrength (IS) is a function of the colloid size and the nanheterogeneity (e.g., the distribution of charge and roughwithin the zone of electrostatic influence (Bendersky and2011; Duffadar and Davis, 2007). Natural colloid andsurfaces always exhibit some degree of nanoscale heteroity due to surface roughness, mineral defects, isomsubstitution, protonation/deprotonation of hydroxyl gand adsorption of different ions, organics, and clay pa(Suresh and Walz, 1996; Tufenkji and Elimelech,Vaidyanathan and Tien, 1991). Consequently, spatial variof the adhesive force is also expected. The above informindicates that transient physicochemical conditions icolloid release by altering the force and/or torque balancacts on immobilized colloids, and that only a fractionretained colloids may be released because of spatial variin the adhesive and hydrodynamic forces and torques.
Several continuum models have been developed tolate colloid release during transients in solution chem(Bedrikovetsky et al., 2011; Bradford et al., 2012; Groliand Borkovec, 2006; Lenhart and Saiers, 2003; Tosco2009). In general, colloid transport equations are coupledsolution chemistry through explicit dependencies of retand/or release parameters on solute concentrations (e.g.,and/or adsorbed divalent cations). The transport equatiosolution chemistry and colloids are subsequently solvecolloid transport parameters are updated at each time stof the continuum models employ different first-order kformulations for colloid retention and release; e.g.,considered population heterogeneity, blocking, or mretention sites. In addition, the functional dependenretention and release parameters on solution chemistrysignificantly among themodels. Only some of thesemodebe easily extended to describe colloid release with transiewater velocity (Bedrikovetsky et al., 2011; Bradford2012).
One challenge in continuum modeling of colloid reledetermining the amount of colloid release with the phchemical perturbation. A finite number of colloids cretained in porous media under steady-state conditionmaximum solid phase concentration of retained colloidsis obtainedwhen all retention sites are filled. Under steady
r,r
ngcegnn,ey-snce),d-c,s;ynetes
-yd.,en
rdllceefsnn.,
s-ee)e
et al., 1992), inverse optimization of experimental bthrough curve data that exhibit blocking behavior (Adamet al., 1994; Johnson and Elimelech, 1995), or theoreestimated from torque balance calculations (Bradford2013). Experimental and theoretical results demonstratSmax is sensitive to the solution chemistry and hydrodyconditions (Adamczyk et al., 1995; Bradford et al.,Sasidharan et al., 2014). Such changes in Smax with phchemical conditions have been related to the amount of crelease during transient conditions (Bedrikovetsky et al.,Bradford et al., 2012). However, the dependence of Smphysicochemical conditions ismore complicated during crelease than retention because some of the retained cocannot be released by a given perturbation (e.g., irreveretention) (Adamczyk et al., 1992). The functional depenof Smax on IS therefore exhibits hysteresis during retentiorelease phases (Bradford et al., 2012). The importantemporal changes in Smax with transient conditions on crelease is not widely appreciated, and has not yetincorporated into continuum models that account for thrange of equilibrium and/or kinetic release behavior.
A second challenge in continuum modeling of crelease with transient physicochemical conditions is descthe dynamics of colloid release. The adhesive interactioparticular location on the collector surface may changephysicochemical perturbation as ions transfer and/or rethe gap separating the colloid from the collector surface. Svariations in the adhesive (and associated separatiotances) and hydrodynamic forces produce a distributmass transfer and reaction rates for ions on collector suIndeed, various combinations of equilibrium or kinetic mare needed to describe geochemical reactions of specifiin soils (Mayer et al., 2002; Šimůnek and Valocchi, 2Similarly, colloid release with transients has sometimesobserved to occur slowly and at other times very r(Bedrikovetsky et al., 2011; Bradford et al., 2012; Groliand Borkovec, 2006; Khilar and Fogler, 1984; LenharSaiers, 2003; Shen et al., 2012; Torkzaban et al., 2013;et al., 2009). It is therefore logical to anticipate that equilibkinetic, combined equilibrium and kinetic, or even twkinetic modelsmay be needed to describe colloid releasetransient physicochemical conditions. However, contimodels for colloid release have not yet been developdescribe all of these possible conditions.
The overall objective of this research is to improvunderstanding of and ability to simulate colloid releasetransient physicochemical conditions. This aim is accompby relating the amount of colloid release with transiechanges in Smax, and then developing equilibrium, kcombined equilibrium and kinetic, and two-site kinetic mto describe a wide variety of observed colloid release behThese continuum models were subsequently appliexperimental colloid release datasets under various traconditions to investigate the influence of IS, pH,exchange, colloid size, and water velocity on release. Anof these data improves our knowledge of fundamental finfluencing colloid release during transient physicocheconditions, and helps to identify thepropermodel formulto describe such behavior.
2. Materials and methods
(DINaClonathe pHaentiCorpt andughlm thwaithorib
res onanocteriaariderowniD21ainin37 °Crinsedto thationmeteNJ) aeragn waCo) oin thlase6 μmweron aP sizm−3)lution1 foL NPurnee, IA
usheds wasingationtotaroachs waLVOndau
1941; Verwey and Overbeek, 1948). Electrostatic double layerinteractionswere quantified using the expression of Hogg et al.
sed inelechactiveon of1 J forL NPssuredd thendaryarious
on a) thatergieshobicto bexperi-more,f zetah and2011;aturalee ofcalcu-ationistry.
.8 cmuartzengthaboutfittingsand
lectedns at
lowedg these 2).ng ther 4–6tifica-videdng theaction1g orically
udiedases 1e 3d),d thelutionge inble toble 1).D21gg the
143S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
2.1. Electrolyte solutions and porous medium
Electrolyte solutions were prepared using deionizedwater (pH= 5.8), and NaCl (0, 1, 5, 25, 50, and 100 mMor CaCl2 (2mMCaCl2) salts. Sodium bicarbonate and carbsalts were added to the 100 mMNaCl solution to buffer tat values of 7, 8, 9, and 10 (Delory and King, 1945; Wet al., 2009). Ultrapure quartz sand (Iota Quartz, UniminNC) was employed as porous medium in the transporrelease experiments discussed below. The sandwas thororinsed with DI water to eliminate background fines frosand before use. The median grain size of this sandmeasured to be 238 μm (standard deviation of 124 μm) wlaser scattering particle size and distribution analyzer (HLA 930).
2.2. Colloids
Experiments discussed below employed pure cultuEscherichia coli D21g or carboxyl modified latex (CML)particles (NPs). D21g is a gram-negative, nonmotile bastrain that produces minimal amounts of lipopolysacchand extra-cellular polymeric substances. E. coliD21gwas g24 hbefore initiating experiments. A single colony of E. colwas inoculated into 1.0 l of Luria-Bertani media cont30 mg/L gentamycin and incubated with shaking atovernight. The bacterial suspension was centrifuged andthree times before diluting the concentrated suspension indesired electrolyte solution. Influent and effluent concentrof E. coli D21g were determined using a spectrophoto(Unico UV-2000, United Products & Instruments, Dayton,a wavelength of 600 nm and a calibration curve. The avoptical density at 600 nm for the influent cell suspensioabout 0.2, which corresponds to an input concentration (approximately 107 CFU ml−1. The size of E. coli D21gvarious solution chemistries was measured using thescattering particle size and distribution analyzer to be 1.4
The CML NPs (Molecular Probes, Eugene, OR)fluorescent with excitation at 505 nm and emissi515 nm. The manufacturer provided values of the CML N(20 nm in diameter), shape (spherical), density (1.05 g cand hydrophobicity (hydrophilic). The stock CML NP sowas diluted to achieve a value of Co = 5 ∗ 107 N ml−
transport experiments. Average (three measurements) CMconcentrations reported hereinwere determined using a TQuantech Fluorometer (Barnstead/Thermolyne, Dubuquand reproducibility was typically within 1% of Co.
2.3. Interaction energy calculations
The zeta potential of E. coli D21g, CML NPs, and crultrapure quartz sand in the various solution chemistriedetermined from measured electrophoretic mobilities uZetaPALs instrument (Brookhaven Instruments CorporHoltsville, NY) and the Smoluchowski equation. Theinteraction energy of E. coli D21 g and CML NP upon appto the quartz sand under the various solution chemistriecalculated usingDerjaguin–Landau–Verwey–Overbeek (Dtheory and a sphere–plate assumption (Derjaguin and La
))e
g.
yesaa
f-ls
gg
esrtesfer.ete,
r
r)
sa,l
s),
(1966). As is commonly assumed, zeta potentials were uplace of surface potentials in these calculations (Elimet al., 1995). The retarded London–van der Waals attrinteraction force was determined from the expressiGregory (1981). The Hamaker constant was 6.5 ∗ 10−2
D21g (Rijnaarts et al., 1995) and 4.04 ∗ 10−21 J for CM(Bergendahl and Grasso, 1999). Table 1 summarizes meavalues for zeta potentials for D21g, CML NPs, and sand, ancalculated energy barrier height and depth of the secominimum for the DLVO interaction energies in the vsolution chemistries.
It should be mentioned that DLVO theory is basednumber of assumptions (in addition to those noted abovemay be violated. For example, non-DLVO interaction ensuch as Born repulsion, steric interactions, hydropinteractions, and/or hydration effects frequently needincluded in interaction energy calculations to explain emental observations (Elimelech et al., 1995). Furtherconventional DLVO calculations employ mean values opotentials and implicitly assume geometrically smootchemically homogeneous surfaces (Bendersky andDavis,Duffadar and Davis, 2007; Shen et al., 2012). However, ncolloid and solid surfaces always exhibit some degrnanoscale heterogeneity. Consequently, the above DLVOlations should therefore be viewed as only a first approximof expected changes inmean adhesionwith solution chem
2.4. Column experiments
Glass chromatography columns (15 cm long and 4inside diameter) were wet packed with the ultrapure qsand. The saturated water content, bulk density, and lfor the packed column were determined to be0.44 cm3 cm−3, 1.48 g cm−3, and 12.8 cm (adjustableat the column top), respectively. Colloid retention in thewas achieved by pumping six pore volumes (PVs) of a sesuspension upward through the vertically oriented columa steady flow rate using a peristaltic pump (Phase 1), folby continued flushing with colloid free solution havinsame solution chemistry for an additional 4 PVs (PhaColloid releasewas then studied by systematically changichemistry or velocity of the eluting solution (Phase 3) foPVs at each alteration step. Specific experiments and justion for the selected physicochemical sequence are probelow. Effluent sampleswere continuously collectedduritransport experiment at selected intervals using a frcollector. The effluent samples were then analyzed for D2CML NPs as described above. Experiments were typreplicated and exhibited good reproducibility.
The influence of IS reduction on D21g release was stusing the following solution chemistry sequence: 100 (Phand 2), 50 (Phase 3a), 25 (Phase 3b), 5 (Phase 3c), 1 (Phasand 0 (Phase 3e)mMNaCl when the solution pH=5.8 anDarcy water velocity (qw) equals 0.27 cm min−1. This sochemistry sequence was selected to encompass a ranmean adhesive interactions that ranged from favoraprogressively more unfavorable for D21g attachment (Ta
The effects of pH increase in 100mMNaCl solution onrelease was studied when qw = 0.27 cm min−1 usin
following solution chemistry sequence: pH=5.8 (Phases 1 and2), pH = 7 (Phase 3a), pH = 8 (Phase 3b), pH= 9 (Phase 3c),
causcreasfenk. Thion oe anducebasetentialutioeffectleasen th0 mM), anse 3)hasee 3b)in−1
NaClnd pHubsehesivwitwernami
eleasowinasesnd Din−1
create thaationn waffectth
mea
adhesive interaction was dramatically reduced in the presenceof DI water during Phases 3a and 3c (Table 1). Cation exchange
0 mMountCa2+.ed tof thesizes
ideredon theof theDavis,urfacen thed andntion,to bedKim,sed astudies
n andentedckage.re forentedcludesmeter
usinghange
ð1Þ
Table 1Zeta potentials and DLVO interaction energy parameters. The standard error associated with the zeta potentials is given in the parenthesis.
Colloid NaCl orCaCl2 (mM)
pH Sand zetapotential (mV)
Colloid zetapotential (mV)
Energybarrier (kT)
Secondary energyminimum (kT)
D21g 1 5.8 −66.8 (3.0) −57.2 (1.3) 3579.8 0.0D21g 5 5.8 −63.3 (2.4) −54.6 (1.5) 2892.2 −0.4D21g 25 5.8 −57.2 (1.0) −41.4 (1.4) 1453.1 −2.8D21g 50 5.8 −41.4 (1.9) −32.3 (1.1) 600.7 −6.7D21g 100 5.8 −17.3 (1.8) −17.5 (2.3) NB –D21g 100 7.0 −21.0 (7.1) −16.2 (2.6) NB –D21g 100 8.0 −37.0 (4.9) −16.2 (3.1) 56.2 −23.3D21g 100 9.0 −38.9 (2.4) −26.4 (6.4) 214.1 −19.6D21g 100 10.0 −37.2 (3.1) −18.9 (1.6) 49.2 −30.1NP 1 5.8 −66.8 (3.0) −34.1 (2.4) 22.1 0.0NP 100 5.8 −17.3 (1.8) −28.1 (8.9) 1.5 −0.1D21g⁎ 2 5.8 −28.6 (0.9) −24.8 (0.5) 465.9 −0.8NP⁎ 2 5.8 −28.6 (0.9) −14.9 (0.9) 3.2 0.0
NP — Carboxyl modified latex nanoparticle (20 nm in diameter).NB — no barrier to attachment.kT— product of the Boltzmann's constant and the absolute temperature.⁎ — CaCl2 solution.
144 S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
and pH = 10 (Phase 3d). Increases in solution pH candeprotonation of surface hydroxyl groups that may dethe charge of nanoscale chemical heterogeneity sites (Tuand Elimelech, 2005; Vaidyanathan and Tien, 1991)solution IS also increased with pH because of the additvarious amounts of buffering salts (sodium bicarbonatcarbonate salts). The 100mMNaCl solution and buffer proconditions that were mainly favorable for attachmentonmean zeta potentials (Table 1), but that neglect the poeffects of nanoscale chemical heterogeneity. This sochemistry sequence was therefore chosen to study theof changes in nanoscale chemical heterogeneity onD21g re
Another experiment examined the influence of qw orelease of D21g. In this case, D21g was deposited in 10NaCl at pH 5.8 and qw = 0.27 cmmin−1 (Phases 1 and 2then the IS was reduced to 5 mM NaCl at pH = 5.8 (PhaThe value of qwwas then sequentially increased during Pusing the following sequence: 0.27 (Phase 3a), 0.54 (Phas1.08 (Phase 3c), 2.16 (Phase 3d), and 5.4 (Phase 3e) cmmThe solution IS was chosen to be initially high (100 mMin order to achieve similar initial conditions to the IS arelease experiments discussed above. The solution was squently lowered to 5 mM NaCl in order to reduce the adinteraction (Table 1) and thereby facilitate releasechanges in water velocity. Increases in water velocityexpected to initiate release by increasing the hydrodyforce on immobilized D21g.
The influence of cation type and IS (pH=5.8) on the rof D21g and CML NPs was investigated using the follsolution chemistry sequence: 2 mM CaCl2 solution (Phand 2), DI water (Phase 3a), 100 mM NaCl (Phase 3b), awater (Phase 3c) when the pH= 5.8 and qw=0.27 cmmAdsorbed multivalent cations, such as Ca2+, cannanoscale chemical heterogeneity on the solid surfaccan neutralize or reverse the surface charge at specific loc(Grosberg et al., 2002). The initial solution compositiotherefore selected to be 2mMCaCl2 in order to study the eof a nanoscale chemical heterogeneity arising fromadsorption of Ca2+ on colloid retention and release. The
eejiefdddlns.e
d.3,.)
-ehec
eg1I.etsssen
(Ca2+ is exchanged by Na+) may be initiated when 10NaCl is added during (Phase 3b), and thismay alter the amof nanoscale chemical heterogeneity arising for adsorbedThe second DI water pulse (Phase 3c) was conductobserve differences in release following alteration onanoscale heterogeneity by cation exchange. Two colloid(20 nm CML colloids and 1.46 μm D21g) were consbecause the effects of nanoscale chemical heterogeneitylocal adhesive interaction are known to be a functioncolloid size (Bendersky and Davis, 2011; Duffadar and2007). Ideally, both colloids would have the same sproperties. However, the literature indicates that evesurface properties of CML colloids vary with size (BradforKim, 2012; Treumann et al., 2014). Trends for D21g reterelease, and surface properties have been observedgenerally consistentwith 1 μmCML colloids (Bradford an2012; Bradford et al., 2012). Consequently, D21g was uthe larger colloid to be consistent with other release sdiscussed above.
3. Continuummodel development
Continuum scalemodels for colloid transport, retentiorelease are described below. These models were impleminto the Hydrus-1D (Šimůnek et al., 2008) software paDetails of the numerical solution and iterative procedunonlinear flow and transport problems are already presin the literature (Šimůnek et al., 2008). Hydrus-1D ina nonlinear least squares routine for inverse paraoptimization.
3.1. Steady-state colloid retention and release
Colloid transport in the aqueous phase was describedthe advection–dispersion equation that includes an excterm to/from the aqueous and the solid phases:
∂θwC∂t
þ ρb∂S∂t
¼ ∂∂z
θwD∂C∂z
� �−
∂qwC∂z
where C [NL−3; where N and L denote units of number andlength, respectively] is the colloid concentration in the aqueous
is th−3] inotesolidn the and
-staten in
ð2
is thsione andn ap
ð3
nsiennt ots ane areerica0, 50use o/or anerske isen a
ð4
where Ac [L2 N−1] is the cross-sectional area per colloid, As[L−1] is the solid surface area per unit volume, and γ [–] is the
urfaceationently,ld bes of Afnd/orcond-till be
uce af andAif-Af,ation.
ð5Þ
micalthat isly, theual tobutedmax as
ð6Þ
ld beo thecase,
q. (6),
ariousalance
andn theeneityimarythat
145S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
phase, D [L2T−1; where T denotes units of time]hydrodynamic dispersion coefficient for colloids, θw [L3Lthe volumetric water content, ρb [M L−3; where M deunits of mass] is the soil bulk density, and S [NM−1] is thephase colloid concentration. The first and second terms oright hand side of Eq. (1) account for the dispersivadvective fluxes of the colloids, respectively.
The solid phase mass balance equation during steadyphysicochemical conditions (e.g., Phases 1 and 2) is givthis work as:
ρb∂S∂t
¼ θψkswC−ρbkrsS
where ksw [T−1] is the retention rate coefficient, krs [T−1]steady-state release rate coefficient, and ψ [–] is a dimenless blocking function. The parameter ψ accounts for timconcentration dependent blocking using a Langmuiriaproach as (Adamczyk et al., 1994):
ψ ¼ 1−S
Smax
3.2. Amount of transient colloid release
A first step in modeling colloid release with traphysicochemical conditions is determining the amoucolloid release with a given perturbation. Fig. 1 presenillustration of the hypothetical fraction of the solid surfacthat contributes to colloid immobilization (Af) for two sphcollectors after equilibrating with three IS conditions (1and 100 mM). The value of Af increases with the IS becaan increase in the depth of the secondary minimum andincreasing influence of nanoscale heterogeneities (Bendand Davis, 2011; Tufenkji and Elimelech, 2005). Therlinear relationship between Af and Smax that is giv(Bradford et al., 2009):
Smax ¼ 1−γð ÞAsAf
Acρb
IS=10 mM
Af
Fig. 1.An illustration of the hypothetical fraction of the solid surface area that cof 10, 50, and 100mM.When IS is reduced from 100 to 50 and further to 10mto be released. (For interpretation of the references to color in this figure lege
ess
e
e
Þ
e-
-
Þ
tf
al,f
yas
Þ
porosity of a monolayer packing of colloids on the solid s(a value of γ = 0.5 was selected based on informpresented by Johnson and Elimelech (1995)). Consequthe value of Smax also increases with IS in Fig. 1. It shoumentioned that more complex, non-uniform distributionmay occur at the pore-scale as a result of physical achemical heterogeneity that produces primary and/or searyminimum interactions. Nevertheless, Af and Smaxwill sfunctions of IS.
Fig. 1 indicates that a reduction in IS may prodcorresponding decrease in Af and Smax. This change in ASmax induces colloid release within the area defined bywhere Aif [–] is the initial value of Af before chemical alterThe new equilibrium value of S is given as:
S ¼ f nrSi
where Si [N M−1] is the initial value of S before chealteration, and fnr [–] is the fraction of retained colloidsnot released by the chemical alteration (fnr ≤ 1). Similaramount of colloid release with the IS reduction is eq(1-fnr)*Si. If the retained colloids are uniformly distriwithin Aif, then the value of fnr is related to Af and S(Bradford et al., 2012):
f nr ¼Af
Aif¼ Smax
Simax
where Simax [N M−1] is the initial value of Smax. It shoumentioned that the above analysis also applies trepresentative elementary area or volume scales. In thisvalues of Af and Smax are continuous functions of IS in Eand Si and S may be functions of depth in Eq. (5).
Theoretical estimates of Af have been made for vphysicochemical conditions by conducting a torque bover an idealized porous medium surface (BradfordTorkzaban, 2012; Bradford et al., 2013). Variations iamount, size, and charge of nanoscale chemical heterogon the solid and colloid surfaces produced localized prminimum interactions and corresponding Af values
IS=50 mM IS=100 mM
ontributes to colloid immobilization (Af) for two spherical collectors at ionic strengths (IS)M, particles originally deposited on the “non Af” part (white) of the collector surface tendnd, the reader is referred to the web version of this article.)
changed with the IS and colloid size (Bradford and Torkzaban,2012). In the presence of a secondary minimum, results
entiasize od sizedforach iolloie, thminiety oatio
modele, antionslectemaset alelowrtancr Af.
nt ons calds fomumnsienate o
urintransr geotons)catioan btransnd oet ality oangea ver
ithd (6e anssion. 1:
ð7a
ð7b
), anand
when−∂CIS∂t ≥0to turn release onwhen the IS decreases and the
depth of the secondary or primary minimum is reduced.. Notelloidsa firstof thecauselease,e netnts ofmicalurredy, the
belowolloiddition,entalet al.,may
d thatbriumthese
ð8Þ
ð9Þ
ð10Þ
d CH isn mayelease
∂Af
∂t
!
ð11Þ
nal touationner totheir–(11)istryqw is
146 S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
demonstrate that Af will depend on the IS, the zeta potof the colloid and porous medium, qw, the amount andnanoscale heterogeneity on the solid surfaces, the colloiand the surface roughness and pore–space geometry (Braet al., 2013). A potential advantage of the theoretical approindependent model predictions for the amount of crelease over a wide range of conditions. Furthermoramount of colloid release from primary and secondarymum interactions can be explicitly quantified for a varisolid and colloid properties. Unfortunately, a priori informon all the required nanoscale physical and chemicalparameters for the theoretical approach is still not availabfuture research is still needed to overcome these limitaConsequently, values of fnr (Eq. (6)) as a function of sephysicochemical conditions were obtained directly usingbalance information (Bradford et al., 2012; Torkzaban2013) from transient release experiments discussed bExperimental data for fnr is expected to be of critical impofor calibration and validation of theoretical predictions fo
3.3. Models for transient colloid release
The previous section demonstrates that the amoucolloid release due to transient physicochemical conditiobe related to changes in Af. Furthermore, this analysis hocolloids interacting in either a secondary or primary miniA second critical step inmodeling colloid release with traphysicochemical conditions is accurately describing the rrelease. This issue is addressed in this section.
Eq. (1) is again used to describe colloid transport dtransient physicochemical conditions. In addition, similarport equations with associated reactions are solved fochemical species of interest (e.g., cations, anions, and proand quantities such as the IS, pH, and the fraction ofexchange sites occupied by multivalent cations (f++) ccalculated. The specific number of geochemical species,port equations, and reactions types that are needed depethe solution chemistry and the soil properties (Mayer2002; Šimůnek and Valocchi, 2002). The travel velocchromatographic fronts (e.g., IS, pH, and cation exchapproaches that of a conservative tracer for sand withlow cation exchange capacity (Torkzaban et al., 2013).
An equilibrium expression for colloid release wchemical perturbation can be derived from Eqs. (5) anby taking the partial derivative of S with respect to timapplying the chain rule. The following equilibrium expreapply for colloid release with changes in IS shown in Fig
ρb∂S∂t
¼ ρbSiAif
∂Af
∂tHo −
∂Af
∂t
!
ρb∂S∂t
¼ ρbSiAif
dAf
dCIS
∂CIS
∂t
� �Ho −
∂CIS
∂t
� �
¼ ρbSidf nrdCIS
∂CIS
∂t
� �Ho −
∂CIS
∂t
� �
where CIS is the IS of the aqueous phase (e.g., moles/literHo is a Heaviside function that is equal to 0when−∂CIS
∂t b0
lf,dsde-fnld.ds.,.e
fnr.tf
g--,ne-n.,f)y
a)ds
Þ
Þ
d1
Eq. (7a) indicates that release only occurs when ∂A f
∂t b0that potential retention (e.g., reattachment) of released cois not explicitly considered in Eq. (7a) and (7b). Asapproximation we assume that subsequent retentionreleased colloids during Phase 3 was negligible bechemical conditions were altered in favor of colloid reand it is only possible to experimentally determine thchange in colloid release and retention. Significant amoucolloid release occurred during transient physicocheconditions (Fig. 2), whereas negligible detachment occunder steady-state conditions (Table 2). Consequentlvalue of krs was also set to zero during Phase 3.
In addition to IS, experimental information presentedindicates that Af is also a function of pH and qw, with crelease initiated when the pH and qw increases. In adtheoretical information discussed above and experimresults (Grolimund and Borkovec, 2006; Torkzaban2013) indicate that adsorption of multivalent cationsalter the amount of nanoscale chemical heterogeneity, anAf may therefore be a function of f++. Similar equiliexpressions for colloid release may be derived for each ofcases as:
ρb∂S∂t
¼ ρbSiAif
dAf
dCpH
∂CpH
∂t
!Ho
∂CpH
∂t
!
¼ ρbSidf nrdCpH
∂CpH
∂t
!Ho
∂CpH
∂t
!
ρb∂S∂t
¼ ρbSiAif
dAf
dfþþ
∂ fþþ∂t
� �Ho −
∂ fþþ∂t
� �
¼ ρbSidf nrdfþþ
∂ fþþ∂t
� �Ho −
∂ fþþ∂t
� �
ρb∂S∂t
¼ ρbSiAif
dAf
dqw
∂qw∂t
� �Ho
∂qw∂t
� �
¼ ρbSidf nrdqw
∂qw∂t
� �Ho
∂qw∂t
� �
where CpH is the aqueous phase pH (e.g.,− log10(CH); anmoles of hydrogen ions per liter). A composite expressioalso be developed for the total exchange during colloid rwith changes in CIS, CpH, f++, and qw as:
ρb∂S∂t
¼ ρbSiAif
dAf
dCIS
∂CIS
∂tþ dAf
dCpH
∂CpH
∂tþ dAf
dfþþ
∂ fþþ∂t
þ dAf
dqw
∂qw∂t
!Ho −
Eq. (11) indicates that transient release is proportiothe total derivative of Af with respect to time. This eqmay also be rewritten in terms of fnr in a similar manEqs. (7b)–(10). The determination of CIS, CpH, and f++ andpartial derivatives with respect to time in Eqs. (7b)follows directly from the solution of the geochemtransport equations, whereas similar information forobtained from the solution of the water flow equation.
A kinetic expression for colloid release with transients insolution chemistry that is consistent with Eqs. (5) and (6) i
ð12
t. This then bif, and) andte th
release of latex colloids, microbes, and nanoparticles undertransient IS conditions and/or cation exchange.
olloidusingbriumnew
ð13Þ
is thend Seqsolid. Theirectly
ð14Þ
ð15Þ
in aividedvalue
ð16Þ
enoteineticecond
ð17Þ
c sitestweenulated
binedineticand 3ationsmodelwhenmitedineticaviors
(a)
(b)
(c)
Fig. 2. Experimental values of fnr as a function of IS (Fig. 2a), pH (Fig. 2b), and q(Fig. 2c) for E. coli D21g. The cells were initially deposited in 100 mM NaCsolution at pH = 5.8. The IS and pH were successively altered in a and brespectively. In c the IS was first decreased to 5 mM, and then qw wasuccessively increased. Values of fnr where determined from mass balancinformation on cell release during Phase 3.
147S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
given as (Bradford et al., 2012):
ρb∂S∂t
¼ −ρbkdet1 S− f nrSið ÞHo S− f nrSið Þ
where kdet1 [T−1] is the transient release rate coefficiendriving force for colloid release in this kinetic modeldifference in the actual S and the equilibriumvalue of S givfnrSi in Eq. (5). Recall that Eq. (6) indicates that fnr = Af/AAf is a function of CIS, CpH, f++, and qw. Bradford et al. (2012Torkzaban et al. (2013) employed Eq. (12) to simula
Table 2
ineticn kdet1lease.bineduse oframe-rium)ioneduent-uringFitted model parameters to the colloid breakthrough curves during Phasesand 2. The standard error associated with the parameter fit is given in thparenthesis.
Figures Transient kswmin−1
krsmin−1
Smax/Cocm3g−1
R2
2a, 3a IS 0.087 (0.002) 0.002 (0.000) 2.11 (0.11) 0.982b, 3b pH 0.090 (0.002) 0.001 (0.000) 5.36 (0.63) 0.982c qw 0.076 (0.002) 0.002 (0.000) 4.27 (0.78) 0.964a Exchange/IS 0.057 (0.001) 0.002 (0.000) 3.35 (0.48) 0.984b Exchange/IS 0.195 (0.009) 0.002 (0.000) 5.03 (1.11) 0.75
s
Þ
eey
e
A combined equilibrium and kinetic model for crelease during transient conditions can also be derivedsimilar approaches. In this case, S is divided into equiliand kinetic sites, and Eq. (5) is rewritten to give theequilibrium value as:
S ¼ Seq þ Sk1 ¼ Feq f nrSi þ Fk1 f nrSi
where Feq [–] is the fraction of equilibrium sites, Fk1 [–]fraction of kinetic sites that is equal to Fk1 = 1-Feq, a[N M−1] and Sk1 [N M−1] are the equilibrium and kineticphase concentrations of retained colloids, respectivelyexchange terms for equilibrium and kinetic sites follow dfrom above as:
ρb∂Seq∂t
¼ −ρb FeqSiAif
∂Af
∂tHo −
∂Af
∂t
!
ρb∂Sk1∂t
¼ −ρbkdet1 Sk1−Fk1 f nrSið ÞHo Sk−Fk1 f nrSið Þ
A two-site kinetic release model can be developedsimilar manner to Eqs. (13)–(15). In this case, S is dbetween the two kinetic sites to give the new equilibriumas:
S ¼ Sk1 þ Sk2 ¼ Fk1 f nrSi þ Fk2 f nrSi
where the subscripts k1 and k2 on variables are used to dkinetic sites 1 and 2, respectively. Release from the first ksite is again given by Eq. (15), whereas release for the skinetic site is given as:
ρb∂Sk2∂t
¼ −ρbkdet2 Sk2−Fk2 f nrSið ÞHo Sk2−Fk2 f nrSið Þ
where kdet2 [T−1] is the release rate coefficient for kineti2 and Fk2 = 1-Fk1. Similarly, S can be divided beequilibrium and two kinetic sites, and releasemay be simusing Eqs. (14), (15), and (17).
The equilibrium (Eq. (11)), kinetic (Eq. (12), comequilibrium and kinetic (Eqs. (14)–(15)), and two-site k(Eqs. (17)–(18)) models have 0, 1 (kdet1), 2 (Feq, kdet1),(Fk1, kdet1, kdet2) fitting parameters, respectively. Simulcan be quite different when using the various releaseformulations. In general, release occurs very rapidlyusing the equilibrium model and this approach has liflexibility due to the lack of fitting parameters. The kmodel can reproduce a wide range of release behdepending on the value of kdet1. When kdet1 is high the kmodel approaches equilibrium conditions, whereas wheis low the kinetic model predicts slow and prolonged reThe greatest model flexibility occurs with the comequilibrium and kinetic or two-site kinetic models becathe greater number of parameters. Variation of these paters can produce different combinations of rapid (equiliband slow kinetic release behavior. It should also be mentthat all of the above models are proportional to Si. Conseqly, factors that promote smaller amounts of retention d
w
l,se
1e
Phases 1 and 2 (e.g., lower IS and influent colloid concentra-tions), will also produce smaller amounts of release during
is thich ind/owerm thenta
e cell5.8. Aally ain thum. Ireasees foin Dunt ondarvereexceset alD21patianamiion 1Fig.q. (4) thaurinsmaNaCmencell
caused bs. Foan
ed tangeimumme oscepolloimicaroge
of pH0mMostangectionin thd thaeverwer
predicted for all of these pH conditions because of the high ISconditions (Table 1). Consequently, these DLVO calculations
DLVOntials,oscaleoscalen they andly, thent orith anely ormicalin DINaClmical.e thewas
), andlue ofin−1
r as aD21grcherseasingreaterrasso,ed bynamicr, thesistingr pH).s withfinerhnessticallyppliedon to005).qw on
ulateitions.haviornts ofectionwereeleaseroughrs arelationrsivityual toesultsesultsetersd the
148 S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
Phase 3.
4. Results and discussion
4.1. Amount of transient colloid release
A critical issue in the application of the above modelsdetermination of the functional dependency of fnr (whrelated to Af and Smax by Eq. (6)) on solution chemistry ahydrodynamic parameters. In this work, values of fnrdirectly determined using mass balance information frotransient release experiments. Fig. 2a presents experimvalues of fnr as a function of IS for E. coli D21g when thwere initially deposited in 100mMNaCl solution at pH=decrease in IS produces a nonlinear decrease in fnr, especilower IS. This behavior reflects successive decreasesadhesive interaction between D21g and the porousmediparticular, the calculated height of the energy barrier incand the depth of the secondary minimum decreasdecreasing IS (Table 1). The final value of fnr = 0.47water at pH= 5.8, which indicates that a significant amoD21g was still retained in the sand even when the secominimum was eliminated. Most of the D21g can be recofrom quartz sand after excavation of the sand intosolution of the same solution chemistry (Torkzaban2008). The nonlinearity of fnr at lower IS and continuedretention in DI water likely reflect the effects of svariations in the distribution of the applied hydrodyand resisting adhesive torques that are discussed in Sect
It should also bementioned that values of fnr shown incan be converted to Af= fnrAif using Eq. (6). In this case, Ecan be used to calculate Aif from values of Smax (Table 2were obtained by fitting to the breakthrough curve dPhases 1 and 2. Interestingly, the value of Aif was very(b0.8–1.9%) even though the solution chemistry (100mMandpH=5.8)was predicted to be favorable for cell attach(Table 1). Furthermore, DLVO theory predicts that thewould be irreversibly retained in a primary minimum beof its infinite depth. These discrepancies can be explainfactors that are not considered in these DLVO calculationexample, the combined influence of Born repulsionnanoscale surface roughness has been demonstratproduce a finite depth of the primary minimum that chwith solution IS in a similarmanner to the secondarymin(Bradford and Torkzaban, 2013; Shen et al., 2012), and sothe colloids in a primary minimum may therefore be sutible to hydrodynamic removal (Treumann et al., 2014). Crelease from a primary minimum during physicocheperturbations has also been attributed to chemical heteneity and steric forces (Pazmino et al., 2014).
Fig. 2b presents experimental values of fnr as a functionfor E. coliD21gwhen the cellswere initially deposited in 10NaCl solution at pH= 5.8. An increase in pH produces almlinear decrease in fnr. Similar to the IS data, these chreflect successive decreases in the mean adhesive interaAn increase in solution pH tends to produce a decreasezeta potentials (more negative) for D21g and the sanmake conditions less favorable for attachment. Howstrong primary or deep secondary minima (b−19.6 kT)
esreels
tensrIfyds.,glc.2)tgllltseyrdos
f-dl-
as.et,e
cannot explain the observed release behavior. Thecalculations employed macroscopic values of zeta poteand therefore do not account for the influence of nanchemical heterogeneity on interaction energies. Nanchemical heterogeneity can have a large influence omean and variance of the interaction energy (BenderskDavis, 2011; Bradford and Torkzaban, 2013). Consequentobserved sensitivity of fnr to pH implies that the amoucharge of the chemical heterogeneity is decreasing wincrease in solution pH due to deprotonation of positivneutrally charged sites. The presence of nanoscale cheheterogeneity may also explain some of the cell retention(Fig. 2a). However, the final value of fnr=0.58 in 100mMsolution at pH= 10, and this indicates that nanoscale cheheterogeneity cannot explain most of the D21g retention
Additional experiments were conducted to examininfluence of qw on D21g release. In this case, D21gdeposited in 100 mM NaCl at pH 5.8 (Phases 1 and 2then the IS was reduced to 5 mM NaCl (Phase 3). The vaqw was then sequentially increased from 0.27 to 5.4 cmm(Phase 3). Fig. 2c presents experimental values of fnfunction of qw for D21g when the IS = 5 mM NaCl. Littlerelease was observed with increases in qw. Some reseahave noted a similar insensitivity of colloid release to incrqw (Johnson et al., 2010), whereas others have shown a gdependency of colloid release on qw (Bergendahl and G1998, 2000). These differences can likely be explaindifferences in the adhesive interaction, the hydrodyconditions, and the locations for retention. In particulaeffects of qw are expected to increase when the readhesive torque is smaller (e.g., lower IS and/or higheFurthermore, the applied hydrodynamic torque increasethe cube of the colloid radius, and also increases intexturedmedia (Torkzaban et al., 2007). Larger scale rouglocations and grain–grain contact points will dramaincrease the resisting adhesive torque and decrease the ahydrodynamic torque at these locations in comparissmooth surfaces (Bradford et al., 2013; Burdick et al., 2Both of these factors will tend to diminish the role ofrelease.
4.2. Simulated colloid release
The developed models are used in this section to simcolloid release during transient solution chemistry condWe did not attempt to simulate the colloid release bewith increases in qw (Fig. 2c) because only small amoucolloid release occurredwhichwere near the analytic detlimit. The initial conditions for these simulationsdetermined by fitting steady-state retention and rmodel parameters (ksw, krs, and Smax/Co) to breakthcurve data for Phases 1 and 2. These model parameteprovided in Table 2, along with the Pearson correcoefficient (R2) for the goodness of model fit. The dispe(λ = D/v; where v is the pore water velocity) was set eq0.1 cm for all experiments based on published tracer r(Wang et al., 2013), and preliminary optimization rduring Phases 1, 2, and 3. Fitted release model paramduring Phase 3 are provided in Table 3, along with R2 an
Akaike information criterion (AIC) (Akaike, 1974) for thegoodness of model fit. The AIC value was determined as:
ð18
siduaed byvaluefittingess ofl thatallestd.eleaseulatedhownM to
roundariousst AICd AICtes oflationtively.l wasd thatnableet1 =ges inmini-y andaluesscribeded ae firstdet1 =ced a). Then ther to IS
reduction (Fig. 3a). Conversely, the slow colloid release likely isassociated with alteration of nanoscale chemical heterogeneity
ost ofate of
Table 3Model parameters for the colloid release curve during Phase 3. The standard error is given in the parenthesis.
Fig. Transient Model kdet1min−1
kdet2min−1
Feq Fk1 Fk2 R2 AIC
4a IS E NA NA 1.0 NA NA 0.54 NA4a IS K 0.395 (0.064) NA NA 1.00 NA 0.78 −6314a IS EK 0.420 (0.115) NA 0.01 (0.19) 0.99 0.00 0.78 −6284a IS 2 K 0.063 (1.450) 0.391 (0.144) NA 0.01 (0.30) 0.99 0.78 −6264b pH E NA NA 1.0 NA NA 0.25 NA4b pH K 0.027 (0.002) NA NA 1.00 NA 0.47 −9634b pH EK 0.023 (0.002) NA 0.10 (0.01) 0.90 NA 0.60 −10074b pH 2 K 0.019 (0.003) 0.392 (0.118) NA 0.84 (0.03) 0.16 0.65 −10175a Ex./IS K 1.000 (0.275) NA NA 1.00 NA 0.94 −4295b Ex./IS K 0.192 (0.008) NA NA 1.00 NA 0.95 −552
NA — denotes not applicable.Ex. — denotes cation exchange.E — denotes equilibrium model.K — denotes kinetic model.EK— denotes equilibrium and kinetic model.2K— denotes 2 site kinetic model.
0
20
40
60
80
100
20
0.0
0.5
1.0
1.5
2.0
IS (
mM
)
C/C
o
Time (min)
(a)DataModelIS
0
2
4
6
8
10
12
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500
0 100 200 300 400 500 600
pH
C/C
o
Time (min)
(b)
DataModelpH
Phases 1 & 2 Phase 3
Fig. 3. Observed and simulated breakthrough and release curves for D21g withchanges of IS (a) and pH (b) using experimental values of fnr shown in Fig. 2.Cells were initially deposited in 100 mM NaCl at pH 5.8 (Phases 1 and 2), thenthe IS (100, 50, 25, 5, 1, and 0 mM) or pH (5.8, 7, 8, 9, and 10) was sequentiallychanged during Phase 3. The value of qwwas 0.276 cmmin−1. The 1 site kineticmodel was used in (a), and the 2 site kinetic model was used in (b). Modelparameters are given in Tables 2 and 3.
149S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
AIC ¼ n log σ2� �
þ 2kþ 2k kþ 1ð Þn−k−1
where n [–] is the number of observations, σ2 [–] is the revariance estimated as the sum of squared residuals dividn, and k [–] is the number of estimated parameters. Theof R2 tends to increase with the number of modelparameters. Conversely, the AIC is ameasure of the goodnfit that penalizes for adding fitting parameters. The modeproduces that best description of the data with the smnumber of fitting parameters (the lowest AIC) is preferre
Fig. 3 presents observed D21g breakthrough and rcurves with changes in IS (Fig. 3a) and pH (Fig. 3b). Simchanges in the solution composition (IS or pH) are also sin these figures. The final reduction in solution IS from 1mDI water is difficult to see in Fig. 3a, but it occurs after a420 min. The release curves were simulated using the vmodel formulations and the model result with the loweis shown in the figure. Release model parameters aninformation provide valuable information on the racolloid release and the most appropriate model formuunder the considered physicochemical conditions, respecValues of AIC indicate that the one-site kinetic modepreferred for D21g release with changes in solution IS, anthe agreement between the model and data was reaso(Table 3). The fitted value of kdet1 was high (kd0.395 min−1). This implies that colloid release and chanthe mean adhesive interaction (primary or secondarymum) with IS reduction (Table 1) occurred very rapidlapproached equilibrium conditions. In contrast, AIC vindicated that the two-site kinetic model was best to derelease with changes in solution pH and that it provireasonable characterization of the data (Table 3). Thkinetic site exhibited a slow rate of colloid release (k0.019 min−1), whereas the second kinetic site produmuch more rapid rate of release (kdet2 = 0.392 min−1
rapid colloid release behavior likely reflects changes imean adhesive interaction (Table 1) in a manner simila
Þ
l
by deprotonation of hydroxyl sites as the pH increases. Mthe initial colloid mass was associated with this slow rcolloid release (Fk1 = 0.84).
12.5 Phases 1 & 2 Phase 3
Fig. 4 presents observed and simulated values of D21g(Fig. 4a) and CML NP (Fig. 4b) breakthrough and release curves
ence2 mMe 3a)shinenceeleasreate2mMxplaiter foy highle 1)pulsurre
usiblntioratiogenealleainlDavis
2011; Duffadar and Davis, 2007). Greater retention of CML NPsthan D21g is therefore expected during Phases 1 and 2 due to
Ca2+
eleasen theeatestwaterter forvity ofion ofta notndarys of fnre first
f clay,cessesdeghind IS013).irectlyPhaseat thisunt ofL NPs.a, the
150 S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
when employing the following solution chemistry sequdeposition in 2 mM CaCl2 solution (Phase 1); eluting inCaCl2 solution (Phase 2); flushing with DI water (Phasflushing with 100 mM NaCl solution (Phase 3b); and fluwithDIwater (Phase 3c). Note that there are drastic differin the amount of D21g and CML NP retention and rfor this solution chemistry sequence. In particular, gamounts of retention occurred for CML NPs than D21g inCaCl2 solution. Traditional DLVO calculations cannot ethis difference because the secondary minimum is greaD21g than CML NPs and the energy barrier is sufficientlto eliminate most primary minima interactions (TabRelease of D21g mainly occurred in the first DI water(Phase 3a). Conversely, release of CML NPs mainly occwith the second DI water pulse (Phase 3c).
Nanoscale chemical heterogeneity provides one plaexplanation for the differences in D21g and CML NP reteand release shown in Fig. 4. In particular, surface integcalculations demonstrate that nanoscale chemical heteroity can produce strong primaryminima interactions for smcolloids, whereas larger colloids will continue to minteract in a weak secondary minimum (Bendersky and
Phases 1 & 2 Phase 3
apidlynablyitionalAf oner tocondi-olloidte thetion ofn (Af).micalalancenge isrium,els toin Af.eleaseoscaleimary
uctedundertions,e thiswas
ectedion ofn theortantntactsreases
0
0
0
0
00
20
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 50 100 150 200 250 300 350
C/C
o
Time (min)
(a)
DataModelIS
0
0
0
0
00
20
0.0
0.2
0.4
0.6
0.8
1.0
0 50 100 150 200 250 300 350
C/C
o
Time (min)
(b)
DataModelIS
Phases 1 & 2 Phase 3
Fig. 4. Observed and simulated breakthrough and release curves for 21g (aand 20 nm CML NPs (b) when employing the following solution c emistrsequence: deposition in 2 mM CaCl2 solution (Phase 1); eluting in 2 mM CaCsolution (Phase 2); flushing with DI water (Phase 3a); flushing with 00 mMNaCl solution (Phase 3b); and flushing with DI water (Phase c). Thsimulations employed values of fnr that were directly obtained m thexperimental balance information and by fitted release parameters iven iTable 3.
0
2
4
6
8
1
1
0
2
4
6
8
1
1
Dh
13frog
:
;gser
nr
.ed
enn-ry,
nanoscale chemical heterogeneity created by adsorbed(Grosberg et al., 2002). The greatest amount of D21g roccurred with the first DI water pulse (Phase 3a) whesecondary minimum was eliminated. Conversely, the gramount of CML NP release occurred with the second DIpulse (Phase 3c). This difference in release with DI waD21g and CMLNPs is also due to differences in the sensitiD21g and CML NPs to chemical heterogeneity. Addit100 mM NaCl (Phase 3b) initiates cation exchange (dashown) that likely converts some of the primary to secominima interactions for CML NPs but not for D21g. Valuefor CML NPs were therefore lower for the second than thDI water pulse.
Others have similarly observed that the release ocoliphage, and nanoparticles was sensitive to the proof cation exchange (Grolimund and Borkovec, 2006; Saet al., 2013) or the sequence of cation exchange areduction (Bradford and Kim, 2010; Torkzaban et al., 2Fig. 4 indicates that D21g and CML NP release was not dinitiated by decreasing f++ (e.g., cation exchange during3b). This implies thatAfwasmainly a function of IS, but thdependency on IS was altered by a decrease in the amoadsorbed Ca2+ (Phase 3b), especially for the smaller CMSimilar to release with a reduction of IS shown in Fig. 3release behavior of D21g and CML NPs occurred very rand approached equilibrium conditions that were reasodescribed by the one-site kinetic model (Table 3). Addresearch is needed to better resolve the dependence off++ and IS.
5. Summary and conclusions
Two fundamental issues must be resolved in ordsimulate colloid release with transient physicochemicaltions. One challenge is determining the amount of crelease with a given perturbation. In this work, we relaamount of transient colloid release to changes in the fracthe solid surface area that contributes to colloid retentioFunctional relations between Af and selected physicocheconditionsmaybedetermined fromexperimentalmass binformation or estimated theoretically. A second challemodeling the rates of colloid release. We develop equilibkinetic, and combined equilibrium and kinetic moddescribe various colloid release behavior with changesOur approach is quite general and is applicable to colloid rinitiated by alteration of mean and/or local (nanheterogeneity) adhesive interactions (secondary or prminima), as well as hydrodynamic forces.
Column transport and release experiments were condto study the release behavior of E. coliD21g and CMLNPsdifferent physicochemical conditions, to determine Af relaand to test the ability of the developed models to describdata. Release of E. coli D21g from a primary minimumpromoted by a decrease in solution IS, similar to exptrends for a secondary minimum. However, a large fractthe D21g was still retained in the sand even whesecondary minimumwas eliminated, suggesting the improle ofmacroscopic surface roughness and grain–grain coon cell retention. Cell release was also promoted by inc
IS (
mM
)IS
(m
M)
)yl2
eisn
in solution pH even though strong primary or secondaryminimum were predicted. This observation suggested that a
n inD21gsenc2+ bations cannongenelarglikelorqu-scal
ion oto thof thn. Focribedbriumesiv
uctionges in, withsmaangethe Iue tooton
Bradford, S.A., Kim, H., 2010. Implications of cation exchange on clay releaseand colloid-facilitated transport in porous media. J. Environ. Qual. 39,
id and3–92.mically
ysically676.., 2009.ort and–7002.tions tolization.
oid andn ionic0.1029/
colloidmedia.
particle
alkaline
hargedlutions
es with–29.ion andrworth-
Waals
naturalrol. 87,
port oflts and
ysics of74, 329.
151S.A. Bradford et al. / Journal of Contaminant Hydrology 181 (2015) 141–152
reduction in nanoscale chemical heterogeneity with acrease in pHalso contributed to cell release. In contrast torelease of CMLNPs that were initially deposited in the preof 2mMCaCl2 solution occurred only after exchange of CaNa+ and then a reduction in the solution IS. These observsuggest that reversible primary minimum interactionoccur for colloids on solid surfaces due to factors such asDLVO forces and nanoscale physical and chemical heteroity. Temporal changes in thewater velocity did not have ainfluence on the release of D21g. This insensitivity wasdue to factors that reduce the applied hydrodynamic tand/or increase the resisting adhesive torque; e.g., largeroughness locations and grain–grain contacts.
The developedmodels provided a reasonable descriptthe colloid release when parameters were optimizedexperimental data. However, the required complexityreleasemodel depended on the specific transient conditioexample, D21g release with changes in IS was well deswith a one-site kinetic model that approached equiliconditions. This implies that changes in the mean adhinteraction (primary or secondaryminimum)with IS redoccurred very rapidly. In contrast, D21g releasewith chanpH was better quantified with a two-site kinetic modelmost of the colloid release occurring slowly and only afraction rapidly. The rapid colloid release likely reflects chin the mean adhesive interaction in a similar manner todata. The slow colloid release presumably occurred dalteration of nanoscale chemical heterogeneity by depration of hydroxyl sites as the pH increases.
Acknowledgments
e andion oes noUSDAendanents
olloidal
porousuir 11,
tentionicationses. 44,
tion for
porousnol. 37,
This research was supported by the 214 ManurByproduct Utilization Project of the USDA-ARS. Menttrade names and company names in this manuscript doimply any endorsement or preferential treatment by theWe would also like to acknowledge the help of Dr. BrHeadd in conducting these transport and release experim
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