sorption nonequilibrium effects on colloid-enhanced transport of hydrophobic organic compounds in...

Ž .Journal of Contaminant Hydrology 30 1998 179–200

Sorption nonequilibrium effects oncolloid-enhanced transport of hydrophobic organic

compounds in porous media

Sujoy B. Roy 1, David A. Dzombak )

Carnegie Mellon UniÕersity, Department of CiÕil and EnÕironmental Engineering, Pittsburgh, PA 15213, USA

Received 16 July 1996; revised 17 April 1997; accepted 17 April 1997

Abstract

This paper presents the results of modelling and experimental investigations of factorsŽ .affecting enhanced transport of hydrophobic organic compounds HOCs on colloids in porous

media, especially effects of nonequilibrium sorptionrdesorption. Simulations were performed witha model that considers equilibrium and rate-limited exchange of contaminant between the truedissolved phase, the suspended and attached colloids, and the fixed solid phase as well as theadvection, dispersion, deposition, and release of colloidal particles from the porous medium. Themodel was also applied to laboratory column data for colloid-facilitated transport of a commonHOC, phenanthrene. Simulations of colloid-enhanced transport and fitting of experimental dataindicated that colloid-enhancement of hydrophobic organic contaminant transport can be signifi-cant for sufficiently high colloid concentrations, a high partition coefficient of contaminant oncolloids with respect to the fixed porous medium, a low deposition efficiency of the colloids onthe fixed porous medium surfaces, and a slow desorption rate of contaminant from the colloids.The last of these conditions was identified as probably the most important in enhancing transportdistances of contaminants in natural systems with mobile colloids which usually occur atconcentrations not exceeding a few mgrl. q 1998 Elsevier Science B.V.

Keywords: Colloid-facilitated transport; Nonequilibrium; Hydrophobic compounds; Porous media; Modelling

) Corresponding author.1 Presently at Tetra Tech, 3746 Mt. Diablo Blvd., Suite 300, Lafayette, CA 94549.

0169-7722r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.Ž .PII S0169-7722 97 00040-5

( )S.B. Roy, D.A. DzombakrJournal of Contaminant Hydrology 30 1998 179–200180

1. Introduction

ŽEvidence of colloid movement in groundwater Ryan and Gschwend, 1990; Ronen et. Žal., 1992; Backhus et al., 1993 has led to a concern that these colloids may enhance or

.‘facilitate’ the transport of contaminants, particularly strongly sorbing compounds suchŽ .as radionuclides and hydrophobic organic compounds HOC that are not predicted to

Ž .migrate significant distances in the subsurface McCarthy and Zachara, 1989 . Thisconcern is based on data from three sources. First, there are numerous reports in theliterature of contaminant association in batch systems with mineral and organic phases

Žsimilar to those observed in some groundwaters e.g., Baker et al., 1986; Chin and.Gschwend, 1992; Gounaris et al., 1993; Herbert et al., 1993 . Second, laboratory column

studies have demonstrated the potential for enhancement of transport of contaminants inthe presence of colloidal material in either polymeric form, such as dissolved natural

Žorganic matter or surrogates of it, or in particulate form, such as mineral oxides e.g.,Enfield and Bengtsson, 1988; Enfield et al., 1989; Magee et al., 1991; Dunnivant et al.,

.1992; Puls and Powell, 1992; Saiers and Hornberger, 1996; Grolimund et al., 1996 .Finally, there is actual evidence of association of radionuclides with groundwater

Žcolloids at several field sites Buddemeier and Hunt, 1988; Penrose et al., 1990; Kaplan.et al., 1994; Harnish et al., 1995 . Even though field evidence of enhancement of

transport of other contaminants, such as HOCs and heavy metals, is less conclusiveŽ .e.g., see discussion by Backhus et al., 1993 and Kaplan et al., 1995 , based on the fielddata for radionuclide transport it is reasonable to include the effects of mobile colloidswhen making conservative predictions of transport distances of all strongly sorbingchemicals.

ŽSeveral models have been developed or have been modified from established.models to assess the significance of such colloid-enhanced transport in porous media.

Most have assumed equilibrium interactions between the colloids and the contaminant inŽthe dissolved phase Magee et al., 1991; Enfield and Bengtsson, 1988; Mills et al., 1991;

.Abdel-Salam and Chrysikopoulos, 1995 . These models predict a reduction of theeffective retardation depending on the concentration of the colloids and the partitioncoefficient for contaminant sorption on the colloids. Even when the partition coefficientfor contaminant sorption on the colloids is much higher than for the fixed solid phase,

Žthe sorption capacity of the mobile colloidal phase generally present at concentrations.of a few mgrl is much lower than of the fixed solid phase. If equilibrium interactions

are applicable, as colloids bearing contaminants move into an uncontaminated porousmedium they are rapidly stripped of contaminants because of the greater sorptioncapacity of the fixed solid phase. In contrast, if contaminant desorption kinetics fromcolloids are slow, the assumption of equilibrium would tend to underpredict thedistances of colloid-facilitated transport. Because slow desorption from colloidal phases,or a resistant fraction that does not desorb at all, has often been reported in batch testsŽ .e.g., Penrose et al., 1990; Carroll et al., 1994 , it is clear that for reasonable predictionsof colloid facilitated transport, the kinetics of contaminant exchange between differentphases must be taken into account.

Recent studies have incorporated the possibility of kinetic limitations in the exchangeŽ .of contaminant between the colloidal and dissolved phases. Smith and Degueldre 1993

( )S.B. Roy, D.A. DzombakrJournal of Contaminant Hydrology 30 1998 179–200 181

showed that when irreversible sorption of contaminants on colloids was considered,enhancement of transport distances through fractured porous media could be significant,depending on the extent of interaction between the colloids and the fracture walls. This

Žmodel assumed constant colloid concentrations rates of colloid deposition and release.were assumed to be equal and equilibrium interactions with the surfaces of the fixed

Ž .solid phase in this case, fracture walls . A model presented by Corapcioglu and JiangŽ .1993 could account for conditions of equilibrium between colloids and the dissolvedphase, and for rate limited contaminant exchange between these phases as well as

Žvariable colloid concentrations rates of colloid deposition and release could be differ-.ent , but with separate equations for the equilibrium and non-equilibrium cases. This

Ž .approach was modified by Saiers and Hornberger 1996 to account for equilibrium andrate limited exchange of contaminant with the colloidal particles with a single set of

Ž .equations using the commonly used ‘two-site’ or ‘two-box’ approach for the porousŽmedia transport of sorbing compounds Selim et al., 1976; Parker and van Genuchten,

.1984 where sorption is assumed to occur on a fraction of sites in local equilibrium withthe dissolved phase, and with rate-limited exchange of contaminant on the remainingsites. Apart from allowing investigation of a continuum of conditions from equilibriumto irreversible sorption on colloids, this formulation is useful because it builds on anextensive body of literature where the parameters of the two-box model have been

Žrelated to the contaminant partition coefficient e.g., Brusseau et al., 1990, 1991; Lee et. Ž .al., 1991 . Saiers and Hornberger 1996 applied the model to describe successfully data

for cesium transport on kaolinite suspensions through sand columns.In this work we incorporated the two-box model in a general model for colloid-

Ž .facilitated transport as used by Saiers and Hornberger, 1996 and applied it to interpretlaboratory column data for transport of a common HOC, phenanthrene, through twosands. The modelling and experiments were conducted to identify the factors that, innatural systems, are most important for inducing facilitated transport of contaminants.Model simulations focused on the effects of parameters relating to sorption nonequilib-rium that have been explored in less detail in previous work. The data analyzed in this

Ž .work were originally presented by Roy and Dzombak 1997 from two types ofŽ .experiments: i where previously sorbed phenanthrene and in situ colloids were

Ž .simultaneously mobilized from a sand column, and ii where phenanthrene and asuspension of strongly sorbing colloids were injected into a sand column. Although thephysical processes are related, these experiments represent two idealizations of situationsin the field where colloid-facilitated transport can play a significant role. For example,the first scenario can be representative of contaminant mobilization from a highlycontaminated source near the surface upon changes in chemistry of infiltrating water,and the second may be representative of the long range transport potential of contami-nants on colloids through uncontaminated porous media. Results of the modelling alsohighlight areas for further experimental investigation in field situations where enhance-ment of transport by colloids is suspected.

2. Theory

Modelling of colloid facilitated contaminant transport requires consideration of theadvection and dispersion of particles, their deposition and release from the surfaces of


the fixed porous medium, and interactions between contaminants and the three solidŽ .phases the attached and suspended colloidal phases and fixed solid phase . Contaminant

interactions are modelled by assuming that a fraction of the sites on each type of solidphase are in equilibrium with the dissolved aqueous phase and that the remainder of thesites are in mass-transfer-limited exchange with the aqueous phase. This approachŽ .commonly known as the ‘two-box’ model is an approximation to represent the variousmechanisms, such as diffusion limitations, that may cause sorption nonequilibrium andwas used because of its relative simplicity and past success in describing solute transport

Ž .data in columns Brusseau et al., 1991; Lee et al., 1991 . In each of the three solidphases present in the system, the contaminant may be sorbed on sites in equilibrium with

Ž .the dissolved phase species marked with a subscript ‘1’ or on sites that are in massŽ .transfer-limited exchange with the dissolved phase subscript ‘2’ . Including the dis-

solved phase, the contaminant can therefore exist in one of seven compartments asŽ y1 .shown in Fig. 1. All solid phase concentrations are dimensionless MM and aqueous

Fig. 1. Conceptual model of solid-water-colloid partitioning of a sorbing contaminant. K and K are theps pp

equilibrium partition coefficients of the contaminant with the solid and the colloidal phases, F and F are thes p

fractions in equilibrium with the dissolved phase, and a and a are the mass transfer rates of thes p

contaminant from the nonequilibrium phase. The contaminant concentration in the dissolved phase is C , incd

the solid phase, C , on the suspended colloids, C , and on the attached colloids, C .cs cp ca


phase concentrations have dimensions of MLy3. The subscript p is used for colloidalparticle concentrations, and the subscript c for contaminant concentrations in each phase.Contaminant concentrations in the different phases, and parameters in the differenttransport equations are summarized in Tables 1 and 2.

2.1. MoÕement of colloidal particles in porous media

The mass balance for the suspended colloids in the aqueous phase is given by:

Eu Cpsy=PJ yS 1Ž .p pE t

Žwhere u is the porosity of the porous medium volume of voidsrtotal porous medium. Ž y3 .volume , C is the concentration ML of suspended colloidal particles, J is the fluxp p

Ž y1 y2 .of suspended colloidal particles MT L , and S is a sink term for suspendedpŽ y3 y1.colloidal particles ML T .

The mass balance for the attached colloids is given by

E Cpa1yu r sS 2Ž . Ž .s pE t

Ž y1 .where C is the concentration of the attached particles MM , and r is the densitypa sŽ y3 .ML of the solids that make up the porous medium.The flux of particles at any pointcan be described by:

J sJ qqC 3Ž .p pD p

Ž y1 y2 .where J is the flux of particles due to dispersion MT L , and q is the specificpDŽ y1 .discharge or darcy velocity, LT . This formalism is similar to that used for the

transport of dissolved solutes. J is given by:p

J syD = u C qqC 4Ž .p p p p

Ž 2 y1.where D is the dispersion coefficient of the particles L T . S can be described byp p

assuming first order deposition and detachment of particles from the porous mediumŽsurfaces e.g., as presented in theoretical developments by Spielman and Friedlander,

.1974; Dahneke, 1975; Ruckenstein and Prieve, 1976 ,

S sk u C yk C r 1yu 5Ž . Ž .p pd p pr pa s

Ž y1 .where k is the particle deposition coefficient T , and k is the particle releasepd prŽ y1 .coefficient T . k and k can be estimated from experimental data or from theory.pd pr

Theoretical calculations of k have been found to be fairly accurate only whenpdŽelectrical double layer repulsions are insignificant e.g., see review by McDowell-Boyer

.et al., 1986 . Theoretical calculations of k are unlikely to be of use for most complexprŽ .environmental systems Roy and Dzombak, 1996 .

Ž . Ž . Ž . Ž .Including Eqs. 4 and 5 in Eqs. 1 and 2 , for a one-dimensional system inCartesian coordinates, and assuming D and the one dimensional darcy velocity, q, top

()

S.B.R

oy,D.A

.Dzom

bakrJournalof

Contam

inantHydrology

301998

179–

200184

Table 1Species considered for transport in a porous medium

aSpecies description Symbol Concentration units Equations describing transport3 Ž .Suspended colloidal particles C grcm Eq. 6p

Ž .Attached colloidal particles C grg Eq. 7pa3 Ž .Dissolved contaminant C grcm Eq. 21cd

Ž .Contaminant sorbed on equilibrium compartment on suspended colloidal particles C grg Eq. 14cp1Ž .Contaminant sorbed on mass-transfer-limited compartment on suspended colloidal particles C grg Eq. 12cp2Ž .Contaminant sorbed on equilibrium compartment on attached colloidal particles C grg Eq. 15ca1Ž .Contaminant sorbed on mass-transfer-limited compartment on suspended colloidal particles C grg Eq. 13ca2Ž .Contaminant sorbed on equilibrium compartment on fixed solid phase C grg Eq. 17cs1Ž .Contaminant sorbed on mass-transfer-limited compartment on fixed solid phase C grg Eq. 18cs2

aCompartments are represented in Fig. 1.

Table 2Porous medium properties and rate constants

Parameter Description Dimensions Units2 2D Dispersion coefficient of colloidal particles L rT cm rhp2 2D Dispersion coefficient of dissolved contaminant L rT cm rh

3 3r Density of solid matrix MrL grcms

k Rate of colloidal particle deposition 1rT 1rhpd

k Rate of colloidal particle release from solid matrix surfaces 1rT 1rhpr3 3K , K Equilibrium partition coefficient of contaminant with colloidal particles and with fixed solid phase L rM cm rgpp ps

a , a Rate of contaminant exchange in mass transfer-limited fraction of colloids and fixed solid phase 1rT 1rhp s

F , F Fraction of sites on colloids and on fixed solid phase that are in equilibrium y yp s


Žbe constant, two equations for particle transport are obtained e.g., Corapcioglu and.Jiang, 1993; Saiers et al., 1994 :

E C E 2 C E Cp p pu su D yq yk u C qk C r 1yu 6Ž . Ž .p pd p pr pa s2E t E xE x

E Cpa1yu r sk u C yk C r 1yu 7Ž . Ž . Ž .s pd p pr pa sE t

2.2. Contaminant interactions with suspended and attached colloids

The mass balance for contaminant on the suspended colloids can be written as,Eu C Ccp i p

sy=P C J yS 8Ž .Ž .cp i p cp iE tŽ .where C is the concentration of contaminant in the equilibrium is1 or thecp i

Ž . Žmass-transfer-limited is2 compartment on the mobile colloids mass of contami-y1 .nantrmass of colloids, MM , and S is a sink term for colloid-associated contami-cp i

Ž y3 y1. Ž .nant ML T in the equilibrium or mass transfer-limited compartment is1 or 2 .S is given bycp i

Contaminant lost on Contaminant added fromS s ycp i ½ 5½ 5depositing colloids released colloids

Net contaminant added ony ½ 5suspended colloids

Note that contaminant in the above expression refers to contaminant either in theequilibrium compartment or mass-transfer-limited compartment. The processes above

Ž .can be written for rate-limited sites is2 as follows,

S sk u C C yk C 1yu r C ya 1yF K C yC C uŽ . Ž .cp 2 pd p cp2 pr pa s ca2 p p pp cd cp2 p

9Ž .where C is the concentration of contaminant in the mass-transfer-limited compartmentca2

Žon the attached colloidal particles mass of contaminantrmass of attached particles,y1 .MM , a is the mass transfer coefficient for exchange of contaminant with thep

Ž y1 .colloids T , K is the partition coefficient of the contaminant on the colloidsppŽ 3 y1.L M , and F is the fraction of sites in equilibrium with the dissolved phasepŽ y1 .MM .

The mass balance for contaminant on the attached colloids, C , is given by,ca i

E C Cpa ca i1yu r syS 10Ž . Ž .s ca iE t

Ž y3 y1.where S is a sink term for contaminant on attached colloids ML T and can beca i

described as,

Contaminant added fromContaminant lost onS s yca i ½ 5 ½ 5deposited colloidsreleased colloids

Net contaminant added ony ½ 5attached colloids


As above, the contaminant in this expression refers to contaminant either in theŽ .equilibrium or mass-transfer-limited compartment is1 or 2 . For mass transfer-limited

exchange, S can be expressed as:ca2

S sk C 1yu r C yk u C C ya 1yF K C yCŽ . Ž .ca 2 pr pa s ca2 pd p cp2 p p pp cd ca2

= 1yu r 11Ž . Ž .s

Ž . Ž . Ž .Substituting Eqs. 9 and 4 into Eq. 8 , and assuming one-dimensional Cartesiancoordinates, yields, after some simplification, an equation describing the movement ofcontaminant associated with the mass-transfer-limited compartment of the mobile col-

Ž .loids assuming, as before, that u and D are constant :p

E C D E C E C q E C k C 1yu rŽ .cp 2 p cp2 p cp2 pr pa ss y y C yCŽ .cp 2 ca2E t C E x E x u E x u Cp p

qa 1yF K C yC 12Ž .Ž .p p pp cd cp2

Ž . Ž .Similarly, by substituting Eq. 11 into Eq. 10 , and simplifying, an equation describingthe variation of contaminant on the mass-transfer-limited compartment of the attachedcolloids may be obtained,

E C k u Cca 2 pd ps C yC qa 1yF K C yC 13Ž .Ž . Ž .cp 2 ca2 p p pp cd ca2E t 1yu r CŽ . s pa

Ž . Ž .Equations similar to Eqs. 12 and 13 can be written for contaminant on the sites inequilibrium with the dissolved phase. However, because these sites are in localequilibrium with the aqueous phase, the contaminant concentrations on mobile andattached colloids can be derived directly from the concentration of the contaminant in

Ž .the dissolved phase C ,cd

C sF K C 14Ž .cp1 p pp cd

C sF K C 15Ž .ca1 p pp cd

2.3. Contaminant interactions with the fixed solid phase

Ž y1 .C is the concentration of the contaminant on the solid phase MM and iscs

expressed with the two-box model as,

C sC qC 16Ž .cs cs1 cs2

where C is the concentration of contaminant in the compartment that is in equilibriumcs1

with the aqueous phase, and C is the concentration of contaminant in the compart-cs2Ž .ment that is mass transfer limited. The two terms in Eq. 16 can be written as,

C sF K C 17Ž .cs1 s ps cd

E Ccs 2sa 1yF K C yC 18Ž . Ž .s s ps cd cs2E t


F is the mass fraction of the solid phase that is in equilibrium with the aqueous phasesŽ y1 .MM , K is the partition coefficient of the contaminant between the aqueous phaseps

Ž 3 y1.and the solid phase L M , and a is a mass transfer coefficient for contaminants

exchange between the aqueous and mass-transfer-limited compartments in the porousŽ y1 .medium T .

2.4. MoÕement of contaminants in the true dissolÕed phase

The mass balance for contaminant in the true dissolved phase can be written as,

Eu C E Ccd ssy=P J y 1yu r qS qS qS qS 19Ž . Ž . Ž .c s cp1 cp2 ca1 ca2E t E t

where C is the dissolved-phase concentration, J is the flux of contaminantcd cŽ y1 y2 .MT L . J is given by,c

w xJ syD= u C qqC 20Ž .c cd cd

where D is the coefficient of dispersion of the contaminant.Ž . Ž . Ž . Ž . Ž .Substituting Eqs. 8 , 10 , 16 and 20 into Eq. 19 , and simplifying for one

dimension with constant q and D, the following solute transport equation is obtained:

E C E 2 C q E C E C E C E Ccd cd cd cp cp psD y y C qD qk C Cp p pd cp p2E t u E x E t E x E xE x

r 1yu E C C E CŽ .s pa ca csy k C C q q 21Ž .pr cp pa

u E t E t

where C sC qC and C sC qC . The C and C terms appear becausecp cp1 cp2 ca ca1 ca2 cp ca

solute desorbed from suspended and attached colloids must be taken into account. WhenŽ . Ž .C and C are zero i.e., no colloids present , Eq. 21 reduces to the commonly usedp pa

Žform of the two-box advective–dispersive transport equation Parker and van Genuchten,.1984 .

2.5. Model integration and testing

Ž .The nine species modelled in this work Table 1 can be described by nine coupledŽ . Ž . Ž . Ž . Ž . Ž . Ž .equations: Eqs. 6 , 7 , 12 – 15 , 17 , 18 and 21 . These equations were solved

with a fully implicit finite difference formulation. Solutions of portions of this modelŽi.e., contaminant transport without colloids; transport of colloids alone without contami-

. Žnants were compared with a published analytical solution Parker and van Genuchten,.1984 . Results of the numerical solutions of these submodels matched very well with the

previously published analytical solution. In addition, mass balances of colloids andcontaminants in the model were very close to 100% for the model runs. Details of thetesting procedures and the implicit finite difference implementation of the differential

Ž . Ž . Ž . Ž . Ž . Ž . Ž .Eqs. 6 , 7 , 12 , 13 , 18 and 21 are presented in Roy 1995 .


3. Model application

The model presented above was used to simulate the colloid-facilitated transport ofphenanthrene in sand columns for the purpose of assessing effects of sorption nonequi-

Ž .librium. Key porous medium properties K , F , a were obtained from sorptionps s s

experiments on a low organic carbon sand, and the effects of colloids on phenanthrenetransport were investigated for different partition coefficients on colloids, and forvarying degrees of nonequilibrium of contaminant exchange between the colloids andthe contaminants.

The model was used to fit data from the two types of column experiments presentedŽ .in Roy and Dzombak 1997 : contaminant sorptionrmobilization experiments, where

sorbed phenanthrene was mobilized from packed columns by inducing colloid release,and transport experiments, where colloid-facilitated transport of phenanthrene on latexcolloids through a relatively high organic content sand was observed. Total effluent

Ž .contaminant concentrations dissolved and colloid associated from the columns weredescribed with the model presented here.

3.1. Nature of experimental data

All experiments were performed with a 10-cm long, stainless steel column, packedŽwith either of two sands: Lincoln sand a fine, low organic content sand, f s0.04%oc

. Žfrom near the surface in Oklahoma , and Eustis sand a relatively high organic carbon.content sand, f s0.5%, from Florida .oc

Phenanthrene mobilization experiments involved passing 60 pore volumes of a 1mgrL phenanthrene solution with ionic strength of 0.1 M NaCl through a column ofLincoln sand and then inducing colloid release by changing the influent to a phenan-

Ž .threne-free solution at lower ionic strength 0.01 M and 0.001 M NaCl . In previousŽ .work Roy and Dzombak, 1996 it was shown that ionic strength reduction in the

Lincoln sand leads to a relatively rapid release of colloids, and the objective of theexperiments described here was to study the effect of this colloid release on themobilization of previously sorbed contaminants. All colloids in the effluent wereinitially present in situ in the Lincoln sand. The size and composition of the Lincolnsand colloids were studied using scanning electron microscopy and were found to bemostly smaller that 1 mm, and comprised of pure and impure forms of silica and clay

Ž .minerals Roy and Dzombak, 1996 . Ionic strength reduction is an important, althoughnot the sole mechanism causing colloid release in natural porous media. Other aqueouschemistry parameters such as changing redox potential or pH may also be importantŽ .McCarthy and Zachara, 1989; Ryan and Gschwend, 1990 .

Eustis sand was used in transport experiments where a 1 mgrl phenanthrene solutioncontaining a 100 mgrl suspension of 0.468-mm latex colloids was passed through thecolumn. In contrast with Lincoln sand, Eustis sand showed limited colloid release uponreduction in ionic strength. Thus, it was used for experiments where the effects of the

Ž .injected colloids could be studied and compared to transport without colloids withminimal interference from in situ colloids.

Ž .Properties related to the transport of colloids D , k , k were estimated forp pr pdŽ . Ž .Lincoln sand by fitting Eqs. 6 and 7 to effluent colloid concentration profiles from


separate column experiments without phenanthrene. Details of these experiments areŽ .provided in Roy and Dzombak 1996 .

In addition to the column experiments, batch tests were performed to determine thepartitioning of phenanthrene with each of the four phases above: whole Lincoln sand,colloids from Lincoln sand, Eustis sand, and latex colloids. Fluoride tracer tests wereperformed to estimate the dispersion coefficient of solutes. Further details of all these

Ž .experiments are provided in Roy and Dzombak 1997 .

3.2. Estimation of base–case model parameters

To fit effluent data and assess the effects of colloids and nonequilibrium sorption oncontaminant transport, key porous medium properties were held constant at valuesdetermined experimentally for Lincoln sand, and colloid-related parameters were variedto estimate their relative significance. The porous medium parameters held constantwere K , F , a , r , D, D , and u . The colloid-related parameters varied in theps s s s p

different simulations were the inlet concentration and K , F , a , and k .pp p p pd

Porous medium properties used in the simulations were obtained by fitting theeffluent profile for phenanthrene from laboratory column tests with Lincoln sand and aresummarized in Table 3. The column effluent profiles were fitted with an analyticalsolution of the advective–dispersive transport model that includes two-box sorptionŽ .Parker and van Genuchten, 1984 . The data and the model fit are shown in Fig. 2. Theparameters estimated for phenanthrene transport in Lincoln sand were: K s5.8 mlrg;ps

F s0.428; and a s0.12rh. D was fixed at 10 cm2rh as determined by fluoride tracers s3 Ž .experiments, r was fixed at 2.65 grcm typical of quartz and u was fixed at ans

experimentally determined values of 0.376. D was fixed at a very low value, aspŽ . 2justified by Roy and Dzombak 1996 , of 0.01 cm rh. This follows from the fact that

the colloid effluent profiles showed very sharp concentration peaks that were indicativeof minimal dispersion. In the simulations described below, unless specifically noted, theporous medium parameters were held constant at the values shown in Table 3 and the

Žcolloid-related parameters were varied. In natural systems, colloids and the fixed solid

Table 3Base values of porous medium properties used in simulations

Parameter Value used2 )D 0.01 cm rhp

2 ) )D 10 cm rh3†r 2.65 grcms

3 ††K 5.8 cm rgpp††a 0.12rhs

†F 0.428s

L 10 cm

) Ž .From Roy and Dzombak 1996 .) ) Determined from fluoride tracer breakthrough.† Value considered reasonable for quartz.†† Ž .Estimated from the program of Parker and van Genuchten 1984 .


Fig. 2. Effluent phenanthrene concentration data, normalized to inlet concentration C , from a 10 cm-long,0

2.2-cm inner diameter Lincoln-sand-packed column. No colloids were present in the influent. Solid line is thefit with an advection–dispersion model including two-box sorption. The fitted parameters obtained byregression were K s5.8 mlrg, a s0.12rh, F s0.428. Other system parameters were the average flowps s s

Ž . 2 3velocity qru s18.22 cmrh, Ds10 cm rh, and r s2.65 grcm . Data shown are from three replicates

experiments.

phase may have different sorptive properties as the colloids may be transported from.their source to a region where the fixed solid phase properties are different .

3.3. Initial and boundary conditions used

For transport experiments, where colloids with sorbed contaminants are injected intoclean columns with no attached colloids or sorbed contaminants, the appropriate initialand boundary conditions are,

C x ,t sC for xs0 22Ž . Ž .p p ,0

E C x ,tŽ .ps0 for xs2 L 23Ž .

E xC x ,t s0 for ts0 24Ž . Ž .pa

C x ,t sC for xs0 25Ž . Ž .cd cd ,0

C x ,t s 1yF K C for xs0 26Ž . Ž .Ž .cp 2 p pp cd ,0

C x ,t s0 for ts0, is1, 2 27Ž . Ž .cs 2

C x ,t s0 for ts0, is1, 2 28Ž . Ž .cp i

C x ,t s0 for ts0, is1, 2 29Ž . Ž .ca i

E C x ,tŽ .cp is0 for xs2 L, is1, 2 30Ž .

E xC x ,t s0 for ts0 31Ž . Ž .cd

E C x ,tŽ .cds0 for xs2 L 32Ž .

E x


where C and C are the inlet colloid and dissolved contaminant concentrations andp,0 cd,0Ž . Ž . Ž . ŽL is the column length. Eqs. 23 , 30 and 32 represent a semi-infinite column as

used in the analytical solution of Parker and van Genuchten, 1984, for flux-averaged.concentrations . Depending on the value of Peclet number and the time period of the

simulation, establishment of the boundary at a value greater than 2 L may be required forŽ .Eq. 30 .

Sorptionrmobilization experiments involve two distinct stages with different bound-Ž .ary conditions. In the first stage from ts0 to ts t , where contaminant without0

colloids is first sorbed in the column, the initial and boundary conditions for contami-Ž . Ž . Ž .nant concentrations are defined by Eqs. 24 , 31 and 32 and all other concentrations

are zero. After this stage, the effective partition coefficient of the contaminant on thesolid phase, K , excludes the partitioning with the initial attached colloids, C , andps,eff pa,0

is given by,

K yK Cps pp pa ,0K s 33Ž .ps ,eff 1yCpa ,0

The sorbed phase concentrations in the first stage include sorbed contaminant on theŽ .attached colloids as well the fixed solid phase. At the start of the second stage t) t ,0

the sorbed contaminant is distributed between the fixed solid phase and the attachedŽ .colloids in proportion to their sorption capacities. C x,t in the column is known atcd 0

the start of the second stage. The other boundary conditions during this stage are,

C x ,t s0 for xs0 and t) t 34Ž . Ž .cd 0

C x ,t s0 for all x and ts t 35Ž . Ž .p 0

C x ,t sC for ts t 36Ž . Ž .pa pa ,0 0

4. Results

4.1. Simulations of colloid-facilitated transport with nonequilibrium sorption

Simulations were performed with the model described for equilibrium interactions ofcolloids and contaminants. For colloids with sorbing contaminants injected into cleansand columns, it was found that colloid-enhanced transport increased with increasinginlet colloid concentrations and partition coefficient of the contaminant for the colloids,and decreased with increasing deposition coefficient. These results are similar to those

Ž .presented in earlier studies e.g., Corapcioglu and Jiang, 1993 and are presented in RoyŽ .1995 .

ŽThe effects of nonequilibrium of contaminant exchange with colloid surfaces i.e.,.F -1.0 were explored through simulation and results are given in Figs. 3–5. Resultsp

Ž .are presented for total effluent concentrations dissolved and colloid-associated at


Ž .Fig. 3. Model simulations of total phenanthrene concentration for systems with colloids 100 mgrl in theinfluent for different fractions F of reversibly sorbing sites. Other parameters were a s0.0, K s6600p p pp

mlrg, k s0.1rh, k s0.3rh, D s0.01 cm2rh. Porous medium properties were as listed in Table 3. Thepd pr pŽconcentrations are normalized to C , the total inlet phenanthrene concentration dissolved and colloid0

.associated which was 1 mgrl in all cases.

Ž .xs10 cm i.e., concentrations at the outlet of a 10 cm long column and normalized tothe inlet concentration. Transport duration on the x-axis is represented as pore volumes.For K of 6600 mlrg, the effect on transport is shown in Fig. 3 for different fractionspp

Ž .of irreversible sorption sites a s0.0, and F s1.0 to 0.0 . As F was decreased, thep p p

potential for colloids to cause rapid breakthrough of phenanthrene increased when thecontaminant was irreversibly sorbed. The effect of different rates of desorption of

Ž .contaminants from colloids a for F s0.0 is shown in Fig. 4. The breakthrough wasp p

Ž .Fig. 4. Model simulations of total phenanthrene concentration for systems with colloids 100 mgrl in theŽ .influent for different mass transfer rate constants from colloids a , and assuming F s0.0. Other parametersp p

were K s6600 mlrg, k s0.1rh, k s0.3rh, D s0.01 cm2rh. Porous medium properties were aspp pd pr p

listed in Table 3. The concentrations are normalized to C , the total inlet phenanthrene concentration0Ž .dissolved and colloid associated which was 1 mgrl in all cases.


Ž .Fig. 5. Model simulations of total phenanthrene concentration for systems with colloids 100 mgrl in theinfluent for different values of K when contaminant desorption from all sites colloids is irreversibleppŽ . 2a s0.0 and F s0.0 . Other parameters were k s0.1rh, k s0.3rh, D s0.01 cm rh. Porous mediump p pd pr p

properties were as listed in Table 3. The concentrations are normalized to C , the total inlet phenanthrene0Ž .concentration dissolved and colloid associated which was 1 mgrl in all cases.

more rapid for slow rates of desorption, but for these conditions, the overall effect ontransport was not very significant. The effect of K on transport with rate-limitedpp

sorptionrdesorption is shown in Fig. 5 for conditions where F s0.0, and a s0.0. Itp p

may be seen from this plot that when K is high, the breakthrough of phenanthrene canpp

be very rapid.The effects of colloids on transport distances are shown in Figs. 6 and 7 for

Ž .conditions where nonequilibrium may be important. Distance x on the x-axis isrepresented as normalized distance xrÕt, where Õ is the darcy velocity qru . For

Ž .Fig. 6. Model simulations of total phenanthrene concentration versus normalized distance xr Õt for systemsŽ .with colloids 100 mgrl in the influent for different fractions of reversibly sorbing sites, F . Other parametersp

were a s0.0, K s6600 mlrg, k s0.1rh, k s0.3rh, D s0.01 cm2rh. Porous medium propertiesp pp pd pr p

were as listed in Table 3. The concentrations are normalized to C , the total inlet phenanthrene concentration0Ž .dissolved and colloid associated which was 1 mgrl in all cases.


Ž .Fig. 7. Model simulations of total phenanthrene concentration versus normalized distance xr Õt for systemsŽ .with colloids 100 mgrl in the influent for different vales of a . Other parameters were F s0.0,p p

K s6600 mlrg, k s0.1rh, k s0.3rh, D s0.01 cm2rh. Porous medium properties were as listed inpp pd pr pŽTable 3. The concentrations are normalized to C , the total inlet phenanthrene concentration dissolved and0

.colloid associated which was 1 mgrl in all cases.

irreversibly sorbed contaminants, the transport distances can be much larger than whenequilibrium is assumed. The effect of a on transport distances is shown in Fig. 7. Asp

a increases, concentrations fall off more rapidly, and would be expected to approachp

equilibrium conditions at very high values of this parameter.

4.2. Fitting of colloid-facilitated transport data for phenanthrene

Data and model fits are shown in Fig. 8 for an experiment where phenanthrene wassorbed in a column packed with Lincoln sand and the total effluent phenanthrene andcolloid concentrations were monitored as colloid release, induced by injection of 0.001

Ž .M NaCl, took place Roy and Dzombak, 1997 . The colloid particle concentration datafrom the experiment were fitted by keeping C constant and equal to valuespa,0

Ž .determined for release at 0.001 M equal to 0.019 grg, Roy and Dzombak, 1996 andŽadjusting k to fit the shape of the colloid concentration profile. For the conditions ofpr

these experiments, i.e., for high C , the system was not sensitive to k , and this valuepa,0 pd.was held constant at 0.1rh . The fitted value of k was 0.45rh. Using thesepr

parameters, phenanthrene concentrations were predicted for a value of K of 300pp

mlrg, close to the measured value for colloids from Lincoln sand in Roy and DzombakŽ . Ž Ž ..1997 , 334 mlrg. Defining K sK given by Eq. 33 after release, predictionsps ps,eff

Ž .were made a by assuming all colloids to be equilibrium with the dissolved phase andŽ .b by assuming F sF , and a sa . While the total predicted concentrations with thep s p s

two assumptions did not differ significantly, both overestimated substantially the extentof phenanthrene mobilization on colloids. To describe the data, the different system

Ž .parameters F , a , K , F , and a were adjusted until a reasonable fit was obtained.p p pp s s

The concentration peak height as a result of mobilization was found to be sensitive onlyto K , and the peak width was affected by F and a . The parameters estimated withpp s s


Fig. 8. Total phenanthrene concentrations and colloid concentrations in the effluent from 10 cm-long, 2.2-cmŽ .inner diameter Lincoln sand packed columns during sorption 0 to 61 pore volumes and during release of

Ž .colloids with 0.001 M NaCl after 61 pore volumes . Also shown on the plots are model fits for differentconditions. Porous medium properties were as listed in Table 3. The concentrations are normalized to C , the0

Ž .total inlet phenanthrene concentration dissolved and colloid associated which was 1 mgrl in all cases.

this approach were K s30 mlrg, F s0.1, a s0.06rh, and F s1.0. A similarpp s s p

approach was taken to describe phenanthrene mobilization data for colloid release atŽ .0.01 M, with the results shown in Fig. 9 C s0.004 grg, k s0.1rh, k s0.45rh .pa,0 pd pr

In this case as well, the prediction based on the experimental value of K greatlypp

overestimated the phenanthrene mobilization, but the latter could be described withparameters very close to those used for Fig. 8: K s30 mlrg, F s0.3, a s0.06rh,pp s s

and F s1.0.p

Data and model fits for phenanthrene transport in Eustis sand in the presence of latexcolloids and at two different pH values are shown in Fig. 10. The latex colloids, which


Fig. 9. Total phenanthrene concentrations and colloid concentrations in the effluent from 10 cm-long, 2.2-cmŽ .inner diameter Lincoln sand packed columns during sorption 0 to 61 pore volumes and during release of

Ž .colloids with 0.01 M NaCl after 61 pore volumes . Also shown on the plots are model fits for differentconditions. Porous medium properties were as listed in Table 3. The concentrations are normalized to C , the0

Ž .total inlet phenanthrene concentration dissolved and colloid associated which was 1 mgrl in all cases.

Ž .have a very high sorption capacity for phenanthrene K s214,600 mlrg , exhibited app

dramatic effect on phenanthrene transport at pH 9.8, but not at pH 7.5. In comparison,for an influent without colloids at pH 9.8, the effluent phenanthrene concentrations were

Žbelow 5% of influent concentrations after the passage of 35 pore volumes Roy and.Dzombak, 1997 . The data for phenanthrene transport in the presence of colloids were

wdescribed using an experimentally determined value of K average of measured valuespsŽ . Ž .xat pH 7.6 69 mlrg and pH 9.2 87 mlrg , values of F and a from Lincoln sand,s p

and k s0rh. F , a , and k were adjusted manually to obtain the fits shown in Fig.pr p p pd

10. The values that best described the data at pH 9.8 were k s0.23rh, F s0.2, andpd p

a s2.0rh; and at pH 7.5, k s2.5rh, F s0.2, and a s2.0rh.p pd p p


Fig. 10. Total phenanthrene concentrations in the effluent from 10 cm-long, 2.2-cm inner diameter Eustis-sand-packed columns upon injection of a 100 mgrl latex colloid suspension with 1 mgrl phenanthrene for

Ž .two pH values 7.5 and 9.8 . Also shown on the plots are model fits for different conditions and simulatedcolloid concentrations. Properties used in the simulations were K s78.1 mlrg, K s214,600 mlrg,ps pp

qru s26.03 cmrh, r s2.36 grcm3, a s0.12rh, F s0.428. The concentrations are normalized to C , thes s s 0Ž .total inlet phenanthrene concentration dissolved and colloid associated .

Thus, from the data for the Eustis sand experiments, it was found that the value ofk and the kinetics of contaminant exchange with colloids strongly affect whetherpd

transport through a column will be enhanced as a result of the presence of colloids. Ifthe colloids and contaminant are in equilibrium, contaminant transport will be enhancedto a lesser extent than when sorptionrdesorption kinetics are slow, as shown in Fig. 10for identical parameters that fitted data for the phenanthrene transport experiment at pH

Ž .9.8, but with F s1.0 i.e., all sites in equilibrium . In contrast to the fitting of data forp

Lincoln sand, for Eustis sand consideration of two-box sorption on colloids was requiredand made a significant difference.

5. Discussion

Using basic porous medium properties from a natural sand, the simulations presentedabove showed that for colloid-facilitated transport to be significant, the followingconditions must exist: sufficiently high colloid concentrations, a high partition coeffi-cient for contaminant sorption on colloids relative to the fixed porous medium, and alow deposition efficiency of the colloids in the porous medium. If one or more of theseconditions is not satisfied, colloids usually will not have a discernible effect oncontaminant transport. In addition, the existence of a slow desorption rate of contami-nant from colloids is likely to enhance transport distances greatly over what is predictedfor equilibrium interactions. It appears from the simulations presented in Figs. 3–7 thatthe lack of contaminant equilibrium with colloids is likely to be the most significantfactor in the long-range transport of colloid-borne contaminants, a conclusion similar to

Ž .that put forward by Smith and Degueldre 1993 .


The model simulations and fitting conducted in this work helped to identify mecha-nisms that are important in determining the extent of colloid-facilitated transport. Forexample, by analyzing phenanthrene mobilization data associated with colloid release,we were able to establish that the partition coefficient of phenanthrene on the colloidswas lower than what was determined for similar colloids in batch tests. The reasons forthis discrepancy are unclear, but may be related to the fact that properties of colloidsobtained from the first few pore volumes after release induced by ionic strengthreduction are different from the average properties of colloids obtained over the entire

Ž Ž ..experiment which were used for determining K in Roy and Dzombak 1997 . It ispp

also possible that the colloids initially released were from the outlet end of the columnand sorption sites on them may have been saturated to a lesser extent than predicted bythe two-box transport model. The modelling thus points to the need for more experimen-tal data of the variation of colloid properties over the time course of release. It alsoappears from the data for the experiments on latex colloid transport of phenanthrenethrough Eustis sand that contaminant desorption kinetics can play an important role inenhanced transport, and that the two-box model or a similar model is needed to describesuch data.

The simulations with the model also served to highlight the areas where betterunderstanding and data are needed to assess the possibility and extent of colloidfacilitated transport. One need is to obtain more empirical information of colloid releaseand deposition rate constants where there are surface chemical and physical hetero-geneities in the colloids as well as in the fixed porous medium. Such rate constants may

Ž .not be easily related to interparticle interaction energies Roy and Dzombak, 1996 , butorder-of-magnitude estimates and correlations of colloid transport in relation to parame-ters such as colloid and porous medium zeta potential may be useful in makingpredictions for unknown systems. Also, the extent of strong sorption needs to beinvestigated with colloidal materials found in natural porous media. For example, thepresence of strong and weak surface sites for metal ion sorption on hydrous ferrous

Ž .oxide has been reported Dzombak and Morel, 1990 . Similarly, when HOCs are incontact for prolonged periods with colloids containing natural organic matter, they tend

Ž .to form strong bonds, and result in very slow desorption rates Carroll et al., 1994 . It islikely that for these cases, if colloids were to be mobile, measurable facilitated transportof contaminants may result.

6. Summary and conclusions

This paper described the application of a model for colloid-facilitated contaminanttransport that accounted for different rates of colloid deposition and release, anddifferent degrees of nonequilibrium in contaminant exchange between colloid surfacesand the dissolved phase. The model was used to assess the significance of variouscolloid and porous medium parameters and to interpret experimental data for colloid-facilitated contaminant transport. It was shown that significant enhancement of transportwill occur only with high colloid concentrations and high partition coefficients ofcontaminants for colloids, or when contaminant desorption kinetics from colloids are


slow. Since groundwater colloid concentrations observed in the field are lower thanwthose induced by large ionic strength changes used in these simulations e.g., Backhus et

Ž . xal. 1993 generally reported concentrations of a few mgrl it is likely that slowsorptionrdesorption kinetics of contaminants will be the most important factor thatdetermines whether or not colloids enhance the transport of a contaminant in an aquifer.

Acknowledgements

ŽThis study was supported by the U.S. Environmental Protection Agency Grant No.. Ž .R819266-01-0 , the National Science Foundation PYI Grant No. BCS-9157086 , and

Ž .the Aluminum Company of America TC 943095 .

References

Abdel-Salam, A., Chrysikopoulos, C.V., 1995. Analysis of a model for contaminant transport in fracturedmedia in the presence of colloids. J. Hydrol. 165, 261–281.

Backhus, D., Ryan, J.N., Groher, D.M., MacFarlane, J.K., Gschwend, P.M., 1993. Sampling colloids andŽ .colloid-associated contaminants in ground water. Ground Water 31 3 , 466–479.

Baker, J.E., Capel, P.D., Eisenreich, S.J., 1986. Influence of colloids on sediment-water partition coefficientsŽ .of polychlorobiphenyl congeners in natural waters. Environ. Sci. Technol. 20 11 , 1236.

Brusseau, M.L., Jessup, R.E., Rao, P.S.C., 1990. Sorption kinetics of organic chemicals: evaluation ofŽ .gas-purge and piscible-displacement techniques. Environ. Sci. Technol. 24 5 , 727.

Brusseau, M.L., Jessup, R.E., Rao, P.S.C., 1991. Nonequilibrium sorption of organic chemicals: elucidation ofŽ .rate limiting processes. Environ. Sci. Technol. 25 1 , 134–142.

Buddemeier, R.W., Hunt, J.R., 1988. Transport of colloidal contaminants in groundwater: radionuclidemigration at the Nevada test site. Appl. Geochem. 3, 535–548.

Carroll, K.M., Harkness, M.R., Bracco, A.A., Balcarcel, R., 1994. Application of a permeantrpolymerdiffusional model to the desorption of polychlorinated biphenyls from Hudson River sediments. Environ.

Ž .Sci. Technol. 28 2 , 253–258.Chin, Y.-P., Gschwend, P.M., 1992. Partitioning of polycyclic aromatic hydrocarbons to marine porewater

Ž .colloids. Environ. Sci. Technol. 26 8 , 1621–1626.Corapcioglu, Y., Jiang, S., 1993. Colloid-facilitated groundwater contaminant transport. Water Resources Res.

Ž .29 7 , 2215–2226.Ž .Dahneke, B., 1975. Kinetic theory of the escape of particles from surfaces. J. Colloid Interface Sci. 50 1 ,

89–107.Dunnivant, F.M., Jardine, P.M., Taylor, D.L., McCarthy, J.F., 1992. Cotransport of cadmium and hexachloro-

biphenyl by dissolved organic carbon through columns containing aquifer material. Environ. Sci. Technol.25, 360–368.

Dzombak, D.A., Morel, F.M.M., 1990. Surface Complexation Modeling, Wiley-Interscience, New York.Enfield, C.G., Bengtsson, G., 1988. Macromolecular transport of hydrophobic contaminants in aqueous

Ž .environments. Ground Water 26 1 , 64–70.Enfield, C.G., Bengtsson, G., Lindqvist, R., 1989. Influence of macromolecules on chemical transport.

Ž .Environ. Sci. Technol. 23 10 , 1278–1286.Gounaris, V., Anderson, P.R., Holsen, T.M., 1993. Characteristics and environmental significance of colloids

Ž .in landfill leachate. Environ. Sci. Technol. 27 7 , 1381–1387.Grolimund, D., Borkovec, M., Bartmettler, K., Sticher, H., 1996. Colloid-facilitated transport of strongly

Ž .sorbing contaminants in natural porous media: a laboratory column study. Environ. Sci. Technol. 30 10 ,3118–3123.


Harnish, R.A., McKnight, D.M., Ranville, J., Stephens, V.C., Orem, W.H., Honeyman, B.D., 1995. ActinideReactivity with Colloidal Particles and Dissolved Phases in Ground and Surface Waters at the Rocky FlatsPlant, Colorado, in: Preprints of Papers Presented at the 209th National ACS National Meeting, Anaheim,

Ž .CA, 35 1 pp. 655–659.Herbert, B.E., Bertsch, P.M., Novak, J.M., 1993. Pyrene sorption by water-soluble organic carbon. Environ.

Ž .Sci. Technol. 27 2 , 398–403.Kaplan, D.I., Bertsch, P.M., Adriano, D.C., Orlandini, K.A., 1994. Actinide association with groundwater

colloids in a coastal plain aquifer. Radiochim. Acta 66–67, 181–187.Kaplan, D.I., Bertsch, P.M., Adriano, D.C., 1995. Facilitated transport of contaminant metals through an

Ž .acidified aquifer. Ground Water 33 5 , 708–717.Lee, L.S., Rao, P.S.C., Brusseau, M.L., 1991. Nonequilibrium sorption and transport of neutral and ionized

Ž .chlorophenols. Environ. Sci. Technol. 25 4 , 722–729.Magee, B.R., Lion, L.W., Lemley, A.T., 1991. Transport of dissolved organic macromolecules and their effect

Ž .on the transport of phenanthrene in porous media. Environ. Sci. Technol. 25 2 , 323–331.Ž .McCarthy, J.F., Zachara, J.M., 1989. Subsurface transport of contaminants. Environ. Sci. Technol. 23 5 ,

496–502.McDowell-Boyer, L., Hunt, J.R., Sitar, N., 1986. Particle transport through porous media. Water Resources

Ž .Res. 22 13 , 1901–1921.Ž .Mills, W.B., Liu, S., Fong, F.K., 1991. Literature review and model COMET for colloidrmetals transport in

Ž .porous media. Ground Water 29 2 , 199–208.Parker, J.C., van Genuchten, M.Th, 1984. Determining Transport Parameters from Laboratory and Field

Tracer Experiments, Virginia Agricultural Experiment Station, Bulletin 84-3, Virginia Polytechnic Instituteand State University, 1984.

Penrose, W.R., Polzer, W.L., Essington, E.H., Nelson, D.M., Orlandini, K.A., 1990. Mobility of plutoniumŽ .and americium through a shallow aquifer in a semiarid region. Environ. Sci. Technol. 24 2 , 228–234.

Puls, R.W., Powell, R.M., 1992. Transport of inorganic colloids through natural aquifer material: implicationsŽ .for contaminant transport. Environ. Sci. Technol. 26 3 , 614–621.

Ronen, D., Magaritz, M., Weber, U., Amiel, A.J., Klein, E., 1992. Characterization of suspended particlesŽ .collected in groundwater under natural gradient flow conditions. Water Resources Res. 28 5 , 1279–1291.

Roy, S.B., 1995. Colloid-Facilitated Transport of Contaminants in Porous Media, Ph.D. Thesis, Department ofCivil and Environmental Engineering, Carnegie Mellon University, October, 1995.

Roy, S.B., Dzombak, D.A., 1996. Colloid release and transport processes in natural and model porous media.Colloids Surf. 107, 245–262.

Roy, S.B., Dzombak, D.A., 1997. Chemical Factors Influencing Colloid-Facilitated Transport of ContaminantsŽ .in Porous Media, Environ. Sci. Tech. 31 3 , 656–664.

Ruckenstein, E., Prieve, D.C., 1976. Adsorption and desorption of particles and their chromatographicŽ .separation. AIChE J. 22 2 , 276–283.

Ryan, J.N., Gschwend, P.M., 1990. Colloid mobilization in two Atlantic coastal plain aquifers: field studies.Ž .Water Resources Res. 26 2 , 307–322.

Saiers, J.E., Hornberger, G.M., Liang, L., 1994. First- and second-order kinetics approaches for modeling theŽ .transport of colloidal particles in porous media. Water Resources Res. 30 9 , 2499–2506.

Saiers, J.E., Hornberger, G.M., 1996. The role of colloidal kaolinite on the transport of cesium throughŽ .laboratory sand columns. Water Resources Res. 32 1 , 33–41.

Selim, H.M., Davidson, J.M., Mansell, R.S., 1976. Evaluation of a Two-site Adsorption-desorption Model forDescribing Solute Transport in Soils, in: Proceeding of the Summer Conference on Computer Simulation,Washington, DC, July, 1976, pp. 444–448.

Smith, P.A., Degueldre, C., 1993. Colloid-facilitated transport of radionuclides through fractured media. J.Contam. Hydrol. 13, 143–166.

Spielman, L.A., Friedlander, S.K., 1974. Role of the electrical double layer in particle deposition byŽ .convective diffusion. J. Colloid Interface Sci. 46 1 , 22–31.

sorption nonequilibrium effects on colloid-enhanced transport of hydrophobic organic compounds in...

Documents