Role of Low Flow and BackwardFlow Zones on Colloid Transport inPore Structures Derived from RealPorous MediaX I Q I N G L I , * , † , ‡ Z H E L O N G L I , ‡ A N DD O N G X I A O Z H A N G * , ‡

Laboratory of Earth Surface Processes, College of Urban andEnvironmental Sciences, Peking University, Beijing, 100871, P.R. China, and Department of Energy and ResourcesEngineering, College of Engineering, Peking University,Beijing, 100871, P. R. China

Received December 2, 2009. Revised manuscript receivedMay 15, 2010. Accepted June 2, 2010.

To examine the relevance of low flow zones and flowvortices to colloid transport in real porous media, lattice-Boltzmann (LB) simulations were combined with X-raymicrotomography (XMT) to simulate flow fields in glass beadsand quartz sand. Backward flow zones were demonstratedto be widely present in both porous media, with a greater volumefraction in the former relative to the latter porous media.Glass beads in the XMT images were approximated as spheresand their coordinates and radii were extracted to allowreconstruction of pore structures. LB simulations were againperformed and the simulated flow fields in the reconstructedpore structures were coupled to a three-dimensional particletracking algorithm. Particle tracking simulations demonstratedthat significant amounts of colloids stayed in the simulateddomains for long periods (up to 50 pore volumes). The percentagesof colloids with long residence time increased as the depthof the secondary energy minimum increased. The majority ofthe colloids with long residence time were translated to low flowzones while being associated with grain surfaces via secondaryminima. A small fraction of colloids entered low flow zoneswithout being associated with the grains surfaces. Backwardflow zones were also found to trap a small fraction ofcolloids for significantly long time (up to 10 pore volumes). Inoverall, however, backward flow zones trapped fewer colloidsfor shorter durations than low flow zones. In summary, thiswork demonstrates the importance of temporary trapping ofcolloids by the low flow and backward flow zones in real porousmedia. This trapping process can explain a number ofintriguing experimental observations.

IntroductionThe colloid filtration theory (CFT) considers colloid removalby porous media as a two-step process: first, the masstransport of colloids to the proximities of grain surfaces; andsecond, the deposition of colloids to the surfaces (1). Thetransport step is characterized by the single-collector ef-

ficiency (η), which is the number of colloids colliding withthe collector (i.e., the grain) divided by the number of colloidsmoving toward the collector. The equations correlating η tothe parameters (e.g., fluid velocity, grain size) of theenvironmental conditions have been developed using trajec-tory analysis based on the Happel sphere-in-cell model (2-4).In this model, the porous medium is idealized as a collectionof spheres, each surrounded by a concentric fluid shell (5).The deposition step is described by the collision efficiency(R), which is the number of collisions that result in depositiondivided by the total number of collisions. The R is thoughtto be dependent on the interaction between grain and colloidsurfaces (6). From η andR, the rate constant of colloid removalcan be calculated and colloid concentrations at differenttransport distances predicted (1, 7).

CFT predicts colloid transport in porous media fairly wellin the absence of an interaction energy barrier between grainand colloid surfaces (conditions favorable for deposition)(e.g., ref 8). Under these conditions, every collision resultsin deposition (R ) 1). However, dramatic discrepanciesbetween CFT predictions and experimental observations existin the presence of an energy barrier (conditions unfavorablefor deposition). CFT predicts that colloid deposition wouldbe negligible at most (R ≈ 0) in the presence of even smallbarriers (e.g., >10 kT), whereas numerous laboratory andfield studies demonstrated that significant colloid depositionoccurs commonly (e.g., ref 9). The observed discrepancieswere traditionally attributed to the neglect of grain and colloidsurface charge heterogeneity and roughness which can locallyreduce or eliminate the energy barrier (e.g., refs 10 and 11).

Recently, increasing evidences suggest that the lack ofincorporating correct mechanisms of colloid retention isanother source of CFT failure under conditions unfavorablefor deposition (12). Both direct observations and mechanisticsimulations have demonstrated that colloids could depositat grain-to-grain contacts (13-16), a feature that is notaccounted for in the Happel model (5). Deposition and elutionexperiments in packed columns and impinging jet systemsindicate that significant fractions of retained colloids underunfavorable conditions are associated with collector surfacesvia secondary energy minima (17-19). These associatedcolloids are expected to translate along the grain surfacesdue to the tangential hydrodynamic drag, until they reachlow flow zones (e.g., rear stagnation zones) where the dragforce is insufficient to overcome the forces that resist theirfurther downgradient movement. Mechanistic simulationsof colloid transport have confirmed this process (16). Whenenhanced colloid retention in low flow zones was accountedfor in a kinetic model, superior fits to experimental break-through curves and retained profiles were obtained (20).

More recently, Li and co-workers demonstrated anotherpotential colloid removal mechanism, retention by flowvortices (where flow is in the opposite direction of the overallflow) (21). Colloids retained by flow vortices were tens ofmicrometers from grain surfaces, that is, they are notassociated with secondary energy minima (which are typicallyless than 100 nm away from grain surfaces). Flow vorticesnear grain contact areas have also been demonstrated byCardenas and Torkzaban et al. using the COMSOL software(22, 23) and by Biggs et al. using a lattice-gas automata-based method (24). However, these simulation studies andthe mechanistic simulations that revealed retention in lowflow zones by Johnson et al. (16) all dealt with unit cells ofidealized packing systems. In addition, colloids retained byflow vortices were directly released into the vortices (21).Whether flow vortices are widely present in real porous media

* Address correspondence to either author. Phone/fax: 86-10-62753246 (X.L.); 86-10-62757432 (D.Z.). Fax: 86-10-62757427 (D.Z.).E-mail: xli@urban.pku.edu.cn (X.L.); dxzhang@coe.pku.edu.cn (D.Z.).

† College of Urban and Environmental Sciences.‡ College of Engineering.

Environ. Sci. Technol. 2010, 44, 4936–4942

4936 9 ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 44, NO. 13, 2010 10.1021/es903647g 2010 American Chemical SocietyPublished on Web 06/14/2010

and whether colloids can get into the vortices have not beenexamined. As such, the role of low flow zones and flow vorticeson colloid transport in real porous media is not wellunderstood.

In this work, LB flow simulations were performed basedon X-ray microtomography-derived images of glass beadsand quartz sand to verify the existence of flow vortices in realporous media. The glass beads were approximated as perfectspheres and their coordinates and radii were obtained fromthe images. Based on the extracted coordinates and radii, LBsimulations were again conducted at a higher grid resolution.The derived flow fields were coupled to a three-dimensionalparticle-tracking algorithm to simulate the transport ofcolloids of various sizes under different flow and solutionchemistry conditions. Based on the simulation results, therole of low flow zones on colloid transport in real pore mediawas elucidated.

Materials and MethodsAcquisition of X-ray Microtomography Images. Soda limeglass beads (Cataphote Inc., Jackson, MS) and quartz sand(Fisher Scientific, Fair Lawn, NJ) had a size range of 710-850µm (20-25 mesh, American standard). The porous mediawere packed in a borosilicate glass column (75 mm in lengthand 8 mm in inner diameter) and scanned using the cone-beam X-ray microtomography system (Konoscope 40-130,Aracor Inc., Sunnyside, CA) at a spatial resolution of 20 µm.Images of the two porous media were reconstructed usinga filter back projection algorithm. Details of the XMT system,the scanning procedures, and the reconstruction algorithmare available elsewhere (13, 25). Representative images ofglass beads and quartz sand have been provided in a previouspublication (13).

LB Flow Simulation. For both porous media, five do-mains, each consisting of 220 × 220 × 220 pixels (4.4 × 4.4× 4.4 mm), were randomly selected from the XMT images.A D3Q15 lattice-Boltzmann BGK model was used for flowsimulations in the selected domains, with the voxel lengthexactly equal to the pixel length of the images (20 µm).Pressure boundaries were applied at the inlet and outletplanes (overall flow oriented in z direction). Solid (no-slip)boundaries were imposed at the x and y bounding planesand grain surfaces inside the domains. Details of the D3Q15model and boundary conditions were described in a previouspublication (21).

To mechanistically elucidate the role of low flow zonesand flow vortices on colloid retention, trajectory analysis ofcolloid movement needs to be performed. This requires theknowledge of colloid-grain interaction and other forces ateach position. The interaction force depends on the separa-tion distance between the colloid and grain surfaces. Sinceeven the glass beads are not perfectly spherical (see repre-sentative images in ref 13), the grain surfaces and theseparation distances can not be easily defined, disallowingcalculation of the colloid-grain interaction force and sub-sequent trajectory analysis. To bypass this hurdle, the glassbeads were approximated as perfect spheres in this work.Two 110 × 110 × 110 domains within two of the above 220× 220 × 220 domains of glass beads were selected. The actuallength in each dimension of the two domains was 2.2 mm.The coordinates of the centers and radii (in pixels) of thegrains within the two domains were obtained from the XMTimages using Image J. Both domains included 40 grains thatfully or partly fell within the domains.

Using the extracted coordinates and radii, the domainswere reconstructed (denoted as Domain 1 and 2, respectively)and discretized to yield 220 × 220 × 220 voxels. LB simulationswere again performed to obtain the flow fields in the tworeconstructed domains. During LB simulations, the lengthof the domains was turned to a dimensionless value of 1. The

coordinates and radii were turned dimensionless accordinglyand are provided in Table S1 and S2 in the SupportingInformation (SI). The porosities of Domain 1 and 2 were0.368 and 0.370, respectively, whereas the porosities beforereconstruction were 0.367 and 0.324, respectively. The averagediameter of the grains in the two domains was about 0.36(corresponding to an actual size of 360 µm) (SI Table S1 andS2). Thus, the ratio of voxel size (1/220 ) 0.0045) to averagegrain diameter is about 0.0129 (0.0045/0.36), very close tothe critical ratio at which simulated deposition converges atgroundwater flow regimes for colloids down to 1 µm (21).

Particle Tracking. The simulated flow fields of Domain1 and 2 were coupled to a three-dimensional particle trackingalgorithm. This algorithm tracked colloid trajectories in thepore spaces by performing complete force and torquebalances to determine the colloid velocities in the threedimensions. The force and torque balances and the derivationof colloid velocities were described in detail in two previouspublications (16, 21). A trilinear interpolation algorithm wasused to obtain fluid velocities at any position in the porespace from the discrete flow fields derived from LB simula-tions. Details of this algorithm were provided in the recentpublication (21).

Simulation Conditions. Simulations were conducted forthree sizes of colloids (0.5, 1.0, and 2.0 µm in diameter) attwo superficial velocities in both domains (1.0 × 10-4 and 1.0× 10-5 m s-1). At the higher velocity and in Domain 1,simulations were performed under four solution chemistryconditions: in the absence of an energy barrier (denoted asFAV); in the presence of energy barrier and with a secondaryenergy minimum of about 3 kT (UNFAV1), in the presenceof an energy barrier and with a secondary minimum of about0.5 kT (UNFAV2), and in the presence of an energy barrierand with a secondary minimum less than 0.1 kT (UNFAV3).The four solution conditions were created by assigningdifferent ionic strengths and zeta potentials of colloid andgrain surfaces (SI Table S3). At the low velocity in Domain1 and at both velocities in Domain 2, simulations wereperformed under two conditions, FAV and UNFAV1.

Under each simulation condition, four simulation runsusing four different random seeds (the number used togenerate particle entry positions) were carried out to allowa statistical analysis. For each simulation run, 500 colloidswere simulated under UNFAV1 at the lower superficialvelocity in Domain 1. Under the rest conditions, 1000 colloidswere simulated. The colloids were released into the entryplane, z ) 0.1. Positions where the simulated fluid velocitieswere negative were excluded for entry. Colloids deposited atgrain-to-grain contacts and at noncontact areas were re-corded. Criteria for colloid deposition were provided in theprevious paper (21).

Also recorded were the colloids that stayed in the domainsfor more than 5 times of the mean residence time of watermolecules at a particular superficial velocity. The meanresidence time of water molecules is equivalent to theduration of a pore volume (PV). The duration of a pore volumecan be calculated by dividing the displacement in z directionof an exiting water molecule (0.9 mm) by the fluid velocity.Simulation was terminated when the residence time of acolloid in the domain exceeded 50 PVs.

ResultsBackward Flow Zones in the Porous Media. LB simulationsat the spatial resolution of the XMT images revealed thatflow zones with negative z-direction velocities were widelypresent in both glass beads and quartz sand, as were in theunit cells (21). Representative flow fields of the z-directionvelocities in glass beads and quartz sand are shown in Figure1 and SI Figure S1, respectively. The white areas in the figuresare grains, whereas the red areas represent pore spaces where

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fluid velocity is positive (in the direction of overall flow). Theyellow-green areas represent zones where z-direction fluidvelocities are negative. Plotting the flow fields using vectors,however, indicates that the flow lines in the yellow-greenareas are not closed (SI Figure S2). As such, flows in thesezones do not form vortices, as opposed to the cases in unitcells (21, 22). These zones are hereinafter referred as backwardflow zones to indicate that in these zones flows have backwardcomponents. Our previous definition in ref 21 that equatedzones with negative z-velocity as flow vortices was incorrect,although flows in the zones of negative z-velocity in ref 21do form vortices (flow lines are closed, vector plot not shown).

The backward flow zones are typically located near thecontact areas between grains, as demonstrated in previoussimulation studies in unit cells (21-24). The volume ofbackward flow zones (derived by dividing the number ofnodes with negative z-velocity by the total number of nodesin the pore space) took up 1.25 ( 0.33% (n ) 5) and 1.86 (0.14% (n ) 5) of the entire pore spaces in glass beads andquartz sand, respectively. The Student t test indicates thatthe volume fraction of backward flow zones in the quartzsand is significantly higher than in glass beads (t-probability) 0.01).

The largest negative dimensionless velocity in z-directionamong the ten domains (five for each porous media) was-2.23 (the superficial velocity is 1). This velocity was usedto normalize all the negative z-direction velocities in the twoporous media. Numbers of nodes where the normalizedvelocities fell into specific ranges were summed up andcompared to the total numbers of nodes in backward flowzones to derive the percentages. The majority of negativez-direction velocities (93.5% and 88.9% in glass beads andquartz sand, respectively) were less than 1/10 of the largestnegative velocity (in magnitude) (SI Table S4). The percentageof nodes that had negative z-direction velocities greater thanone tenth of the largest negative velocity was significantlyhigher in quartz sand than in glass beads (11.1% vs 6.5%).

Simulated Colloid Retention in Reconstructed PoreStructures. Colloid Deposition and Retention in Domain 1.Under conditions favorable for deposition (FAV), simulatedcolloid deposition in Domain 1 increased with decreasingcolloid size (ranging from 0.5 to 2.0 µm) and with decreasingfluid velocity (SI Table S5), consistent with filtration theorypredictions (2, 3). The correlation equation developed byTufenkji and Elimelech (2) predicts a η value of 0.0076, 0.0049,

and 0.0046 at a superficial velocity of 1.0 × 10-4 m s-1 forcolloids with sizes of 0.5, 1.0, and 2.0 µm, respectively. At thesame velocity and porosity (0.37), 10.3, 7.4, and 5.8% of the0.5, 1.0, and 2.0 µm colloids were deposited, respectively (SITable S5 and S6). The deposited percentages can not bedirectly compared with the η values, as the simulated domainconsists of many grains, whereas η represents the probabilityof deposition onto a single grain under favorable conditions(R ) 1). At a porosity of 0.37, a domain of 1 × 1 × 1 mmcorresponds to 12.3 full grains with a size of 360 µm. Usingthis number, the percentages of deposition translate to ηvalues of 0.0084, 0.006, 0.0047, respectively, which differ fromthe corresponding theory-predicted values by a factor of 1.2at most. At the low fluid velocity, the simulated and predictedη values differ by less than a factor of 2.5. Apparently, particletracking based on the flow field simulated by the LB methoddoes a fairly good job in simulating colloid transport in porousmedia under favorable conditions.

Under the unfavorable conditions examined, no colloiddeposition occurred at noncontact areas (SI Table S5 andS6), as the lowest energy barrier (14.5 kT) used in simulationwas too high to cross by diffusion. However, at both superficialvelocities, significant fractions of simulated colloid stayed inthe domain for at least five PVs before they exited the domainor became deposited ( SI Table S5 and S6). For example,about 2.6% of the 1.0 µm colloids stayed in the domain formore than 10 PVs at the superficial velocity of 1.0 × 10-4 ms-1 and under UNFAV1. If these colloids were consideredremoved, this percentage would translate into an apparentcollector efficiency of 0.0021 ()0.026/12.3) and an apparentcollision efficiency of 0.35 ()0.0021/0.006, where 0.006 is thecollector efficiency under FAV). The amount of these colloidsdecreased as their residence time increased (Figure 2, left).As deposition conditions become more unfavorable, thepercentages of the long residence time colloids also decreasedat the velocity of 1.0 × 10-4 m s-1. For example, under UNFAV1and UNFAV2, a small fraction of 1.0 µm colloids stayed inthe domain for more than 50 PVs (i.e., colloids remained inthe domain throughout the maximum simulation duration),whereas under UNFAV3, all the simulated colloids exited thedomain within 50 PVs (Figure 2, left). Under favorableconditions, the residence time of some simulated colloidsalso exceeded 5 PVs (but all less than 30 PVs) at bothsuperficial velocities (SI Table S5 and S6). However, thepercentages of these colloids were lower than those underUNFAV1 and UNFAV2 (Figure 2). In addition, significantfractions (up to 71.4%) of colloids with residence time longerthan 5 PVs were deposited under favorable conditions,whereas only small fractions (typically less than 10%) of longresidence time colloids deposited (at grain-to-grain contacts)under unfavorable conditions (SI Table S7). The causes andimplications of the observation that colloids could stay inthe domain for long time are discussed in details in theDiscussion section.

Colloid Deposition and Retention in Domain 2. Underfavorable conditions, simulated colloid deposition in Domain2 also increased with decreasing colloid sizes and withdecreasing fluid velocities (SI Table S8), consistent withfiltration theory predictions. In addition, at the same fluidvelocity, the percentage of deposition in Domain 2 was veryclose to the percentage in Domain 1 for an identical colloidsize (SI Tables S5-S7). This means that simulated depositionin Domain 2 also agreed well with theory predictions. Underunfavorable conditions, there were also colloids that stayedin the domain for over 5 PVs before exiting or depositing.The percentages of these colloids decreased as the residencetime increased and when the deposition conditions becamemore unfavorable, as was observed in Domain 1 (Figure 2,right panel). The percentages of colloids with long residencetime were significantly lower than those in Domain 1 under

FIGURE 1. Representative flow fields showing backward flowzones in glass beads. Shown in the figure is the x-z plane at y) 0.464. The vector representation of the flow field in theboxed area is provided in SI Figure S2. The LB simulation wasperformed at a voxel length equal to the pixel length of theXMT image (20 µm).

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otherwise identical simulation conditions (Figure 2 and SITable S5-S7). The percentages of colloids with long residencetime that were deposited were also lower than those inDomain 1 under identical conditions (SI Tables S7 and S9).It seems that the differences in domains of the same porousmedium have a greater impact on colloid transport underunfavorable deposition conditions.

DiscussionRole of Low Flow Zones on Colloid Transport. To reveal themechanisms that caused certain colloids to stay in thedomains for a very long time, the trajectories of the colloidswith residence time longer than 5 PVs were examined. It was

found that the majority of these colloids were associatedwith the secondary energy minima for certain periods oftime during their transport in the domains. Figure 3 showsthe representative time series of the separation distance, thez-direction velocity, and the z coordinate of such a colloid.The colloid (1.0 µm) was simulated in Domain 1 underUNFAV1 at a superficial velocity of 1.0 × 10-4 m s-1. Thecolloid was released at a few to a few tens of micrometersfrom the grains (the 10th and 14th grain) and then becameassociated with the 25th grain via the secondary minimum(separation distance ) 16 nm) (Figure 3A and B). After about10 s, it left the grain, moved toward the 34th grain and becameassociated again via the secondary minimum. This time the

FIGURE 2. Percentages of colloids with different residence time. Simulations were performed in both domains at a superficialvelocity of 1.0 × 10-4 m s-1, under both favorable and unfavorable deposition conditions. Colloid size was 1 µm.

FIGURE 3. Time series of separation distance (H), z-coordinate (Z), z-direction fluid velocity (Vz), the nearest grains (J) of arepresentative colloid that experienced low fluid velocities (e.g., <1.0 × 10-6 m s-1) for significantly long time (>16 PVs) while beingassociated with grain surfaces via secondary energy minima.

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association lasted for nearly 90 s (with a few short inter-ruptions), followed by further downgradient movement. Thetotal duration of association with the grain surfaces via thesecondary minimum was more than half of its total residencetime (about 150 s) in the domain.

When the colloid was associated via the secondaryminimum, its velocity in the z-direction (the direction of theoverall flow) was typically low (Figure 3C). This is especiallytrue for the time period between 50 and 110 s, where thevelocity was lower than 1.0 × 10-6 m s-1, about 2-3 ordersof magnitude lower than the average fluid velocity (2.7 ×10-4 m s-1). During the period of low z-direction velocities,the displacement rate of the colloid in the z-direction wasminimal (Figure 3D). For example, during the time periodfrom 41 to 115 s, the colloid only moved 35 µm in thez-direction, with an average rate less than 0.5 µm per second.During the same period, the displacements in the x and ycoordinates were also quite small (less than 50 and 20 µmin x and y direction, respectively) (SI Figure S3). Theseobservations confirm that translation of secondary minimum-associated colloids on grain surfaces to low flow zones, amechanism operating in unit cells (16), is an importantprocess that causes long residence time of colloids in realporous media. It is also clear that zones of complete stagnantflow are not needed for colloids to be retained for significantlylong time (26).

Examination of colloid trajectories also revealed thatcolloids of long residence time were not necessarily associatedwith secondary energy minima. For example, at the superficialvelocity of 1.0 × 10-4 m s-1 and under UNFAV1, about 13%of the 1.0 µm colloids with residence time longer than 5 PVsdid not reach the secondary energy minimum, that is, theirseparation distances throughout their residence in thedomain were significantly greater than the separationdistance of the secondary minimum. At separation distancesof a few micrometers, some colloids also experienced lowfluid velocities and stayed in the domain for up to 25 PVs (SIFigure S4). This indicates that association with secondaryminima is not a prerequisite for long residence time. Theexistence of low flow zones in the pore domains seems to bemore critical. Trapping in low flow zones without associationvia secondary minima is consistent with the observation thatsome colloids could also stay in the domain for a significantlylong time (>10 PVs) under conditions favorable (FAV) orextremely unfavorable (UNFAV3) for deposition. Underfavorable conditions, colloids reaching the proximities ofgrain surfaces will deposit due to the lack of an energy barrier.As a result, association with grain surfaces via secondaryminima would not occur. Under conditions extremelyunfavorable for deposition, the secondary minimum is tooshallow to effectively keep the colloids from diffusing intothe bulk solution. Finally, it is worth noting that some colloidsthat once became associated with grain surfaces via second-ary minima exited the domains quickly (within 5 PVs) (datanot shown), indicating that association via secondary minimaalone is not sufficient for long residence time.

Role of Backward Flow Zones on Colloid Transport.Simulations in this work also demonstrated that colloids couldget into backward flow zones (i.e., they experienced negativez-direction fluid velocities) for certain periods of time duringtheir transport in the domains. Less than 10% of the simulatedcolloids once entered the backward flow zones in Domain1, whereas around 20% of the simulated colloids onceexperienced negative z-direction velocities in Domain 2 (SITables S10 and S11). In Domain 1, up to 55% of colloids thathad residence time longer than 5 PVs once entered backwardflow zones (SI Table S10). In Domain 2, the percentages weremuch lower (30% at most) under identical simulationconditions (SI Table S11), despite the fact that much morecolloids experienced negative z-direction velocities in this

domain. Clearly, there is no strong correlation betweenentering backward flow zones and long residence time.

The total time periods during which the colloids expe-rienced negative z-direction fluid velocities were also re-corded. A small fraction of these colloids could stay inbackward flow zones for over 3 PVs (SI Table S12). Morecolloids stayed in these zones for over 1 PV under UNFAV1than under FAV and UNFAV3, indicating that enteringbackward flow zones is dependent on solution chemistry. Ina few cases, colloids stayed in backward flow zones for upto 10 PVs (data not shown), indicating that backward flowzones could potentially trap the colloids for significantly longperiods of time. However, the number of such colloids ismuch lower than the total number of colloids of longresidence time. Hence, low flow zones play a more importantrole in trapping the colloids in the domains.

Occasionally, colloids in backward flow zones were a fewmicrometers from grain surfaces and could travel backwardin z-direction (flow forward) for significant distances (Figure4). In most cases, however, colloids experiencing negativez-direction fluid velocities were associated with grain surfacesvia secondary minima (SI Figure S5). Such colloids did notmove backward significantly in z-direction. This is consistentwith the observation that the magnitudes of fluid velocitiesthat colloids experienced were quite low. In this sense,backward flow zones can be regarded as special cases of lowflow zones.

Implications. Most laboratory and field studies on colloidtransport in porous media at groundwater flow regimestypically involved elution of only a few pore volumes (e.g.,ref 8). In these studies, colloids that remained in the porousmedia after elution were commonly considered as beingremoved from aqueous solutions due to deposition onto grainsurfaces. Hence, if elution lasts for less than 5 PVs, the colloidswith residence time longer than 5 PVs shown in this studywould be considered to be deposited. However, the simula-tions in this work demonstrate that colloid removal may bedue to temporary trapping (or more accurately, delaying ofmovement) of colloids in low flow and backward flow zones.Thus, the common practice in many previous papers thatequated removal or retention to deposition is inappropriate.

In addition, a number of experimental observations thathave intrigued the research community of colloid transportfor many years can be explained on the basis of the temporarytrapping process. First, this process can explain colloidremoval under conditions extremely unfavorable for deposi-tion, without resorting to surface roughness and chargeheterogeneities. As shown in Figure 2, there are still a smallfraction of colloids trapped in low flow zones for over 10 PVsunder such conditions (UNFAV3). Second, gradual increasesin the numbers of trapped colloids with decreasinglyunfavorable conditions is consistent with the previousobservations that colloid removal gradually increased asdeposition conditions becomes less unfavorable (e.g., ref 9).Under less unfavorable conditions, deeper secondary minimawould keep more colloids at grain surfaces for longer time,allowing more of them to be translated into low flow zones.Third, colloids with long residence time shown in this studywere loosely associated with or even quite away from grainsurfaces. They would continue to move downgradient withflow, which could well explain the observation of low colloidconcentrations during elution in the absence of macroscopicperturbations (e.g., refs 27 and 28). The downgradientmovement of loosely associated colloids can also cause thedowngradient movement of the mass center of retainedcolloids, leading to nonmonotonic profiles of retained colloidconcentrations with the transport distance. Nonmonotonicretained profiles have been observed in many columnexperiments (e.g., refs 29-32).

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In summary, this work demonstrated that combinationof XMT and the LB simulation is a powerful approach tostudy colloid transport mechanisms in porous media. Thepore domains used in this work consisted of 3-4 grains ineach dimension. At this scale, the solid wall boundariesapplied at the x and y bounding planes of the domains may

have a significant impact on the simulated flow field and onsubsequent particle tracking. Future work is required toextend simulations to larger domain sizes to allow quantita-tive comparisons between simulation results and experi-mental observations. Finally, it is also worth noting that ourparticle tracking approach did not explicitly consider colloidmigration across multiple flow lines due to combined inertialand wall (grain surfaces) effects (e.g., refs 33 and 34). Thefact that simulated η agreed well with theory-predicted valuesunder favorable conditions indicates that neglect of colloidmigration cross-flow lines may have a minor impact on theaccuracy of the simulated deposition under such conditions.Further investigation will be conducted to examine howcolloid migration across flow lines affects the simulatedresults under unfavorable deposition conditions (i.e., trappingof colloids by low flow zones).

AcknowledgmentsThis material is based on work funded by the National ScienceFoundation of China (Grant No. 40772147 and 50688901).We thank Dr. C. L. Lin at the Department of MetallurgicalEngineering of the University of Utah for providing the XMTimages. We are also grateful to two anonymous reviewers fortheir critical comments.

Supporting Information AvailableCoordinates and radii of grains in the simulated domains,solution chemistry conditions, tabulated simulation results,and representative trajectories of colloids with long residencetime. This material is available free of charge via the Internetat http://pubs.acs.org.

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FIGURE 4. Time series of z-direction fluid velocity (Vz),separation distance (H), and z-coordinate (Z) of a representativecolloid that was carried backward in z-direction for significantdistance. The simulation was performed in Domain 1 underUNFAV1 at a superficial velocity of 1.0 × 10-4 m s-1, with acolloid size of 1.0 µm. Shown in the insets are the fluidvelocity, separation distance, and z-coordinate during theperiod when the colloid was within the backward flow zone.Throughout the duration within the backward flow zone, thecolloid was away from the grain surface by at least a fewmicrometers.

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