does water content or flow rate control colloid transport in unsaturated porous media?

Does Water Content or Flow Rate Control Colloid Transport inUnsaturated Porous Media?Thorsten Knappenberger,*,† Markus Flury,† Earl D. Mattson,‡ and James B. Harsh§

†Department of Crop and Soil Sciences, Washington State University, Puyallup, Washington 98371, United States‡Idaho National Laboratory, Idaho Falls, Idaho 83415, United States§Department of Crop and Soil Sciences, Washington State University, Pullman, Washington 99164, United States

*S Supporting Information

ABSTRACT: Mobile colloids can play an important role incontaminant transport in soils: many contaminants exist incolloidal form, and colloids can facilitate transport of otherwiseimmobile contaminants. In unsaturated soils, colloid transportis, among other factors, affected by water content and flow rate.Our objective was to determine whether water content or flowrate is more important for colloid transport. We passednegatively charged polystyrene colloids (220 nm diameter)through unsaturated sand-filled columns under steady-stateflow at different water contents (effective water saturations Seranging from 0.1 to 1.0, with Se = (θ − θr)/(θs − θr)) and flowrates (pore water velocities v of 5 and 10 cm/min). Watercontent was the dominant factor in our experiments. Colloidtransport decreased with decreasing water content, and below a critical water content (Se < 0.1), colloid transport was inhibited,and colloids were strained in water films. Pendular ring and water film thickness calculations indicated that colloids can moveonly when pendular rings are interconnected. The flow rate affected retention of colloids in the secondary energy minimum, withless colloids being trapped when the flow rate increased. These results confirm the importance of both water content and flowrate for colloid transport in unsaturated porous media and highlight the dominant role of water content.

■ INTRODUCTION

Subsurface colloids can enhance the movement of stronglysorbing contaminants, a phenomenon called colloid-facilitatedcontaminant transport.1 In the presence of mobile subsurfacecolloids, some contaminants may move faster and farther,thereby bypassing the filter and buffer capacity of soils andsediments. Many contaminants can sorb onto colloids insuspension; this increases their mobile-phase concentrationsbeyond thermodynamic solubilities.2 Colloid-facilitated trans-port has been reported in several studies for heavy metals,3,4

radionuclides,5,6 pesticides,7,8 hormones,9 and other contami-nants.10,11 Failure to account for colloid-facilitated solutetransport will underestimate the transport potential for thesecontaminants.As colloids can enhance the transport of contaminants

through soils, it is important to measure and understand colloidmobilization, deposition, and movement. Experimental andtheoretical results reveal that colloid mobilization anddeposition rates are sensitive to several physical and chemicalfactors, including water content, flow rate, porewater ionicstrength, and colloid size and composition.12 Colloids arefiltered from the bulk fluid to mineral grains by Browniandiffusion, interception, and sedimentation.13 The transportrates due to these three mechanisms can be calculated forwater-saturated media as functions of physical factors of the

porous medium-water-colloid system, including colloid diam-eter and density, grain size, and flow velocity.13−15 Underunfavorable attachment conditions, a repulsive energy barrierexists between mineral grains and colloids. Colloids may notovercome this energy barrier for attachment to mineral grainsbut can be immobilized by a secondary energy minimum.12

Compared with the saturated groundwater zone, much less isknown about colloid transport in the unsaturated vadose zone.1

The amounts of colloids transported are usually less underunsaturated flow than under saturated flow.16,17 The interactionof colloids with the air−water interface has been invoked as adominant process in colloid retention in the vadose zone.1

Colloids can be captured at the air−water interface18,19 andmove through a porous medium with an infiltration front.20

When colloids are attached to the air−water interface, thecapillary forces acting on the colloids are so strong that theattachment of colloids to the air−water interface can beconsidered irreversible.21−23

It has been proposed in the literature16,23−25 that both watercontent as well as water flow rate are important drivers for

Received: October 21, 2013Revised: February 15, 2014Accepted: March 3, 2014Published: March 3, 2014

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colloid mobilization and transport in unsaturated porous media.However, no conclusive experimental evidence exists on whichfactor is more important. Under gravity alone, water contentand flow rate in unsaturated porous media are not independentand cannot be varied independently: the relationship betweenwater content and flow rate is a characteristic property of theporous medium. However, if the body force (e.g., gravity) canbe changed, then we can change water content and flow rateindependently. This can be done with a centrifuge, throughwhich the body force can be increased.Centrifuges have been used to study colloid transport under

both saturated26−28 and unsaturated flow.27,29 However, nosystematic evaluation of effects of water content versus flow rateon colloid transport has been reported. Such an evaluation willclarify important mechanisms of colloid transport in unsatu-rated porous media. The objective of our study was toexperimentally determine the effects of water content and flowrate on colloid transport in unsaturated porous media. Wehypothesized that the water content will dominate over flowrate in its effect on colloid transport because both configurationand surface area of the air−water interface are expected todrastically change with water content. We used a geocentrifugeto change the body force, so that we could independently varywater contents and flow rates.

■ EXPERIMENTAL METHODSGeneral Approach. We investigated how colloid transport

was affected by water content and flow rate by conductingcolloid transport experiments under unsaturated steady-stateflow in a geocentrifuge. We designed column experiments withconstant pore water velocities but different water contents andobtained a series of column breakthrough curves.Unsaturated Water Flow in a Centrifugal Field. In

unsaturated porous media, steady-state water flow is describedby the Darcy−Buckingham law:

ψψ ψ

= −∂∂

+∂

∂

⎛⎝⎜⎜

⎞⎠⎟⎟q K

z z( )w m

m g

(1)

where qw is the water flux, K(ψm) is the unsaturated hydraulicconductivity, ψm is the matric potential of the medium, ψg is thegravimetric potential, and z is the depth. Under centrifugalacceleration, eq 1 can be written as30

ψψ

ρω= −∂∂

−⎛⎝⎜

⎞⎠⎟q K

rr( )w m

m 2

(2)

where ρ is the density of the liquid, ω is the angular speed, andr is the radius from the center of rotation. In a centrifugal fieldit is possible, by varying the angular speed, to establish differentfluxes qw at a given matric potential ψm and hence constantwater content. Furthermore, a given flux can be established atdifferent matric potentials ψm and hence different watercontents. Consequently, in a centrifugal field it is possible tovary flow rates at constant water contents and vice versa.Column Setup. We used a Plexiglas column with an inner

diameter of 5.1 cm and a length of 15 cm (Figure S1,Supporting Information). As the bottom boundary, we used anylon membrane, mesh size 500 (NM-E #500, GilsonCompany, Inc., Lewis Center, OH) supported by a metal frit.Suction was applied with a vacuum pump and a vacuumchamber. The suction at the bottom of the column wasmeasured with a pressure transducer (26PCCFG6G, ±1 bar,

Honeywell, Morristown, NJ) placed under the metal frit. At adistance of 4 and 11 cm from the bottom, we installedtensiometers and TDR probes to measure the matric potentialand the water content. The suction on the tensiometers wasmeasured with pressure transducers (26PCCFG6G). The TDRprobes were connected to a cable tester (1502C, Tektronixs,Beaverton, OR), and the reflection curves were recorded with adata logger (CR23X, Campbell Scientific, Inc., Logan, UT).Pressure transducers and TDR probes were calibrated undernormal gravity. We designed the TDR probes to fit the columndiameter and used 3D printing techniques to produce theprobe heads. The liquids were introduced into the columnthrough a porous stone (L8405, Hogentogler & Co., Inc.,Columbia, MD) to ensure even distribution over the wholesectional area of the column. The column was designedspecifically for use in a geocentrifuge, so that centrifugal forcewould not affect the column operation.

Porous Medium. Silica sand (3382-05, Mallinckrodt Baker,Inc., Phillipsburg, NJ), fractioned between 250 and 425 μm bywet sieving, was used for the porous medium. The sand waspretreated with 2 M HCl at 90 °C temperature for 24 h toremove organic and iron impurities. The sand was packed intothe column in 1 cm depth increments into standing water toensure saturated conditions. The packed sand had a porosity ofε = 0.38 cm3/cm3. The saturated pore volume in the columnwas 114.6 cm3. We determined the water retention character-istics with the hanging water column method (see SupportingInformation, Section S1 and Figure S2).

Model Colloids and Tracer. We injected carboxylate-modified polystyrene colloids with a diameter of 220 nm(PC02N/6481, Bangs Laboratories, Inc., Fishers, IN) at the topof the column. Selected properties of the colloids are listed inTable S1 (Supporting Information). Nitrate (1 mM NaNO3)was used as a tracer prior to each colloid transport experimentto check for uniformity of flow and to determine mobile-immobile water fractions. We calculated the critical accelerationbeyond which colloid behavior will be affected by centrifuga-tion:28

π ρ=

Δa

kTd r36

critc3

p (3)

where k is the Boltzmann constant, T is the absolutetemperature, dc is the colloid diameter, rp is the average poreradius, and Δρ is the density difference of colloids and liquid.For our polystyrene colloids (density = 1.05 g/cm3, diameter =220 nm) and porous medium (rp = 52.2 μm) the criticalacceleration is 173g. Colloid behavior should therefore not beaffected by centrifugal accelerations up to 173g.

Solution Chemistry and Sequence of Liquids. Colloidswere suspended at a concentration of 1012 particles/L in a100 mM NaCl solution buffered at pH 10 with 1.67 mMNaHCO3 and 1.67 mM Na2CO3. According to DLVOcalculations, colloids would attach to sand particles in asecondary energy minimum (see Supporting Information,Section S2 and Figure S4). We measured the hydrodynamicdiameter of the colloids over time to ensure that the colloidsuspension was stable (Supporting Information Figure S5).The column was first flushed with two pore volumes of

deionized water (E-pure, Brandstaedt, IA, electrical conductiv-ity < 5.5 × 10−6 S/m), followed by the nitrate tracerbreakthrough of four pore volumes. Afterward, the columnwas flushed with two pore volumes of the pH 10, 100 mM

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NaCl solution without colloids to condition the column for thefollowing colloid breakthrough. A seven pore volume pulse ofcolloid suspension was then introduced into the column,followed by elution with five pore volumes of colloid-free NaClsolution. Finally, 10 pore volumes of deionized water wereintroduced to release colloids attached in the secondary energyminimum (see Supporting Information, Table S2 for asummary of the sequence). This sequence was used for eachdifferent water content described below. After each sequence,the sand was removed, sonicated, washed, and then repackedinto the column.Column Transport Experiments. Experiments were

carried out under normal gravity and under centrifugalacceleration to vary water content and flow rates. For theexperiments under centrifugation, we used the geocentrifugefacility at the Idaho National Laboratory31 (50 g-tonne ActidynSystemes model C61-3, France). The centrifuge has a radius of2 m and accepts a pay load of 500 kg and accelerations up to130g with platform dimensions of 70 cm length, 50 cm depth,and 60 cm height.The gravity experiments were essentially the same as under

centrifugation, except that we used a peristaltic pump (IPC 4,Ismatec, Glattbrugg-Zurich, Switzerland) under gravity and apiston pump (Encynova, model 2-4, Broomfield, CO) undercentrifugation. To relate acceleration, water content, and flowrate, we first developed calibration curves by setting thecentrifuge to different accelerations (2, 10, 20, 30, and 40g) andapplying different flow rates. We then determined thecorresponding pore water velocities for the different accel-erations based on the imposed flow rate and the measuredwater content (Figure 1a). On the basis of these measurements,we selected appropriate accelerations to obtain a series ofdistinct water contents and flow rates for the colloid transportexperiments.The selected flow rates, water contents, and water saturations

for all experiments are summarized in Table 1 and Figure 1b.Water saturation was calculated as Se = (θ − θr)/(θs − θr),where θ is the volumetric water content, θr is the residual watercontent, and θs is the saturated water content. Under gravity,we made a series of experiments at water contents of 0.38 and0.30 cm3/cm3 with corresponding pore water velocities of 10.5and 6.2 cm/min, respectively. The 0.38 cm3/cm3 is thesaturated water content of the medium. Under centrifugalacceleration, we made two series of experiments at constantpore water velocities of v ≈ 5.0 and v ≈ 10.0 cm/min, each withthree different water contents.UV−vis Spectrophotometry and Data Processing.

Nitrate and colloids in the column outflow were measuredreal-time with a in-line flow cell connected to a UV−visspectrophotometer (USB-4000, Ocean Optics, Dunedin, FL).Nitrate breakthrough was measured at 230 nm and thesubsequent colloid breakthrough at 240 nm wavelengths.Calibration curves were developed from dilutions of concen-trated stock solutions (see Supporting Information for details).The nitrate and colloid breakthrough curves were smoothed

with a Savitzky−Golay32 filter to remove instrumental noise.The nitrate breakthrough curves were analyzed with CXTFIT33

to determine mobile-immobile water fractions and to check forchanges of dispersion at different accelerations.

■ THEORETICAL CONSIDERATIONSInterconnection of Pendular Rings. Under unsaturated

flow, the flow pathways for colloids are restricted by the

presence of air. At higher water saturation, continuous flowpathways exist, but as the saturation decreases, these pathwaysdisconnect and water is mostly located in the angular porespace formed by neighboring soil grains. For porous mediamade of spherical grains, the water at low saturation formspendular rings.34,35

The water saturation (and matric potential) at whichpendular rings form is critical for colloid transport, becausewhen pendular rings are not interconnected, colloid movementis restricted to adsorbed water films.23,36,37 Figure 2a shows thegeometrical configuration at the critical water saturation, whenpendular rings interconnect (wetting case). The critical watersaturations and matric potentials where pendular ringsinterconnect have been calculated for porous media made ofmonodisperse spherical grains; for zero-degree contact angleand rhombohedral packing, the critical matric potential is givenas35,37

ψ σλ

= −ccriticalgrain (4)

where ψcritical is the critical matric potential (Pa), c is a constant(c = 9.1 for wetting, and c = 12−18 for drying37), σ is thesurface tension (N/m), and λgrain is the diameter of the grain(m). For a drying medium, the critical matric potentialcorresponds to the air-entry potential.38,39

For non-zero-degree contact angles, the critical matricpotential when pendular rings interconnect becomes less

Figure 1. (a) Pore water velocities as a function of water saturation (Se= θ − θr)/(θs − θr)) for different accelerations. The solid linerepresents the 1 g case, which was calculated on the basis of the fittingparameters of the van Genuchten−Mualem model obtained from thedrainage curve of the water retention. Dashed lines are linearregressions to experimental data. (b) Experimental conditions ofcolloid transport experiments under gravity and centrifugal accel-eration. The dashed and solid lines connect experiments with similarpore water velocity. Horizontal error bars represent one standarddeviation; vertical error bars represent measurement errors calculatedon the basis of error propagation; capital letters denote theexperiments shown in Table 1



negative than predicted by eq 4. We calculated these criticalpotentials as a function of contact angle using a numericalsolution of the Young−Laplace equation (see Section S4,Supporting Information).

Adsorbed Water Films. When the critical water potentialis exceeded and the pendular rings are disconnected, then thegrain surface between the pendular rings is covered with a thinwater film. The thickness of this water film depends on grainsize, surface tension, ionic strength, and the matricpotential.37,40 We calculated the film thickness with theLangmuir and DLVO approaches as described by Tokunaga.37

A summary of the equations is provided in the SupportingInformation (Section S5).

Effect of Acceleration on Pendular Rings. Pendularrings are affected by acceleration, and the extent can be assessedby the Bond number:41

ρσ

= Δa LBo

2

(5)

where a is the acceleration, Δρ is the density differencebetween water and air, L is a characteristic length, and σ is thesurface tension of water. For our accelerations (amax = 40g) andexpected radii of pendular rings (rmax = 106 μm, based onmaximum radius of pendular rings for monodisperse grains inour system), we calculated a Bond number of Bo = 0.06, whichindicates that the system is dominated by surface tension forces,and that pendular ring geometry will not be significantlyaffected by centrifugal acceleration.The Bond number of Bo = 0.06 also indicates that our

porous medium is within the realm of capillary hysteresis, asour Bond number is well below Bo = 0.5, which is the criticalBond number above which capillary hysteresis in a porousmedium made of monodisperse spheres should disappear.42

■ RESULTS AND DISCUSSIONWater Contents, Matric Potentials, and Flow Rates.

Figure S2 in Supporting Information shows the main drainageand imbibition curves of the water retention characteristic,including the measured values for the steady-state transportexperiments under gravity and centrifugal acceleration. Themeasured matric potentials for the gravity experiments wereinbetween the main drainage and imbibition curves. The datafrom the centrifuge experiments, however, show higher (i.e.,less negative) matric potentials at corresponding water contentscompared to normal gravity conditions. We attribute thisdeviation to errors in tensiometric measurements of the matric

Table 1. Experimental Conditions, Modeled Data Obtained from CXTFIT,33 Experimental Mass Balances, and Water FilmThicknessesa

measured data modeled data mass balance film thickness

expa/g(-) Se (cm

3/cm3) θ (cm3/cm3) v (cm/min) ψm (hPa) v (cm/min)D

(cm2/min)λ

(cm)BTC(%)

REL(%)

REC(%)

f DLVO(nm)

f L(nm)

pore water velocity of v ≈ 10.0 cm/minA 1 1.00 ± 0.00 0.38 ± 0.00 10.5 ± 0.0 −4.3 ± 5.0 10.5 ± 0.0 0.8 ± 0.0 0.08 63.5 39.8 103.2 na naB 2 0.71 ± 0.07 0.28 ± 0.03 9.2 ± 1.0 −13.3 ± 1.8 9.2 ± 0.0 2.2 ± 0.1 0.24 45.8 9.9 55.6 7.3 30.2C 10 0.34 ± 0.09 0.15 ± 0.03 9.7 ± 2.4 −15.2 ± 1.5 9.6 ± 0.1 16.3 ± 0.5 1.68 26.7 9.5 36.2 6.8 27.9D 40 0.21 ± 0.06 0.10 ± 0.02 8.9 ± 2.6 −10.8 ± 1.9 8.8 ± 0.0 26.0 ± 0.4 2.93 12.4 12.1 24.5 6.6 27.0

pore water velocity of v ≈ 5.0 cm/minE 1 0.78 ± 0.07 0.30 ± 0.02 6.2 ± 0.5 −16.3 ± 1.2 6.1 ± 0.0 2.3 ± 0.1 0.38 32.2 20.6 52.8 7.4 30.7F 2 0.44 ± 0.06 0.18 ± 0.02 4.5 ± 0.6 −11.8 ± 2.3 4.1 ± 0.0 3.8 ± 0.2 0.84 9.1 23.6 32.8 6.9 28.5G 8 0.22 ± 0.06 0.11 ± 0.02 5.3 ± 1.4 −16.2 ± 2.5 5.1 ± 0.0 9.1 ± 0.4 1.72 6.4 22.1 28.5 6.6 27.1H 20 0.11 ± 0.05 0.07 ± 0.02 5.6 ± 2.8 −8.2 ± 1.4 4.2 ± 0.0 42.9 ± 0.5 7.65 0.0 6.1 6.1 6.4 26.1

aAbbreviations: exp: experiment; a/g: acceleration in multiples of gravity; Se: water saturation (Se = θ − θr)/(θs − θr)); θ: volumetric water content;v: pore water velocity; ψm: matric potential; D: dispersion coefficient; λ: dispersivity; BTC: mass balance breakthough curve; REL: mass balancerelease curve; REC: mass balance of breakthough and release curve; f DLVO: DLVO adsorbed water film thickness after Tokunaga37 representing highionic strength; f L: Langmuir adsorbed water film thickness after Tokunaga37 representing low ionic strength; na: not applicable.

Figure 2. Interconnection of pendular rings. (a) Schematic of pendularring at interconnection between three equal spheres. (b) Critical waterpotentials for interconnection of pendular rings as a function ofcontact angle calculated with eq 4 (symbols) and the Young−Laplaceequation (eq S4, Supporting Information) for two different graindiameters. (c) Range of matric potentials for our experiments andinterconnection of pendular rings in a medium with grain diameter ofλgrain = 250 μm.



potential during centrifugation. The pressure transducers usedto measure matric potentials contain a membrane that isaffected by centrifugation. Although we positioned the pressuretransducers such that the membrane was aligned withcentrifugal acceleration, expecting that this would minimizethese effects,43 it did not appear to eliminate these measure-ment errors. We observed the highest deviations in thetensiometric reading from the hanging column data for thetwo highest accelerations (20 and 40g), supporting oursupposition of inaccurate tensiometer measurements duringcentrifugation.Figure 1b shows the flow rates (pore water velocities) for the

different experiments as a function of water content. The datashow that we were able to establish constant pore watervelocities over a wide range of water contents throughcentrifugation. The results from the gravity experiments showthe expected increase in pore water velocity as the watersaturation increases. The indicated measurement errors of thepore water velocities become larger as the saturation decreasesbecause the pore water velocity is calculated from the measuredflow rate divided by the measured water content. As the watercontent decreases, the relative error of the water contentmeasurement increases, thereby also increasing the error for thepore water velocity because of error propagation.Nitrate Breakthrough Curves. The analysis of the nitrate

breakthrough curves with CXTFIT revealed that in allexperiments, whether under gravity or centrifugal acceleration,the transport of nitrate occurred under equilibrium conditionswithout sorption, i.e., nitrate moved as a conservative tracer,and there was no evidence of a physical nonequilibrium. Ingeneral, the fitted hydrodynamic dispersion and the dispersivityincreased with decreasing water content (Table 1, Figure S6 inSupporting Information), as has been reported by others.16,44,45

Colloid Transport. Figure 3 shows the column break-through curves for the colloids at different water saturations fora pore water velocity of 10 cm/min. The curves show the initialcolloid breakthrough under constant ionic strength, followed bythe colloid release induced by reduction of the ionic strength.The initial colloid breakthrough was strongly affected by watersaturation; the percentage of colloids (relative to the totalamounts of colloids infused) breaking through the columndecreased from 64% at Se = 1.0 to 12% at Se = 0.2 (Table 1).Such effects of water saturation have been reported byothers.16,46 The percentage of released colloids after reductionof ionic strength was highest under saturated conditions (40%)and least for the unsaturated conditions (about 10%, Table 1).The release curves show a steep front and considerable tailing(Figure 3). Similar observations can be made for the lower porewater velocity of 5 cm/min (Supporting Information, FigureS7).Mass balances are plotted in Figure 4 and reveal three

interesting features: First, consistently more colloids wereeluted in the initial breakthrough at higher than at lower porewater velocity (Figure 4a). More colloid transport is expectedunder high pore water velocity, as colloids have less chance tointeract with the solid−water interface.13,47−49 Second, morecolloids were released after change of ionic strength at lowercompared to higher pore water velocity (except for experimentsA and H, which are discussed below). The percentage of thereleased colloids, however, was not affected by water saturation(Figure 4b). Third, the total amount of recovered colloids,which is the sum of breakthrough and released colloids, shows a

positive correlation with water saturation; however, no distincteffect of pore water velocity is discernible (Figure 4c).Under unsaturated flow, colloids are less mobile than under

saturated flow17,50 and can be strained in the pores of themedium,51 strained in thin water films,36 wedged betweengrains,52 trapped on immobile water zones,52 or attached to thesolid−water interface,53 to the air−water interface,17,54,55 or tothe air−water−solid interface line.53,56 The colloids releasedduring the subsequent change of ionic strength are likely thosethat have been initially trapped in the secondary energyminimum. As the flow rates and water saturations did notchange between initial breakthrough and subsequent release,the colloids trapped at locations other than the secondaryenergy minimum should not have been affected by the changeof ionic strength.The observation that more colloids were released under the

lower pore water velocity (Figure 4b) suggests that initiallymore colloids were trapped in the secondary energy minimumunder the low as compared to the high pore water velocity.This is supported by both experimental57,58 and numericalstudies.52,58 The overall colloid recovery (sum of initialbreakthrough and subsequent release), however, was independ-ent of flow rate and depended only on water saturation (Figure4c).

Figure 3. Colloid breakthrough and release curves for a pore watervelocity of v ≈ 10 cm/min, where Se is water saturation, a/g is theacceleration in multiples of normal gravity, v is the pore water velocityin cm/min, and IS is the ionic strength.



The experiments under the wettest and driest conditions didnot follow the release pattern described above. All colloidscould be recovered in the outflow from the saturatedexperiment (Figure 4c, experiment A), which shows that thecolloids initially were reversibly trapped in the secondaryenergy minimum. Our DLVO calculations support thisassertion (Figure S4, Supporting Information). Compared tothe unsaturated flow experiments, considerably more colloidswere released under saturated flow (Figure 4b), which weattribute to the lack of other attachment sites for colloids undersaturated flow. Under unsaturated flow, colloids not only aretrapped in the secondary energy minimum of the solid-waterinterface but also can be retained by other mechanisms such asstraining, wedging, and interactions with air−water interfaces.Consequently, less colloids will partition into the secondaryenergy minimum. The experiment under the driest condition(experiment H) did not show any initial colloid breakthroughand only minimal colloid release (Figure 4, Table 1). Colloidmovement was restricted at this water saturation (θ = 0.07cm3/cm3, Se = 0.11) in such a way that most colloids werestrained in water films, while some were forced into secondaryenergy minima. The latter ones were ultimately released duringthe change of the ionic strength.Pendular Rings and Water Films. Figure 2b shows the

critical matric potentials when pendular rings interconnect ascalculated by eqs 4 and S4 (Supporting Information). The linesshow the critical matric potentials during wetting for theminimum (λgrain = 250 μm) and maximum (λgrain = 425 μm)diameters of our porous medium as a function of contact angle.The solid symbols were calculated with eq 4 and c = 9.1 forwetting and match well with our numerical solution of theYoung−Laplace equation. As the contact angle increases, thecritical matric potential becomes less negative and also lesssensitive to grain size. For a drying medium, pendular ringsstart to disconnect under considerably more negative matric

potentials because of hysteresis.39 For our experiments, whichfollow on an imbibition curve, the wetting conditions are therelevant ones.Because of hysteresis and uncertainties of pressure transducer

measurements in the geocentrifuge, we could not determineexact matric potentials in our transport experiments. Wetherefore use the primary drainage and imbibition curves asboundaries for the expected matric potentials at a given watercontent (Figure 2c). We think that the measurement of thewater content by TDR is not affected by centrifugation and thatTDR is a reliable method to determine water contents in acentrifuge. The measured water contents and expected matricpotentials are indicated by the horizontal lines in the gray areaof Figure 2c. Additionally, the figure shows the calculatedcritical water potentials when pendular rings interconnect as afunction of contact angle for a grain diameter of 250 μm.Assuming a zero-degree contact angle, pendular rings would beinterconnected in all but the driest experiment (experiment H),which indeed did not have any initial colloid breakthrough(Figure 4a). With increasing contact angle, the critical matricpotentials become less negative, and it becomes more likely thatpendular rings are not interconnected.If pendular rings are not interconnected the water film

thickness plays a decisive role in colloid transport. Adsorbedwater film thickness increases with decrease in ionic strength.For higher ionic strength (106 mM), we calculated a water filmthickness of 6 to 7 nm, and for the lower ionic strength(deionized water), we calculated a film thickness of 26 to 31nm (Table 1). For both conditions the water film thickness didnot exceed the colloid diameter of 220 nm and colloids willhave been effectively strained in these water films.36 Colloidtransport in our system therefore only occurred when pendularrings were interconnected.While there is some debate about the accuracy of water film

thickness calculations,59,60 Kibbey61 argued that extensive waterfilms in porous media do not exist, but that the water on grainsurfaces is capillary water held by the surface roughness of thegrains. On the basis of numerical solution of the Young−Laplace equation, Kibbey61 calculated that the thickness ofwater layers on grain surfaces can reach up to several hundredsof nanometers for water potentials ranging from −10 to −100hPa; this is 1−2 orders of magnitude thicker than what ispredicted from adsorbed water film thickness calculations. Inthis case, our colloid of 220 nm diameter could readily movewithin this capillary water held by the grain’s surface roughness.A continuous pathway of thickness larger than 220 nm is

necessary to transport colloids in our column experiments. Inall but the driest experiment (experiment H) a breakthroughcurve was observed (Figure 3 and Figure S7, SupportingInformation) and continuous paths through the media werepresent. Under the driest condition (θ = 0.07 cm3/cm3, Se =0.11), colloid transport was considerably reduced but somecontinuous pathways must have been still present. Otherwiseno colloids would have been released from the secondaryenergy minimum during the change of ionic strength. Watersaturations less than Se = 0.11 are necessary to stop anymovement of colloids with a diameter of 220 nm.

Colloid Retention Mechanisms. Our experiments, asothers,16,24,53,54 have shown significant retention of colloidswith decreasing water saturation in porous media. On the basisof the results of our saturated column experiments, wherecolloids were initially retained in the column, but werecompletely recovered upon change of ionic strength, we

Figure 4. Mass balance of column colloid transport during (a) colloidbreakthrough, (b) release due to change of solution chemistry, and (c)sum of recovered colloids. Capital letters indicate the experimentslisted in Table 1. The solid line represents a pore water velocity of v ≈5.0, and the dashed line represents a pore water velocity of v ≈ 10 cm/min.



conclude that colloids were retained in secondary energyminimum sites only. Under unsaturated flow, however, colloidswere retained by additional mechanisms, as we could recoverless and less colloids when the water saturation decreased.Possible additional mechanisms for colloid retention underunsaturated flow are pore straining, wedging, retention in zoneof flow stagnation, attachment to the air−water interface orair−water−solid interface line, and water film straining.Although we do not have direct evidence where our colloids

were retained in our column, we can can infer plausibility ofretention mechanisms. We believe that the air−water interfaceis likely not a major attachment site for our colloids, as aconsiderable DLVO energy barrier opposes attachment to air−water interface. Only when the air−water interfaces weremoving, as during drainage or imbibition, would we expectcolloids to attach to the air−water interface and be held thereby capillary forces,20,62,63 but under our steady-state flowconditions, the air−water interface is expected to be stationary.Retention in flow stagnation zones can be ruled out also,because our nitrate tracer experiments did not show evidencefor immobile water zones. Under water-saturated conditions,pore straining51,64 and grain−grain wedging52 are considered tobe relevant if the colloid to grain ratio exceeds a threshold of0.0017−0.005. In our experiments, the colloid to grain ratio wasmuch smaller (5.2 × 10−4 to 8.8 × 10−4) than that threshold,making straining and wedging less likely. On the basis of theseconsiderations, the most likely mechanisms for colloidretention in our experiments are straining in water films andin air−water interface-grain wedges; nonetheless, we do notentirely rule out straining and grain−grain wedging, becausethresholds for these mechanisms may decrease underunsaturated flow.The air−water−solid interface line has been shown to be an

important attachment site for colloids,53,55,56 and surfaceroughness may also contribute to immobilization of colloids,65

especially if water saturation decreases and colloids are morelikely to interact with the solid−water interface. Colloids havebeen shown to attach to these sites, but yet it needs to bedetermined how exactly the repulsive energy barriers can beovercome to make such attachment possible under steady-stateflow.Implications. Our results show that colloid transport under

unsaturated flow conditions depends both on water contentand flow rate, but to different extent and due to differentmechanisms. The flow rate affects the retention of colloids inthe secondary energy minimum and higher flow rates lead toless colloid retention. The water content affects the retention ofcolloids and dominates colloid retention, even in the absence offlow transients. Below a critical water content, colloidmovement is inhibited. This critical water content can becalculated for porous media of uniform grain size using theconcept of pendular rings and their interconnections.For natural soils and sediments, where grain sizes are

nonuniform, we expect that some continuous flow pathwaysexist even below water contents that would inhibit colloidmovement in uniform media. Colloid movement would belimited, but not entirely inhibited, which means colloids couldcontribute to contaminant transport at any water saturation.This explanation is consistent with the small but continuousflux of colloids reported from undisturbed sediments at thesemiarid Hanford site,66 where water contents range from 0.08to 0.15 cm3/cm3.

■ ASSOCIATED CONTENT

*S Supporting InformationDetailed descriptions of the experimental setup, water retentioncharacteristics, water content profiles in the columns, colloidstability, DLVO calculations, UV−vis spectrophotometry, andcalculation of pendular rings and adsorbed water films. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.

■ AUTHOR INFORMATION

Corresponding Author*Ph: 1-253-445-4523. Fax: 1-253-445-4571. E-mail: [email protected].

NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

This material is based upon work supported by the U.S.Department of Energy, Office of Science (BER), under AwardNo. DE-FG02-08ER64660. We thank the German ResearchFoundation for supporting this study with a postdoctoralfellowship to T.K. Funding was further provided by theWashington State University Agricultural Research Centerthrough Hatch Projects 0267 and 0152. We thank the fouranonymous reviewers for their comments.

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mailto:[email protected]

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does water content or flow rate control colloid transport in unsaturated porous media?

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