Article pubs.acs.org/est
Does Water Content or Flow Rate Control Colloid Transport in Unsaturated 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 in contaminant transport in soils: many contaminants exist in colloidal form, and colloids can facilitate transport of otherwise immobile contaminants. In unsaturated soils, colloid transport is, among other factors, affected by water content and flow rate. Our objective was to determine whether water content or flow rate is more important for colloid transport. We passed negatively charged polystyrene colloids (220 nm diameter) through unsaturated sand-filled columns under steady-state flow at different water contents (effective water saturations Se ranging from 0.1 to 1.0, with Se = (θ − θr)/(θs − θr)) and flow rates (pore water velocities v of 5 and 10 cm/min). Water content was the dominant factor in our experiments. Colloid transport 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 move only when pendular rings are interconnected. The flow rate affected retention of colloids in the secondary energy minimum, with less colloids being trapped when the flow rate increased. These results confirm the importance of both water content and flow rate for colloid transport in unsaturated porous media and highlight the dominant role of water content.
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INTRODUCTION Subsurface colloids can enhance the movement of strongly sorbing contaminants, a phenomenon called colloid-facilitated contaminant transport.1 In the presence of mobile subsurface colloids, some contaminants may move faster and farther, thereby bypassing the filter and buffer capacity of soils and sediments. Many contaminants can sorb onto colloids in suspension; this increases their mobile-phase concentrations beyond thermodynamic solubilities.2 Colloid-facilitated transport has been reported in several studies for heavy metals,3,4 radionuclides,5,6 pesticides,7,8 hormones,9 and other contaminants.10,11 Failure to account for colloid-facilitated solute transport will underestimate the transport potential for these contaminants. As colloids can enhance the transport of contaminants through soils, it is important to measure and understand colloid mobilization, deposition, and movement. Experimental and theoretical results reveal that colloid mobilization and deposition rates are sensitive to several physical and chemical factors, including water content, flow rate, porewater ionic strength, and colloid size and composition.12 Colloids are filtered from the bulk fluid to mineral grains by Brownian diffusion, interception, and sedimentation.13 The transport rates due to these three mechanisms can be calculated for water-saturated media as functions of physical factors of the © 2014 American Chemical Society
porous medium-water-colloid system, including colloid diameter and density, grain size, and flow velocity.13−15 Under unfavorable attachment conditions, a repulsive energy barrier exists between mineral grains and colloids. Colloids may not overcome this energy barrier for attachment to mineral grains but can be immobilized by a secondary energy minimum.12 Compared with the saturated groundwater zone, much less is known about colloid transport in the unsaturated vadose zone.1 The amounts of colloids transported are usually less under unsaturated flow than under saturated flow.16,17 The interaction of colloids with the air−water interface has been invoked as a dominant process in colloid retention in the vadose zone.1 Colloids can be captured at the air−water interface18,19 and move through a porous medium with an infiltration front.20 When colloids are attached to the air−water interface, the capillary forces acting on the colloids are so strong that the attachment of colloids to the air−water interface can be considered irreversible.21−23 It has been proposed in the literature16,23−25 that both water content as well as water flow rate are important drivers for Received: Revised: Accepted: Published: 3791
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Honeywell, Morristown, NJ) placed under the metal frit. At a distance of 4 and 11 cm from the bottom, we installed tensiometers and TDR probes to measure the matric potential and the water content. The suction on the tensiometers was measured with pressure transducers (26PCCFG6G). The TDR probes were connected to a cable tester (1502C, Tektronixs, Beaverton, OR), and the reflection curves were recorded with a data logger (CR23X, Campbell Scientific, Inc., Logan, UT). Pressure transducers and TDR probes were calibrated under normal gravity. We designed the TDR probes to fit the column diameter and used 3D printing techniques to produce the probe heads. The liquids were introduced into the column through a porous stone (L8405, Hogentogler & Co., Inc., Columbia, MD) to ensure even distribution over the whole sectional area of the column. The column was designed specifically for use in a geocentrifuge, so that centrifugal force would not affect the column operation. Porous Medium. Silica sand (3382-05, Mallinckrodt Baker, Inc., Phillipsburg, NJ), fractioned between 250 and 425 μm by wet sieving, was used for the porous medium. The sand was pretreated with 2 M HCl at 90 °C temperature for 24 h to remove organic and iron impurities. The sand was packed into the column in 1 cm depth increments into standing water to ensure saturated conditions. The packed sand had a porosity of ε = 0.38 cm3/cm3. The saturated pore volume in the column was 114.6 cm3. We determined the water retention characteristics with the hanging water column method (see Supporting Information, Section S1 and Figure S2). Model Colloids and Tracer. We injected carboxylatemodified polystyrene colloids with a diameter of 220 nm (PC02N/6481, Bangs Laboratories, Inc., Fishers, IN) at the top of the column. Selected properties of the colloids are listed in Table S1 (Supporting Information). Nitrate (1 mM NaNO3) was used as a tracer prior to each colloid transport experiment to check for uniformity of flow and to determine mobileimmobile water fractions. We calculated the critical acceleration beyond which colloid behavior will be affected by centrifugation:28
colloid mobilization and transport in unsaturated porous media. However, no conclusive experimental evidence exists on which factor is more important. Under gravity alone, water content and flow rate in unsaturated porous media are not independent and cannot be varied independently: the relationship between water content and flow rate is a characteristic property of the porous medium. However, if the body force (e.g., gravity) can be changed, then we can change water content and flow rate independently. This can be done with a centrifuge, through which the body force can be increased. Centrifuges have been used to study colloid transport under both saturated26−28 and unsaturated flow.27,29 However, no systematic evaluation of effects of water content versus flow rate on colloid transport has been reported. Such an evaluation will clarify important mechanisms of colloid transport in unsaturated porous media. The objective of our study was to experimentally determine the effects of water content and flow rate on colloid transport in unsaturated porous media. We hypothesized that the water content will dominate over flow rate in its effect on colloid transport because both configuration and surface area of the air−water interface are expected to drastically change with water content. We used a geocentrifuge to change the body force, so that we could independently vary water contents and flow rates.
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EXPERIMENTAL METHODS General Approach. We investigated how colloid transport was affected by water content and flow rate by conducting colloid transport experiments under unsaturated steady-state flow in a geocentrifuge. We designed column experiments with constant pore water velocities but different water contents and obtained a series of column breakthrough curves. Unsaturated Water Flow in a Centrifugal Field. In unsaturated porous media, steady-state water flow is described by the Darcy−Buckingham law: ⎛ ∂ψ ∂ψg ⎞ ⎟⎟ qw = −K (ψm)⎜⎜ m + ∂z ⎠ ⎝ ∂z
(1)
where qw is the water flux, K(ψm) is the unsaturated hydraulic conductivity, ψm is the matric potential of the medium, ψg is the gravimetric potential, and z is the depth. Under centrifugal acceleration, eq 1 can be written as30 ⎛ ∂ψ ⎞ qw = −K (ψm)⎜ m − ρω 2r ⎟ ⎝ ∂r ⎠
acrit =
36kT πdc3rpΔρ
(3)
where k is the Boltzmann constant, T is the absolute temperature, dc is the colloid diameter, rp is the average pore radius, 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 critical acceleration is 173g. Colloid behavior should therefore not be affected by centrifugal accelerations up to 173g. Solution Chemistry and Sequence of Liquids. Colloids were suspended at a concentration of 1012 particles/L in a 100 mM NaCl solution buffered at pH 10 with 1.67 mM NaHCO3 and 1.67 mM Na2CO3. According to DLVO calculations, colloids would attach to sand particles in a secondary energy minimum (see Supporting Information, Section S2 and Figure S4). We measured the hydrodynamic diameter of the colloids over time to ensure that the colloid suspension was stable (Supporting Information Figure S5). The column was first flushed with two pore volumes of deionized water (E-pure, Brandstaedt, IA, electrical conductivity < 5.5 × 10−6 S/m), followed by the nitrate tracer breakthrough of four pore volumes. Afterward, the column was flushed with two pore volumes of the pH 10, 100 mM
(2)
where ρ is the density of the liquid, ω is the angular speed, and r is the radius from the center of rotation. In a centrifugal field it is possible, by varying the angular speed, to establish different fluxes qw at a given matric potential ψm and hence constant water content. Furthermore, a given flux can be established at different matric potentials ψm and hence different water contents. Consequently, in a centrifugal field it is possible to vary 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 a nylon membrane, mesh size 500 (NM-E #500, Gilson Company, Inc., Lewis Center, OH) supported by a metal frit. Suction was applied with a vacuum pump and a vacuum chamber. The suction at the bottom of the column was measured with a pressure transducer (26PCCFG6G, ±1 bar, 3792
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NaCl solution without colloids to condition the column for the following colloid breakthrough. A seven pore volume pulse of colloid suspension was then introduced into the column, followed by elution with five pore volumes of colloid-free NaCl solution. Finally, 10 pore volumes of deionized water were introduced to release colloids attached in the secondary energy minimum (see Supporting Information, Table S2 for a summary of the sequence). This sequence was used for each different water content described below. After each sequence, the sand was removed, sonicated, washed, and then repacked into the column. Column Transport Experiments. Experiments were carried out under normal gravity and under centrifugal acceleration to vary water content and flow rates. For the experiments under centrifugation, we used the geocentrifuge facility at the Idaho National Laboratory31 (50 g-tonne Actidyn Systèmes model C61-3, France). The centrifuge has a radius of 2 m and accepts a pay load of 500 kg and accelerations up to 130g 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-Zürich, Switzerland) under gravity and a piston pump (Encynova, model 2-4, Broomfield, CO) under centrifugation. To relate acceleration, water content, and flow rate, we first developed calibration curves by setting the centrifuge to different accelerations (2, 10, 20, 30, and 40g) and applying different flow rates. We then determined the corresponding pore water velocities for the different accelerations based on the imposed flow rate and the measured water content (Figure 1a). On the basis of these measurements, we selected appropriate accelerations to obtain a series of distinct water contents and flow rates for the colloid transport experiments. 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 water content, and θs is the saturated water content. Under gravity, we made a series of experiments at water contents of 0.38 and 0.30 cm3/cm3 with corresponding pore water velocities of 10.5 and 6.2 cm/min, respectively. The 0.38 cm3/cm3 is the saturated water content of the medium. Under centrifugal acceleration, we made two series of experiments at constant pore water velocities of v ≈ 5.0 and v ≈ 10.0 cm/min, each with three different water contents. UV−vis Spectrophotometry and Data Processing. Nitrate and colloids in the column outflow were measured real-time with a in-line flow cell connected to a UV−vis spectrophotometer (USB-4000, Ocean Optics, Dunedin, FL). Nitrate breakthrough was measured at 230 nm and the subsequent colloid breakthrough at 240 nm wavelengths. Calibration curves were developed from dilutions of concentrated 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 for changes of dispersion at different accelerations.
Figure 1. (a) Pore water velocities as a function of water saturation (Se = θ − θr)/(θs − θr)) for different accelerations. The solid line represents the 1 g case, which was calculated on the basis of the fitting parameters of the van Genuchten−Mualem model obtained from the drainage curve of the water retention. Dashed lines are linear regressions to experimental data. (b) Experimental conditions of colloid transport experiments under gravity and centrifugal acceleration. The dashed and solid lines connect experiments with similar pore water velocity. Horizontal error bars represent one standard deviation; vertical error bars represent measurement errors calculated on the basis of error propagation; capital letters denote the experiments shown in Table 1
presence of air. At higher water saturation, continuous flow pathways exist, but as the saturation decreases, these pathways disconnect and water is mostly located in the angular pore space formed by neighboring soil grains. For porous media made of spherical grains, the water at low saturation forms pendular rings.34,35 The water saturation (and matric potential) at which pendular rings form is critical for colloid transport, because when pendular rings are not interconnected, colloid movement is restricted to adsorbed water films.23,36,37 Figure 2a shows the geometrical configuration at the critical water saturation, when pendular rings interconnect (wetting case). The critical water saturations and matric potentials where pendular rings interconnect have been calculated for porous media made of monodisperse spherical grains; for zero-degree contact angle and rhombohedral packing, the critical matric potential is given as35,37 σ ψcritical = −c λgrain (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 the surface tension (N/m), and λgrain is the diameter of the grain (m). For a drying medium, the critical matric potential corresponds to the air-entry potential.38,39 For non-zero-degree contact angles, the critical matric potential when pendular rings interconnect becomes less
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THEORETICAL CONSIDERATIONS Interconnection of Pendular Rings. Under unsaturated flow, the flow pathways for colloids are restricted by the 3793
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Table 1. Experimental Conditions, Modeled Data Obtained from CXTFIT,33 Experimental Mass Balances, and Water Film Thicknessesa measured data
modeled data
exp
a/g (-)
A B C D
1 2 10 40
1.00 0.71 0.34 0.21
± ± ± ±
0.00 0.07 0.09 0.06
0.38 0.28 0.15 0.10
± ± ± ±
0.00 0.03 0.03 0.02
10.5 9.2 9.7 8.9
± ± ± ±
0.0 1.0 2.4 2.6
E F G H
1 2 8 20
0.78 0.44 0.22 0.11
± ± ± ±
0.07 0.06 0.06 0.05
0.30 0.18 0.11 0.07
± ± ± ±
0.02 0.02 0.02 0.02
6.2 4.5 5.3 5.6
± ± ± ±
0.5 0.6 1.4 2.8
Se (cm3/cm3)
θ (cm3/cm3)
v (cm/min)
ψm (hPa)
v (cm/min)
D (cm2/min)
pore water velocity of v ≈ 10.0 cm/min −4.3 ± 5.0 10.5 ± 0.0 0.8 ± 0.0 −13.3 ± 1.8 9.2 ± 0.0 2.2 ± 0.1 −15.2 ± 1.5 9.6 ± 0.1 16.3 ± 0.5 −10.8 ± 1.9 8.8 ± 0.0 26.0 ± 0.4 pore water velocity of v ≈ 5.0 cm/min −16.3 ± 1.2 6.1 ± 0.0 2.3 ± 0.1 −11.8 ± 2.3 4.1 ± 0.0 3.8 ± 0.2 −16.2 ± 2.5 5.1 ± 0.0 9.1 ± 0.4 −8.2 ± 1.4 4.2 ± 0.0 42.9 ± 0.5
film thickness
mass balance λ (cm)
BTC (%)
REL (%)
REC (%)
f DLVO (nm)
fL (nm)
0.08 0.24 1.68 2.93
63.5 45.8 26.7 12.4
39.8 9.9 9.5 12.1
103.2 55.6 36.2 24.5
na 7.3 6.8 6.6
na 30.2 27.9 27.0
0.38 0.84 1.72 7.65
32.2 9.1 6.4 0.0
20.6 23.6 22.1 6.1
52.8 32.8 28.5 6.1
7.4 6.9 6.6 6.4
30.7 28.5 27.1 26.1
Abbreviations: 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 balance release curve; REC: mass balance of breakthough and release curve; f DLVO: DLVO adsorbed water film thickness after Tokunaga37 representing high ionic strength; f L: Langmuir adsorbed water film thickness after Tokunaga37 representing low ionic strength; na: not applicable. a
Adsorbed Water Films. When the critical water potential is exceeded and the pendular rings are disconnected, then the grain surface between the pendular rings is covered with a thin water film. The thickness of this water film depends on grain size, surface tension, ionic strength, and the matric potential.37,40 We calculated the film thickness with the Langmuir and DLVO approaches as described by Tokunaga.37 A summary of the equations is provided in the Supporting Information (Section S5). Effect of Acceleration on Pendular Rings. Pendular rings are affected by acceleration, and the extent can be assessed by the Bond number:41 Bo =
aΔρL2 σ
(5)
where a is the acceleration, Δρ is the density difference between water and air, L is a characteristic length, and σ is the surface tension of water. For our accelerations (amax = 40g) and expected radii of pendular rings (rmax = 106 μm, based on maximum radius of pendular rings for monodisperse grains in our system), we calculated a Bond number of Bo = 0.06, which indicates that the system is dominated by surface tension forces, and that pendular ring geometry will not be significantly affected by centrifugal acceleration. The Bond number of Bo = 0.06 also indicates that our porous medium is within the realm of capillary hysteresis, as our Bond number is well below Bo = 0.5, which is the critical Bond number above which capillary hysteresis in a porous medium made of monodisperse spheres should disappear.42
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Figure 2. Interconnection of pendular rings. (a) Schematic of pendular ring at interconnection between three equal spheres. (b) Critical water potentials for interconnection of pendular rings as a function of contact angle calculated with eq 4 (symbols) and the Young−Laplace equation (eq S4, Supporting Information) for two different grain diameters. (c) Range of matric potentials for our experiments and interconnection of pendular rings in a medium with grain diameter of λgrain = 250 μm.
RESULTS AND DISCUSSION Water Contents, Matric Potentials, and Flow Rates. Figure S2 in Supporting Information shows the main drainage and imbibition curves of the water retention characteristic, including the measured values for the steady-state transport experiments under gravity and centrifugal acceleration. The measured matric potentials for the gravity experiments were inbetween the main drainage and imbibition curves. The data from the centrifuge experiments, however, show higher (i.e., less negative) matric potentials at corresponding water contents compared to normal gravity conditions. We attribute this deviation to errors in tensiometric measurements of the matric
negative than predicted by eq 4. We calculated these critical potentials as a function of contact angle using a numerical solution of the Young−Laplace equation (see Section S4, Supporting Information). 3794
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potential during centrifugation. The pressure transducers used to measure matric potentials contain a membrane that is affected by centrifugation. Although we positioned the pressure transducers such that the membrane was aligned with centrifugal acceleration, expecting that this would minimize these effects,43 it did not appear to eliminate these measurement errors. We observed the highest deviations in the tensiometric reading from the hanging column data for the two highest accelerations (20 and 40g), supporting our supposition of inaccurate tensiometer measurements during centrifugation. Figure 1b shows the flow rates (pore water velocities) for the different experiments as a function of water content. The data show that we were able to establish constant pore water velocities over a wide range of water contents through centrifugation. The results from the gravity experiments show the expected increase in pore water velocity as the water saturation increases. The indicated measurement errors of the pore water velocities become larger as the saturation decreases because the pore water velocity is calculated from the measured flow rate divided by the measured water content. As the water content decreases, the relative error of the water content measurement increases, thereby also increasing the error for the pore water velocity because of error propagation. Nitrate Breakthrough Curves. The analysis of the nitrate breakthrough curves with CXTFIT revealed that in all experiments, whether under gravity or centrifugal acceleration, the transport of nitrate occurred under equilibrium conditions without sorption, i.e., nitrate moved as a conservative tracer, and there was no evidence of a physical nonequilibrium. In general, the fitted hydrodynamic dispersion and the dispersivity increased with decreasing water content (Table 1, Figure S6 in Supporting Information), as has been reported by others.16,44,45 Colloid Transport. Figure 3 shows the column breakthrough curves for the colloids at different water saturations for a pore water velocity of 10 cm/min. The curves show the initial colloid breakthrough under constant ionic strength, followed by the colloid release induced by reduction of the ionic strength. The initial colloid breakthrough was strongly affected by water saturation; the percentage of colloids (relative to the total amounts of colloids infused) breaking through the column decreased from 64% at Se = 1.0 to 12% at Se = 0.2 (Table 1). Such effects of water saturation have been reported by others.16,46 The percentage of released colloids after reduction of 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 pore water velocity of 5 cm/min (Supporting Information, Figure S7). Mass balances are plotted in Figure 4 and reveal three interesting features: First, consistently more colloids were eluted in the initial breakthrough at higher than at lower pore water velocity (Figure 4a). More colloid transport is expected under high pore water velocity, as colloids have less chance to interact with the solid−water interface.13,47−49 Second, more colloids were released after change of ionic strength at lower compared to higher pore water velocity (except for experiments A and H, which are discussed below). The percentage of the released 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
Figure 3. Colloid breakthrough and release curves for a pore water velocity of v ≈ 10 cm/min, where Se is water saturation, a/g is the acceleration in multiples of normal gravity, v is the pore water velocity in cm/min, and IS is the ionic strength.
positive correlation with water saturation; however, no distinct effect 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 the medium,51 strained in thin water films,36 wedged between grains,52 trapped on immobile water zones,52 or attached to the solid−water interface,53 to the air−water interface,17,54,55 or to the air−water−solid interface line.53,56 The colloids released during the subsequent change of ionic strength are likely those that have been initially trapped in the secondary energy minimum. As the flow rates and water saturations did not change between initial breakthrough and subsequent release, the colloids trapped at locations other than the secondary energy minimum should not have been affected by the change of ionic strength. The observation that more colloids were released under the lower pore water velocity (Figure 4b) suggests that initially more colloids were trapped in the secondary energy minimum under the low as compared to the high pore water velocity. This is supported by both experimental57,58 and numerical studies.52,58 The overall colloid recovery (sum of initial breakthrough and subsequent release), however, was independent of flow rate and depended only on water saturation (Figure 4c). 3795
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potentials because of hysteresis.39 For our experiments, which follow on an imbibition curve, the wetting conditions are the relevant ones. Because of hysteresis and uncertainties of pressure transducer measurements in the geocentrifuge, we could not determine exact matric potentials in our transport experiments. We therefore use the primary drainage and imbibition curves as boundaries for the expected matric potentials at a given water content (Figure 2c). We think that the measurement of the water content by TDR is not affected by centrifugation and that TDR is a reliable method to determine water contents in a centrifuge. The measured water contents and expected matric potentials are indicated by the horizontal lines in the gray area of Figure 2c. Additionally, the figure shows the calculated critical water potentials when pendular rings interconnect as a function of contact angle for a grain diameter of 250 μm. Assuming a zero-degree contact angle, pendular rings would be interconnected 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 matric potentials become less negative, and it becomes more likely that pendular rings are not interconnected. If pendular rings are not interconnected the water film thickness plays a decisive role in colloid transport. Adsorbed water film thickness increases with decrease in ionic strength. For higher ionic strength (106 mM), we calculated a water film thickness of 6 to 7 nm, and for the lower ionic strength (deionized water), we calculated a film thickness of 26 to 31 nm (Table 1). For both conditions the water film thickness did not exceed the colloid diameter of 220 nm and colloids will have been effectively strained in these water films.36 Colloid transport in our system therefore only occurred when pendular rings were interconnected. While there is some debate about the accuracy of water film thickness calculations,59,60 Kibbey61 argued that extensive water films in porous media do not exist, but that the water on grain surfaces is capillary water held by the surface roughness of the grains. On the basis of numerical solution of the Young− Laplace equation, Kibbey61 calculated that the thickness of water layers on grain surfaces can reach up to several hundreds of nanometers for water potentials ranging from −10 to −100 hPa; this is 1−2 orders of magnitude thicker than what is predicted from adsorbed water film thickness calculations. In this case, our colloid of 220 nm diameter could readily move within 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. In all but the driest experiment (experiment H) a breakthrough curve was observed (Figure 3 and Figure S7, Supporting Information) and continuous paths through the media were present. Under the driest condition (θ = 0.07 cm3/cm3, Se = 0.11), colloid transport was considerably reduced but some continuous pathways must have been still present. Otherwise no colloids would have been released from the secondary energy minimum during the change of ionic strength. Water saturations less than Se = 0.11 are necessary to stop any movement of colloids with a diameter of 220 nm. Colloid Retention Mechanisms. Our experiments, as others,16,24,53,54 have shown significant retention of colloids with decreasing water saturation in porous media. On the basis of the results of our saturated column experiments, where colloids were initially retained in the column, but were completely recovered upon change of ionic strength, we
Figure 4. Mass balance of column colloid transport during (a) colloid breakthrough, (b) release due to change of solution chemistry, and (c) sum of recovered colloids. Capital letters indicate the experiments listed 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.
The experiments under the wettest and driest conditions did not follow the release pattern described above. All colloids could be recovered in the outflow from the saturated experiment (Figure 4c, experiment A), which shows that the colloids initially were reversibly trapped in the secondary energy minimum. Our DLVO calculations support this assertion (Figure S4, Supporting Information). Compared to the unsaturated flow experiments, considerably more colloids were released under saturated flow (Figure 4b), which we attribute to the lack of other attachment sites for colloids under saturated flow. Under unsaturated flow, colloids not only are trapped in the secondary energy minimum of the solid-water interface but also can be retained by other mechanisms such as straining, wedging, and interactions with air−water interfaces. Consequently, less colloids will partition into the secondary energy minimum. The experiment under the driest condition (experiment H) did not show any initial colloid breakthrough and only minimal colloid release (Figure 4, Table 1). Colloid movement was restricted at this water saturation (θ = 0.07 cm3/cm3, Se = 0.11) in such a way that most colloids were strained in water films, while some were forced into secondary energy minima. The latter ones were ultimately released during the change of the ionic strength. Pendular Rings and Water Films. Figure 2b shows the critical matric potentials when pendular rings interconnect as calculated by eqs 4 and S4 (Supporting Information). The lines show the critical matric potentials during wetting for the minimum (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 for wetting and match well with our numerical solution of the Young−Laplace equation. As the contact angle increases, the critical matric potential becomes less negative and also less sensitive to grain size. For a drying medium, pendular rings start to disconnect under considerably more negative matric 3796
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conclude that colloids were retained in secondary energy minimum sites only. Under unsaturated flow, however, colloids were retained by additional mechanisms, as we could recover less and less colloids when the water saturation decreased. Possible additional mechanisms for colloid retention under unsaturated flow are pore straining, wedging, retention in zone of flow stagnation, attachment to the air−water interface or air−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 of retention mechanisms. We believe that the air−water interface is likely not a major attachment site for our colloids, as a considerable DLVO energy barrier opposes attachment to air− water interface. Only when the air−water interfaces were moving, as during drainage or imbibition, would we expect colloids to attach to the air−water interface and be held there by capillary forces,20,62,63 but under our steady-state flow conditions, 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 evidence for immobile water zones. Under water-saturated conditions, pore straining51,64 and grain−grain wedging52 are considered to be relevant if the colloid to grain ratio exceeds a threshold of 0.0017−0.005. In our experiments, the colloid to grain ratio was much smaller (5.2 × 10−4 to 8.8 × 10−4) than that threshold, making straining and wedging less likely. On the basis of these considerations, the most likely mechanisms for colloid retention in our experiments are straining in water films and in air−water interface-grain wedges; nonetheless, we do not entirely rule out straining and grain−grain wedging, because thresholds for these mechanisms may decrease under unsaturated flow. The air−water−solid interface line has been shown to be an important attachment site for colloids,53,55,56 and surface roughness may also contribute to immobilization of colloids,65 especially if water saturation decreases and colloids are more likely to interact with the solid−water interface. Colloids have been shown to attach to these sites, but yet it needs to be determined how exactly the repulsive energy barriers can be overcome to make such attachment possible under steady-state flow. Implications. Our results show that colloid transport under unsaturated flow conditions depends both on water content and flow rate, but to different extent and due to different mechanisms. The flow rate affects the retention of colloids in the secondary energy minimum and higher flow rates lead to less colloid retention. The water content affects the retention of colloids and dominates colloid retention, even in the absence of flow transients. Below a critical water content, colloid movement is inhibited. This critical water content can be calculated for porous media of uniform grain size using the concept of pendular rings and their interconnections. For natural soils and sediments, where grain sizes are nonuniform, we expect that some continuous flow pathways exist even below water contents that would inhibit colloid movement in uniform media. Colloid movement would be limited, but not entirely inhibited, which means colloids could contribute to contaminant transport at any water saturation. This explanation is consistent with the small but continuous flux of colloids reported from undisturbed sediments at the semiarid Hanford site,66 where water contents range from 0.08 to 0.15 cm3/cm3.
Article
ASSOCIATED CONTENT
S Supporting Information *
Detailed descriptions of the experimental setup, water retention characteristics, water content profiles in the columns, colloid stability, DLVO calculations, UV−vis spectrophotometry, and calculation of pendular rings and adsorbed water films. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Ph: 1-253-445-4523. Fax: 1-253-445-4571. E-mail: tj. [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based upon work supported by the U.S. Department of Energy, Office of Science (BER), under Award No. DE-FG02-08ER64660. We thank the German Research Foundation for supporting this study with a postdoctoral fellowship to T.K. Funding was further provided by the Washington State University Agricultural Research Center through Hatch Projects 0267 and 0152. We thank the four anonymous reviewers for their comments.
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REFERENCES
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Does Water Content or Flow Rate Control Colloid Transport in Unsaturated 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 in contaminant transport in soils: many contaminants exist in colloidal form, and colloids can facilitate transport of otherwise immobile contaminants. In unsaturated soils, colloid transport is, among other factors, affected by water content and flow rate. Our objective was to determine whether water content or flow rate is more important for colloid transport. We passed negatively charged polystyrene colloids (220 nm diameter) through unsaturated sand-filled columns under steady-state flow at different water contents (effective water saturations Se ranging from 0.1 to 1.0, with Se = (θ − θr)/(θs − θr)) and flow rates (pore water velocities v of 5 and 10 cm/min). Water content was the dominant factor in our experiments. Colloid transport 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 move only when pendular rings are interconnected. The flow rate affected retention of colloids in the secondary energy minimum, with less colloids being trapped when the flow rate increased. These results confirm the importance of both water content and flow rate for colloid transport in unsaturated porous media and highlight the dominant role of water content.
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INTRODUCTION Subsurface colloids can enhance the movement of strongly sorbing contaminants, a phenomenon called colloid-facilitated contaminant transport.1 In the presence of mobile subsurface colloids, some contaminants may move faster and farther, thereby bypassing the filter and buffer capacity of soils and sediments. Many contaminants can sorb onto colloids in suspension; this increases their mobile-phase concentrations beyond thermodynamic solubilities.2 Colloid-facilitated transport has been reported in several studies for heavy metals,3,4 radionuclides,5,6 pesticides,7,8 hormones,9 and other contaminants.10,11 Failure to account for colloid-facilitated solute transport will underestimate the transport potential for these contaminants. As colloids can enhance the transport of contaminants through soils, it is important to measure and understand colloid mobilization, deposition, and movement. Experimental and theoretical results reveal that colloid mobilization and deposition rates are sensitive to several physical and chemical factors, including water content, flow rate, porewater ionic strength, and colloid size and composition.12 Colloids are filtered from the bulk fluid to mineral grains by Brownian diffusion, interception, and sedimentation.13 The transport rates due to these three mechanisms can be calculated for water-saturated media as functions of physical factors of the © 2014 American Chemical Society
porous medium-water-colloid system, including colloid diameter and density, grain size, and flow velocity.13−15 Under unfavorable attachment conditions, a repulsive energy barrier exists between mineral grains and colloids. Colloids may not overcome this energy barrier for attachment to mineral grains but can be immobilized by a secondary energy minimum.12 Compared with the saturated groundwater zone, much less is known about colloid transport in the unsaturated vadose zone.1 The amounts of colloids transported are usually less under unsaturated flow than under saturated flow.16,17 The interaction of colloids with the air−water interface has been invoked as a dominant process in colloid retention in the vadose zone.1 Colloids can be captured at the air−water interface18,19 and move through a porous medium with an infiltration front.20 When colloids are attached to the air−water interface, the capillary forces acting on the colloids are so strong that the attachment of colloids to the air−water interface can be considered irreversible.21−23 It has been proposed in the literature16,23−25 that both water content as well as water flow rate are important drivers for Received: Revised: Accepted: Published: 3791
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Honeywell, Morristown, NJ) placed under the metal frit. At a distance of 4 and 11 cm from the bottom, we installed tensiometers and TDR probes to measure the matric potential and the water content. The suction on the tensiometers was measured with pressure transducers (26PCCFG6G). The TDR probes were connected to a cable tester (1502C, Tektronixs, Beaverton, OR), and the reflection curves were recorded with a data logger (CR23X, Campbell Scientific, Inc., Logan, UT). Pressure transducers and TDR probes were calibrated under normal gravity. We designed the TDR probes to fit the column diameter and used 3D printing techniques to produce the probe heads. The liquids were introduced into the column through a porous stone (L8405, Hogentogler & Co., Inc., Columbia, MD) to ensure even distribution over the whole sectional area of the column. The column was designed specifically for use in a geocentrifuge, so that centrifugal force would not affect the column operation. Porous Medium. Silica sand (3382-05, Mallinckrodt Baker, Inc., Phillipsburg, NJ), fractioned between 250 and 425 μm by wet sieving, was used for the porous medium. The sand was pretreated with 2 M HCl at 90 °C temperature for 24 h to remove organic and iron impurities. The sand was packed into the column in 1 cm depth increments into standing water to ensure saturated conditions. The packed sand had a porosity of ε = 0.38 cm3/cm3. The saturated pore volume in the column was 114.6 cm3. We determined the water retention characteristics with the hanging water column method (see Supporting Information, Section S1 and Figure S2). Model Colloids and Tracer. We injected carboxylatemodified polystyrene colloids with a diameter of 220 nm (PC02N/6481, Bangs Laboratories, Inc., Fishers, IN) at the top of the column. Selected properties of the colloids are listed in Table S1 (Supporting Information). Nitrate (1 mM NaNO3) was used as a tracer prior to each colloid transport experiment to check for uniformity of flow and to determine mobileimmobile water fractions. We calculated the critical acceleration beyond which colloid behavior will be affected by centrifugation:28
colloid mobilization and transport in unsaturated porous media. However, no conclusive experimental evidence exists on which factor is more important. Under gravity alone, water content and flow rate in unsaturated porous media are not independent and cannot be varied independently: the relationship between water content and flow rate is a characteristic property of the porous medium. However, if the body force (e.g., gravity) can be changed, then we can change water content and flow rate independently. This can be done with a centrifuge, through which the body force can be increased. Centrifuges have been used to study colloid transport under both saturated26−28 and unsaturated flow.27,29 However, no systematic evaluation of effects of water content versus flow rate on colloid transport has been reported. Such an evaluation will clarify important mechanisms of colloid transport in unsaturated porous media. The objective of our study was to experimentally determine the effects of water content and flow rate on colloid transport in unsaturated porous media. We hypothesized that the water content will dominate over flow rate in its effect on colloid transport because both configuration and surface area of the air−water interface are expected to drastically change with water content. We used a geocentrifuge to change the body force, so that we could independently vary water contents and flow rates.
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EXPERIMENTAL METHODS General Approach. We investigated how colloid transport was affected by water content and flow rate by conducting colloid transport experiments under unsaturated steady-state flow in a geocentrifuge. We designed column experiments with constant pore water velocities but different water contents and obtained a series of column breakthrough curves. Unsaturated Water Flow in a Centrifugal Field. In unsaturated porous media, steady-state water flow is described by the Darcy−Buckingham law: ⎛ ∂ψ ∂ψg ⎞ ⎟⎟ qw = −K (ψm)⎜⎜ m + ∂z ⎠ ⎝ ∂z
(1)
where qw is the water flux, K(ψm) is the unsaturated hydraulic conductivity, ψm is the matric potential of the medium, ψg is the gravimetric potential, and z is the depth. Under centrifugal acceleration, eq 1 can be written as30 ⎛ ∂ψ ⎞ qw = −K (ψm)⎜ m − ρω 2r ⎟ ⎝ ∂r ⎠
acrit =
36kT πdc3rpΔρ
(3)
where k is the Boltzmann constant, T is the absolute temperature, dc is the colloid diameter, rp is the average pore radius, 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 critical acceleration is 173g. Colloid behavior should therefore not be affected by centrifugal accelerations up to 173g. Solution Chemistry and Sequence of Liquids. Colloids were suspended at a concentration of 1012 particles/L in a 100 mM NaCl solution buffered at pH 10 with 1.67 mM NaHCO3 and 1.67 mM Na2CO3. According to DLVO calculations, colloids would attach to sand particles in a secondary energy minimum (see Supporting Information, Section S2 and Figure S4). We measured the hydrodynamic diameter of the colloids over time to ensure that the colloid suspension was stable (Supporting Information Figure S5). The column was first flushed with two pore volumes of deionized water (E-pure, Brandstaedt, IA, electrical conductivity < 5.5 × 10−6 S/m), followed by the nitrate tracer breakthrough of four pore volumes. Afterward, the column was flushed with two pore volumes of the pH 10, 100 mM
(2)
where ρ is the density of the liquid, ω is the angular speed, and r is the radius from the center of rotation. In a centrifugal field it is possible, by varying the angular speed, to establish different fluxes qw at a given matric potential ψm and hence constant water content. Furthermore, a given flux can be established at different matric potentials ψm and hence different water contents. Consequently, in a centrifugal field it is possible to vary 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 a nylon membrane, mesh size 500 (NM-E #500, Gilson Company, Inc., Lewis Center, OH) supported by a metal frit. Suction was applied with a vacuum pump and a vacuum chamber. The suction at the bottom of the column was measured with a pressure transducer (26PCCFG6G, ±1 bar, 3792
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NaCl solution without colloids to condition the column for the following colloid breakthrough. A seven pore volume pulse of colloid suspension was then introduced into the column, followed by elution with five pore volumes of colloid-free NaCl solution. Finally, 10 pore volumes of deionized water were introduced to release colloids attached in the secondary energy minimum (see Supporting Information, Table S2 for a summary of the sequence). This sequence was used for each different water content described below. After each sequence, the sand was removed, sonicated, washed, and then repacked into the column. Column Transport Experiments. Experiments were carried out under normal gravity and under centrifugal acceleration to vary water content and flow rates. For the experiments under centrifugation, we used the geocentrifuge facility at the Idaho National Laboratory31 (50 g-tonne Actidyn Systèmes model C61-3, France). The centrifuge has a radius of 2 m and accepts a pay load of 500 kg and accelerations up to 130g 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-Zürich, Switzerland) under gravity and a piston pump (Encynova, model 2-4, Broomfield, CO) under centrifugation. To relate acceleration, water content, and flow rate, we first developed calibration curves by setting the centrifuge to different accelerations (2, 10, 20, 30, and 40g) and applying different flow rates. We then determined the corresponding pore water velocities for the different accelerations based on the imposed flow rate and the measured water content (Figure 1a). On the basis of these measurements, we selected appropriate accelerations to obtain a series of distinct water contents and flow rates for the colloid transport experiments. 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 water content, and θs is the saturated water content. Under gravity, we made a series of experiments at water contents of 0.38 and 0.30 cm3/cm3 with corresponding pore water velocities of 10.5 and 6.2 cm/min, respectively. The 0.38 cm3/cm3 is the saturated water content of the medium. Under centrifugal acceleration, we made two series of experiments at constant pore water velocities of v ≈ 5.0 and v ≈ 10.0 cm/min, each with three different water contents. UV−vis Spectrophotometry and Data Processing. Nitrate and colloids in the column outflow were measured real-time with a in-line flow cell connected to a UV−vis spectrophotometer (USB-4000, Ocean Optics, Dunedin, FL). Nitrate breakthrough was measured at 230 nm and the subsequent colloid breakthrough at 240 nm wavelengths. Calibration curves were developed from dilutions of concentrated 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 for changes of dispersion at different accelerations.
Figure 1. (a) Pore water velocities as a function of water saturation (Se = θ − θr)/(θs − θr)) for different accelerations. The solid line represents the 1 g case, which was calculated on the basis of the fitting parameters of the van Genuchten−Mualem model obtained from the drainage curve of the water retention. Dashed lines are linear regressions to experimental data. (b) Experimental conditions of colloid transport experiments under gravity and centrifugal acceleration. The dashed and solid lines connect experiments with similar pore water velocity. Horizontal error bars represent one standard deviation; vertical error bars represent measurement errors calculated on the basis of error propagation; capital letters denote the experiments shown in Table 1
presence of air. At higher water saturation, continuous flow pathways exist, but as the saturation decreases, these pathways disconnect and water is mostly located in the angular pore space formed by neighboring soil grains. For porous media made of spherical grains, the water at low saturation forms pendular rings.34,35 The water saturation (and matric potential) at which pendular rings form is critical for colloid transport, because when pendular rings are not interconnected, colloid movement is restricted to adsorbed water films.23,36,37 Figure 2a shows the geometrical configuration at the critical water saturation, when pendular rings interconnect (wetting case). The critical water saturations and matric potentials where pendular rings interconnect have been calculated for porous media made of monodisperse spherical grains; for zero-degree contact angle and rhombohedral packing, the critical matric potential is given as35,37 σ ψcritical = −c λgrain (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 the surface tension (N/m), and λgrain is the diameter of the grain (m). For a drying medium, the critical matric potential corresponds to the air-entry potential.38,39 For non-zero-degree contact angles, the critical matric potential when pendular rings interconnect becomes less
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THEORETICAL CONSIDERATIONS Interconnection of Pendular Rings. Under unsaturated flow, the flow pathways for colloids are restricted by the 3793
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Table 1. Experimental Conditions, Modeled Data Obtained from CXTFIT,33 Experimental Mass Balances, and Water Film Thicknessesa measured data
modeled data
exp
a/g (-)
A B C D
1 2 10 40
1.00 0.71 0.34 0.21
± ± ± ±
0.00 0.07 0.09 0.06
0.38 0.28 0.15 0.10
± ± ± ±
0.00 0.03 0.03 0.02
10.5 9.2 9.7 8.9
± ± ± ±
0.0 1.0 2.4 2.6
E F G H
1 2 8 20
0.78 0.44 0.22 0.11
± ± ± ±
0.07 0.06 0.06 0.05
0.30 0.18 0.11 0.07
± ± ± ±
0.02 0.02 0.02 0.02
6.2 4.5 5.3 5.6
± ± ± ±
0.5 0.6 1.4 2.8
Se (cm3/cm3)
θ (cm3/cm3)
v (cm/min)
ψm (hPa)
v (cm/min)
D (cm2/min)
pore water velocity of v ≈ 10.0 cm/min −4.3 ± 5.0 10.5 ± 0.0 0.8 ± 0.0 −13.3 ± 1.8 9.2 ± 0.0 2.2 ± 0.1 −15.2 ± 1.5 9.6 ± 0.1 16.3 ± 0.5 −10.8 ± 1.9 8.8 ± 0.0 26.0 ± 0.4 pore water velocity of v ≈ 5.0 cm/min −16.3 ± 1.2 6.1 ± 0.0 2.3 ± 0.1 −11.8 ± 2.3 4.1 ± 0.0 3.8 ± 0.2 −16.2 ± 2.5 5.1 ± 0.0 9.1 ± 0.4 −8.2 ± 1.4 4.2 ± 0.0 42.9 ± 0.5
film thickness
mass balance λ (cm)
BTC (%)
REL (%)
REC (%)
f DLVO (nm)
fL (nm)
0.08 0.24 1.68 2.93
63.5 45.8 26.7 12.4
39.8 9.9 9.5 12.1
103.2 55.6 36.2 24.5
na 7.3 6.8 6.6
na 30.2 27.9 27.0
0.38 0.84 1.72 7.65
32.2 9.1 6.4 0.0
20.6 23.6 22.1 6.1
52.8 32.8 28.5 6.1
7.4 6.9 6.6 6.4
30.7 28.5 27.1 26.1
Abbreviations: 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 balance release curve; REC: mass balance of breakthough and release curve; f DLVO: DLVO adsorbed water film thickness after Tokunaga37 representing high ionic strength; f L: Langmuir adsorbed water film thickness after Tokunaga37 representing low ionic strength; na: not applicable. a
Adsorbed Water Films. When the critical water potential is exceeded and the pendular rings are disconnected, then the grain surface between the pendular rings is covered with a thin water film. The thickness of this water film depends on grain size, surface tension, ionic strength, and the matric potential.37,40 We calculated the film thickness with the Langmuir and DLVO approaches as described by Tokunaga.37 A summary of the equations is provided in the Supporting Information (Section S5). Effect of Acceleration on Pendular Rings. Pendular rings are affected by acceleration, and the extent can be assessed by the Bond number:41 Bo =
aΔρL2 σ
(5)
where a is the acceleration, Δρ is the density difference between water and air, L is a characteristic length, and σ is the surface tension of water. For our accelerations (amax = 40g) and expected radii of pendular rings (rmax = 106 μm, based on maximum radius of pendular rings for monodisperse grains in our system), we calculated a Bond number of Bo = 0.06, which indicates that the system is dominated by surface tension forces, and that pendular ring geometry will not be significantly affected by centrifugal acceleration. The Bond number of Bo = 0.06 also indicates that our porous medium is within the realm of capillary hysteresis, as our Bond number is well below Bo = 0.5, which is the critical Bond number above which capillary hysteresis in a porous medium made of monodisperse spheres should disappear.42
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Figure 2. Interconnection of pendular rings. (a) Schematic of pendular ring at interconnection between three equal spheres. (b) Critical water potentials for interconnection of pendular rings as a function of contact angle calculated with eq 4 (symbols) and the Young−Laplace equation (eq S4, Supporting Information) for two different grain diameters. (c) Range of matric potentials for our experiments and interconnection of pendular rings in a medium with grain diameter of λgrain = 250 μm.
RESULTS AND DISCUSSION Water Contents, Matric Potentials, and Flow Rates. Figure S2 in Supporting Information shows the main drainage and imbibition curves of the water retention characteristic, including the measured values for the steady-state transport experiments under gravity and centrifugal acceleration. The measured matric potentials for the gravity experiments were inbetween the main drainage and imbibition curves. The data from the centrifuge experiments, however, show higher (i.e., less negative) matric potentials at corresponding water contents compared to normal gravity conditions. We attribute this deviation to errors in tensiometric measurements of the matric
negative than predicted by eq 4. We calculated these critical potentials as a function of contact angle using a numerical solution of the Young−Laplace equation (see Section S4, Supporting Information). 3794
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potential during centrifugation. The pressure transducers used to measure matric potentials contain a membrane that is affected by centrifugation. Although we positioned the pressure transducers such that the membrane was aligned with centrifugal acceleration, expecting that this would minimize these effects,43 it did not appear to eliminate these measurement errors. We observed the highest deviations in the tensiometric reading from the hanging column data for the two highest accelerations (20 and 40g), supporting our supposition of inaccurate tensiometer measurements during centrifugation. Figure 1b shows the flow rates (pore water velocities) for the different experiments as a function of water content. The data show that we were able to establish constant pore water velocities over a wide range of water contents through centrifugation. The results from the gravity experiments show the expected increase in pore water velocity as the water saturation increases. The indicated measurement errors of the pore water velocities become larger as the saturation decreases because the pore water velocity is calculated from the measured flow rate divided by the measured water content. As the water content decreases, the relative error of the water content measurement increases, thereby also increasing the error for the pore water velocity because of error propagation. Nitrate Breakthrough Curves. The analysis of the nitrate breakthrough curves with CXTFIT revealed that in all experiments, whether under gravity or centrifugal acceleration, the transport of nitrate occurred under equilibrium conditions without sorption, i.e., nitrate moved as a conservative tracer, and there was no evidence of a physical nonequilibrium. In general, the fitted hydrodynamic dispersion and the dispersivity increased with decreasing water content (Table 1, Figure S6 in Supporting Information), as has been reported by others.16,44,45 Colloid Transport. Figure 3 shows the column breakthrough curves for the colloids at different water saturations for a pore water velocity of 10 cm/min. The curves show the initial colloid breakthrough under constant ionic strength, followed by the colloid release induced by reduction of the ionic strength. The initial colloid breakthrough was strongly affected by water saturation; the percentage of colloids (relative to the total amounts of colloids infused) breaking through the column decreased from 64% at Se = 1.0 to 12% at Se = 0.2 (Table 1). Such effects of water saturation have been reported by others.16,46 The percentage of released colloids after reduction of 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 pore water velocity of 5 cm/min (Supporting Information, Figure S7). Mass balances are plotted in Figure 4 and reveal three interesting features: First, consistently more colloids were eluted in the initial breakthrough at higher than at lower pore water velocity (Figure 4a). More colloid transport is expected under high pore water velocity, as colloids have less chance to interact with the solid−water interface.13,47−49 Second, more colloids were released after change of ionic strength at lower compared to higher pore water velocity (except for experiments A and H, which are discussed below). The percentage of the released 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
Figure 3. Colloid breakthrough and release curves for a pore water velocity of v ≈ 10 cm/min, where Se is water saturation, a/g is the acceleration in multiples of normal gravity, v is the pore water velocity in cm/min, and IS is the ionic strength.
positive correlation with water saturation; however, no distinct effect 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 the medium,51 strained in thin water films,36 wedged between grains,52 trapped on immobile water zones,52 or attached to the solid−water interface,53 to the air−water interface,17,54,55 or to the air−water−solid interface line.53,56 The colloids released during the subsequent change of ionic strength are likely those that have been initially trapped in the secondary energy minimum. As the flow rates and water saturations did not change between initial breakthrough and subsequent release, the colloids trapped at locations other than the secondary energy minimum should not have been affected by the change of ionic strength. The observation that more colloids were released under the lower pore water velocity (Figure 4b) suggests that initially more colloids were trapped in the secondary energy minimum under the low as compared to the high pore water velocity. This is supported by both experimental57,58 and numerical studies.52,58 The overall colloid recovery (sum of initial breakthrough and subsequent release), however, was independent of flow rate and depended only on water saturation (Figure 4c). 3795
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potentials because of hysteresis.39 For our experiments, which follow on an imbibition curve, the wetting conditions are the relevant ones. Because of hysteresis and uncertainties of pressure transducer measurements in the geocentrifuge, we could not determine exact matric potentials in our transport experiments. We therefore use the primary drainage and imbibition curves as boundaries for the expected matric potentials at a given water content (Figure 2c). We think that the measurement of the water content by TDR is not affected by centrifugation and that TDR is a reliable method to determine water contents in a centrifuge. The measured water contents and expected matric potentials are indicated by the horizontal lines in the gray area of Figure 2c. Additionally, the figure shows the calculated critical water potentials when pendular rings interconnect as a function of contact angle for a grain diameter of 250 μm. Assuming a zero-degree contact angle, pendular rings would be interconnected 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 matric potentials become less negative, and it becomes more likely that pendular rings are not interconnected. If pendular rings are not interconnected the water film thickness plays a decisive role in colloid transport. Adsorbed water film thickness increases with decrease in ionic strength. For higher ionic strength (106 mM), we calculated a water film thickness of 6 to 7 nm, and for the lower ionic strength (deionized water), we calculated a film thickness of 26 to 31 nm (Table 1). For both conditions the water film thickness did not exceed the colloid diameter of 220 nm and colloids will have been effectively strained in these water films.36 Colloid transport in our system therefore only occurred when pendular rings were interconnected. While there is some debate about the accuracy of water film thickness calculations,59,60 Kibbey61 argued that extensive water films in porous media do not exist, but that the water on grain surfaces is capillary water held by the surface roughness of the grains. On the basis of numerical solution of the Young− Laplace equation, Kibbey61 calculated that the thickness of water layers on grain surfaces can reach up to several hundreds of nanometers for water potentials ranging from −10 to −100 hPa; this is 1−2 orders of magnitude thicker than what is predicted from adsorbed water film thickness calculations. In this case, our colloid of 220 nm diameter could readily move within 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. In all but the driest experiment (experiment H) a breakthrough curve was observed (Figure 3 and Figure S7, Supporting Information) and continuous paths through the media were present. Under the driest condition (θ = 0.07 cm3/cm3, Se = 0.11), colloid transport was considerably reduced but some continuous pathways must have been still present. Otherwise no colloids would have been released from the secondary energy minimum during the change of ionic strength. Water saturations less than Se = 0.11 are necessary to stop any movement of colloids with a diameter of 220 nm. Colloid Retention Mechanisms. Our experiments, as others,16,24,53,54 have shown significant retention of colloids with decreasing water saturation in porous media. On the basis of the results of our saturated column experiments, where colloids were initially retained in the column, but were completely recovered upon change of ionic strength, we
Figure 4. Mass balance of column colloid transport during (a) colloid breakthrough, (b) release due to change of solution chemistry, and (c) sum of recovered colloids. Capital letters indicate the experiments listed 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.
The experiments under the wettest and driest conditions did not follow the release pattern described above. All colloids could be recovered in the outflow from the saturated experiment (Figure 4c, experiment A), which shows that the colloids initially were reversibly trapped in the secondary energy minimum. Our DLVO calculations support this assertion (Figure S4, Supporting Information). Compared to the unsaturated flow experiments, considerably more colloids were released under saturated flow (Figure 4b), which we attribute to the lack of other attachment sites for colloids under saturated flow. Under unsaturated flow, colloids not only are trapped in the secondary energy minimum of the solid-water interface but also can be retained by other mechanisms such as straining, wedging, and interactions with air−water interfaces. Consequently, less colloids will partition into the secondary energy minimum. The experiment under the driest condition (experiment H) did not show any initial colloid breakthrough and only minimal colloid release (Figure 4, Table 1). Colloid movement was restricted at this water saturation (θ = 0.07 cm3/cm3, Se = 0.11) in such a way that most colloids were strained in water films, while some were forced into secondary energy minima. The latter ones were ultimately released during the change of the ionic strength. Pendular Rings and Water Films. Figure 2b shows the critical matric potentials when pendular rings interconnect as calculated by eqs 4 and S4 (Supporting Information). The lines show the critical matric potentials during wetting for the minimum (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 for wetting and match well with our numerical solution of the Young−Laplace equation. As the contact angle increases, the critical matric potential becomes less negative and also less sensitive to grain size. For a drying medium, pendular rings start to disconnect under considerably more negative matric 3796
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conclude that colloids were retained in secondary energy minimum sites only. Under unsaturated flow, however, colloids were retained by additional mechanisms, as we could recover less and less colloids when the water saturation decreased. Possible additional mechanisms for colloid retention under unsaturated flow are pore straining, wedging, retention in zone of flow stagnation, attachment to the air−water interface or air−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 of retention mechanisms. We believe that the air−water interface is likely not a major attachment site for our colloids, as a considerable DLVO energy barrier opposes attachment to air− water interface. Only when the air−water interfaces were moving, as during drainage or imbibition, would we expect colloids to attach to the air−water interface and be held there by capillary forces,20,62,63 but under our steady-state flow conditions, 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 evidence for immobile water zones. Under water-saturated conditions, pore straining51,64 and grain−grain wedging52 are considered to be relevant if the colloid to grain ratio exceeds a threshold of 0.0017−0.005. In our experiments, the colloid to grain ratio was much smaller (5.2 × 10−4 to 8.8 × 10−4) than that threshold, making straining and wedging less likely. On the basis of these considerations, the most likely mechanisms for colloid retention in our experiments are straining in water films and in air−water interface-grain wedges; nonetheless, we do not entirely rule out straining and grain−grain wedging, because thresholds for these mechanisms may decrease under unsaturated flow. The air−water−solid interface line has been shown to be an important attachment site for colloids,53,55,56 and surface roughness may also contribute to immobilization of colloids,65 especially if water saturation decreases and colloids are more likely to interact with the solid−water interface. Colloids have been shown to attach to these sites, but yet it needs to be determined how exactly the repulsive energy barriers can be overcome to make such attachment possible under steady-state flow. Implications. Our results show that colloid transport under unsaturated flow conditions depends both on water content and flow rate, but to different extent and due to different mechanisms. The flow rate affects the retention of colloids in the secondary energy minimum and higher flow rates lead to less colloid retention. The water content affects the retention of colloids and dominates colloid retention, even in the absence of flow transients. Below a critical water content, colloid movement is inhibited. This critical water content can be calculated for porous media of uniform grain size using the concept of pendular rings and their interconnections. For natural soils and sediments, where grain sizes are nonuniform, we expect that some continuous flow pathways exist even below water contents that would inhibit colloid movement in uniform media. Colloid movement would be limited, but not entirely inhibited, which means colloids could contribute to contaminant transport at any water saturation. This explanation is consistent with the small but continuous flux of colloids reported from undisturbed sediments at the semiarid Hanford site,66 where water contents range from 0.08 to 0.15 cm3/cm3.
Article
ASSOCIATED CONTENT
S Supporting Information *
Detailed descriptions of the experimental setup, water retention characteristics, water content profiles in the columns, colloid stability, DLVO calculations, UV−vis spectrophotometry, and calculation of pendular rings and adsorbed water films. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*Ph: 1-253-445-4523. Fax: 1-253-445-4571. E-mail: tj. [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This material is based upon work supported by the U.S. Department of Energy, Office of Science (BER), under Award No. DE-FG02-08ER64660. We thank the German Research Foundation for supporting this study with a postdoctoral fellowship to T.K. Funding was further provided by the Washington State University Agricultural Research Center through Hatch Projects 0267 and 0152. We thank the four anonymous reviewers for their comments.
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REFERENCES
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