Straining of Nonspherical Colloids in Saturated Porous Media

Current address: Department of Geosciences, University of Wisconsin, Milwaukee, ...... Megan B. Seymour , Gexin Chen , Chunming Su , and Yusong Li...
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Environ. Sci. Technol. 2008, 42, 771–778

Straining of Nonspherical Colloids in Saturated Porous Media S H A N G P I N G X U , †,‡ Q I A N L I A O , § A N D J A M E S E . S A I E R S * ,† School of Environmental Studies, Yale University, New Haven, Connecticut, 06511, and Department of Civil Engineering and Mechanics, University of Wisconsin, Milwaukee, Wisconsin 53211

Received June 5, 2007. Revised manuscript received October 3, 2007. Accepted October 19, 2007.

We explore the effects of colloid shape on straining kinetics by measuring the filtration of spherical and nonspherical colloids within saturated columns packed with quartz sand. Our observations demonstrate that the transport of peanut-shaped colloids matches the transport of spherical colloids with diameters equal to the minor-axis length of the peanut-shaped colloids. The straining rates of the spherical colloids vary linearly with the ratio of colloid diameter (dp) to sand-grain diameter (dg) for 0.0083 < dp/dg < 0.06. This linear relationship also quantifies the straining rates of the peanut-shaped particles provided that the particle’s minor axis length is used for dp. Results of pore-scale simulations reveal that a peanutshaped particle adopts a preferred orientation as it approaches a pore-space constriction such that its major axis tends to align with the local flow direction. The extent of this reorientation increases with the particle’s aspect ratio. Findings from this research suggest that straining is sensitive to changes in colloid shape and that the kinetics of this process can be approximated on the basis of measurable properties of the nonspherical colloids and porous media.

1. Introduction An understanding of the mechanisms that control particle filtration within water-saturated porous media is critical to addressing water-quality problems that involve the cotransport of contaminants by mineral colloids and the pollution of drinking water aquifers by microbial pathogens (1, 2). Particle filtration is governed by physicochemical deposition, whereby particles adhere to the solid phase of the porous medium (3), and straining, whereby particles are retained within regions of the pore space that are too narrow to permit their transmission (4–6). Straining contributes to the filtration of inorganic and organic particles of varying size (4, 5, 7–10). Tufenkji et al. (4) reported that straining retained 40% of the Cryptosporidium parvum oocysts immobilized within water-saturated columns of quartz sand, and Foppen et al. (11) concluded that straining rates were 2-fold greater than physiochemical deposition rates in column experiments on Escherichia coli transport. Results of similar experiments that used latex * Corresponding author phone: (203) 432-5121; fax: (203) 4325023; e-mail: [email protected]. † Yale University. ‡ Current address: Department of Geosciences, University of Wisconsin, Milwaukee, Wisconsin 53211. § University of Wisconsin. 10.1021/es071328w CCC: $40.75

Published on Web 01/03/2008

 2008 American Chemical Society

microspheres as the colloids demonstrate that straining can, under some conditions, dominate the filtration response and that straining rates depend on colloid size, grain size, and heterogeneity in the physical properties of the porous medium (5, 7–10, 12). Groundwater particles that may be susceptible to filtration by straining often exhibit nonspherical shapes. Rod-shaped bacteria with length-to-diameter ratios that exceed 2 are common in contaminated aquifers (13). Giardia cysts have a spheroidal shape, resembling that of rugby balls (13). Mineral colloids are also nonspherical and may exhibit even greater variation in geometry than microbes. For instance, surface-reactive clay particles, such as kaolinite, illite, and montmorillonite, are plate-like in appearance with aspect ratios (i.e., ratio of plate diameter to plate thickness) ranging from 2 to greater than 100 (14). Despite the variation in geometry observed among natural groundwater particles, no study has elucidated the response of filtration kinetics to changes in particle shape. The main objective of this research is to address this deficiency by quantifying the sensitivity of straining rates to changes in colloid shape by comparing the transport characteristics of nonspherical colloids to those of equivalently sized spherical colloids. Xu et al. (15) reported that straining rates of spherical particles vary proportionately with the ratio of colloid diameter (dp) to sand-grain diameter (dg) for dp/dg > 0.008. We are interested in determining whether similarly simple relationships exist for nonspherical particles and if these relationships can be interpreted mechanistically through knowledge of the orientation that nonspherical particles assume as they approach pore-space constrictions that are favorable for straining. Our work indicates that colloid shape does influence straining in noticeable ways and provides a means of quantifying this straining on the basis of measurable properties of the nonspherical colloids.

2. Materials and Methods 2.1. Porous Media. High-purity quartz sands (US Silica and Unimin) were used as porous media in the column experiments. Sands received from the manufacturers were separated with stainless steel sieves into four size classes: 0.71–0.85 mm (denoted as 0.78 mm), 0.3–0.355 mm (0.33 mm), 0.125–0.15 mm (0.14 mm), and 0.106–0.125 mm (0.12 mm). Once sieved, the sands were cleaned with boiling nitric acid (70%) to remove surface impurities (e.g., iron hydroxide and organic coatings) that could promote physicochemical deposition of the colloids (16). The duration of this nitric acid treatment was 24 h for the 0.33 and 0.78 mm sands and 48 h for the 0.12 and 0.14 mm sands, which had comparatively larger surface areas and hence greater amounts of surface impurities. The very fine particles that remained on the sand surfaces were removed by alternate rinses with 0.1 M NaOH solutions and deionized water (Barnstead Inc.). After the cleaning steps, the sand was dried in an oven at 80 °C and then stored in covered Pyrex beakers until use in the column experiments. 2.2. Latex Particles. The particles used in this study consisted of sulfate-modified, polystyrene latex particles (Magsphere Inc.) with either a spherical or a peanut shape (Figure 1). These particles were negatively charged when suspended in deionized water (see Table S1, Supporting Information) and had a density of 1.055 g cm-3. The diameters of the spherical particles (i.e., microspheres) were 0.5, 1.9, 2.8, 4.0, 5.1, and 6.1 µm, and the dimensions of peanutshaped particles were 1.9 × 2.8 µm and 4.3 × 6.1 µm (Figure 1). The lengths of the major and minor axes of the peanutVOL. 42, NO. 3, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Scanning electron microscopy (SEM) images of the peanut-shaped particles. shaped particles correspond with the diameters of the 1.9, 2.8, 4.0, and 6.1 µm microspheres, and the 4.3 × 6.1 µm peanut-shaped particles have the same maximum projected area as the 5.1 µm microspheres. We expected that the 0.5 µm microspheres were too small to be strained within the sands and thus we used these submicrometer colloids to evaluate the tendency of sulfate-modified particles to attach (stick to) the sand-grain surfaces (15). All particles received from the manufacturer were collected on Durapore membrane filters (Millipore) and redispersed in deionized water eight times to remove surfactants from their surfaces. Redispersion of the particles was facilitated by placing the suspensions in an ultrasonic bath. 2.3. Column Transport Experiments. The column experiments were conducted in duplicate with glass chromatography columns (Kontes) measuring 2.5 cm in diameter and 15 cm in length. Stainless steel membranes with 51 µm openings (Spectrum Laboratories, Inc.) were emplaced inside the column end fittings to prevent movement of the porous media, while permitting the passage of water and particles. The columns were oriented vertically and packed by slowly pouring the sand into deionized water standing in the bottom of the columns. The porosities, calculated from measurements of the column pore volume, equaled 0.36 for the 0.78 and 0.33 mm sands and 0.37 for the 0.14 and 0.12 mm sands. The sand packs were equilibrated by pumping 40 pore volumes of deionized water through the column with peristaltic pumps at a constant specific discharge of 0.31 cm min-1. An experiment was initiated following the equilibration step by introducing particles suspended in deionized water to the top of the column. The use of deionized water was intended to maximize electrostatic repulsion between the colloids and sand grains and thus to minimize physicochemical deposition (4, 15). Colloid concentrations were 1.45 × 109, 7.92 × 107, 2.47 × 107, 8.47 × 106, 4.09 × 106, 2.39 × 772

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106, 5.24 × 107, and 4.58 × 106 particles mL-1 for the 0.5, 1.9, 2.8, 4.0, 5.1, and 6.1 µm, 1.9 × 2.8 µm, and 4.3 × 6.1 µm particles, respectively. The particle suspensions were applied for 2 h (6.6 pore volumes), whereupon the columns were flushed with colloid-free water at the same specific discharge (0.31 cm min-1) until concentrations in the column effluent returned to baseline levels. Effluent samples were collected by a fraction collector and analyzed for colloid concentrations with a spectrophotometer (Beckman DU 520) at a wavelength of 650 nm. Following completion of the experiments with large colloids (size >4 µm) in the 0.12 and 0.14 mm sands, the depth profiles of strained colloids were measured. The sand was excavated in 1.5 cm increments and each increment was placed with 40 mL of deionized water into a 100 mL vial. After the vial was vigorously shaken, colloid concentrations in the supernatants were measured with a spectrophotometer at a wavelength of 650 nm. The sand samples were dried at 80 °C prior to measuring the mass of the sand in each 1.5-cm increment, and concentrations of strained colloids were expressed as the mass of particles per unit mass of dry sand. The recovery efficiency, computed by dividing the mass of extracted colloids by the difference between masses of injected and eluted colloids, ranged from 0.90 to 1.10. 2.4. Model for Particle Transport and Straining. We quantified particle straining kinetics in the column experiments by comparing the measured breakthrough curves to those calculated by a mathematical model presented by Xu et al. (15). This model is based on the assumption that straining rates decrease as small void spaces capable of straining colloids become clogged with colloids, and pore water flow and colloid transport are relegated to larger neighboring void spaces with a diminished ability to strain colloids. The advection-dispersion equation describes the transport of colloids through the sand columns: ∂2C ∂C ∂C Fb ∂S + ) -w + DL 2 ∂t n ∂t ∂z ∂z

(1)

where C is the concentration of colloids suspended in the pore water, t is time, Fb is the bulk density of the porous medium, n is porosity, S is the concentration of strained colloids, w is the average linear porewater velocity, z is the coordinate parallel to flow, and DL is the hydrodynamic dispersion coefficient. Equation 1 is based on the assumption that pore-scale changes induced by the accumulation of strained particles affect neither the bulk porosity nor the average linear porewater velocity (i.e., the ratio of specific discharge to porosity). This simplification is reasonable given that, in our experiments, strained colloids occupied no more than 0.1% of the total void space. To account for the impact of strained colloids on colloid straining kinetics, we adopt a phenomenological and parametrically simple kinetics expression that is first-order in C and describes an exponential decline in straining rates as S increases, such that Fb ∂S ) koCe-S ⁄ λ n ∂t

(2)

where ko is the straining rate coefficient under clean-bed conditions, when S ≈ 0, and λ quantifies the influence of strained colloids on retention rates (15). Equations 1 and 2 describe the transport and straining of colloids within our sand columns. These equations were approximated by a second-order, implicit finite-difference scheme for a semi-infinite column with a first-type boundary condition at the column inlet. The finite-difference equations were solved iteratively to compute concentrations of pore-

translation between the particle and the fluid is negligible, and the rotational dynamics due to the moment of the viscous force around one particle can be described by an ordinary differential equation for the unit orientation vector b p (19, 20): a2 - 1 dp b )Ω·b p+ 2 [D · b p - (p b·D·b p]p b] dt a +1

FIGURE 2. Two-dimensional domain of the pore-scale hydrodynamics model. The orientation of the spheroidal particle is denoted by unit vector p¯ and θ is the angle between the particle’s major axis and the x-axis. H and r are the half-widths of the domain at the widest and narrowest part of the pore channel, respectively. The narrowest part of the channel is located at x ) L. water and strained colloids as a function of time and depth within the column. Several parameters must be specified to run the model. Values of ko and λ were estimated in an inverse fashion using a Levenberg-Marquadt least-squares algorithm to minimize the sum-of-squared differences between measured and model breakthrough concentrations (17). The value of average linear velocity, w, was estimated from measurements of sandpack porosity and specific discharge, while values of the dispersion coefficient, DL, were determined by least-squares inversion of the bromide breakthrough data. 2.5. Pore-Scale Model of Particle Orientation. Straining occurs when suspended colloids are trapped within pore spaces near grain-to-grain contacts that have dimensions smaller than the colloids themselves (15, 18). Because the relative sizes of the colloids and pore spaces govern straining, the susceptibility of nonspherical particles to straining should depend on the orientation that the particles assume as they enter a pore-space constriction. We evaluated the changes in orientation that a nonspherical particle undergoes within a pore-space constriction by analyzing model simulations of two-dimensional converging flow between adjacent mineral grains (Figure 2). The model tracks a spheroidal particle originating from a point upstream of the pore-space constriction. Without loss of generality, we define the initial location of the particle as the origin of our coordinate system within which the x-axis parallels the main flow direction and the y-axis is oriented in the cross-stream direction. The half-width of the channel at this initial location is H, and the half-width of the narrowest part of the constriction, r, is located at x ) L and equal to the minor semiaxis length of the spheroidal particle (Figure 2). We define the major axis of the spheroidal particle as its orientation, which is denoted by a unit vector b p ) {px,py}T. The angle of the unit vector is θ ) arctan(py ⁄ px)

(3)

We consider Stokesian (creeping) flow through the model pore-space constriction, which is consistent with the low Reynolds Number flow within the pore spaces of our sand columns. Under creeping-flow conditions, relative

(4)

where a is the aspect ratio (ratio of major axis length to minor axis length) of the spheroidal particle, Ω is the rate-ofrotation tensor, and D is the rate-of-strain tensor. Equation 4 does not account for the perturbation of the flow field caused by the particle as it nears the narrowest part of the pore constriction (at x ) L). For the conditions tested in this study, this simplification limits the applicability of eq 4 to the region 0 < x e 0.6L. (We draw inferences on particleorientation kinetics for x g 0.6L from a separate analysis that will be discussed in Section 3.3.) Specification of Ω and D in eq 4 requires consideration of the characteristics of the velocity field. As a first-order approximation, the converging velocity field can be represented as an irrotational flow with the stream-wise velocity u increasing linearly from us at x ) 0 to ue at x ) L (Figure 2). In this case, the rotation tensor Ω in eq 4 is zero and the rate-of-strain tensor D is simply D)

[ ] s 0 0 -s

(5)

where s is positive constant strain rate given by s)

∂u ∂x

(6)

and, according to the continuity equation for incompressible flow, (∂v)/(∂y) ) -s, where ν represents the cross-stream velocity. The appropriateness of our assumption of irrotational flow is supported by solutions of the full Navier–Stokes equations that show the ratio of vorticity to the largest eigenvalue of the rate-of-strain tensor is less than 10% at distances greater than 1.2 µm away from the sand surface. The temporal rate of change in the particle’s position along the x-axis is given by dx ) u(x) ) us + sx dt

(7)

Integration of eq 7 subject to the approximate relations usH ≈ uer, s ≈ (H/rL)us, and H >> r yields x(t) )

rL ( st e - 1) H

(8)

The time required for the particle to travel from the initial location to the throat at x ) L can be approximated by T ) (1/s)ln(H/r). By using this relationship for T with the normalizations t′ ) t/T and x′ ) x/X, eq 8 can be expressed as x′(t′) )

r H t -1 H r

[( ) ]

(9)

Equations 9 and 4 quantify particle position and orientation, respectively. Substitution of eq 5 into eq 4 and scaling time t by T leads to dpx a2 - 1 H ) ln [1 - (p2x - py2)]px dt′ a2 + 1 r

(10)

dpy a2 - 1 H )- 2 ln [1 + (p2x - py2)]py dt′ a +1 r

(11)

Equations 10 and 11 describe the temporal changes in particle orientation vector, which can be used with eqs 3 and 9 to VOL. 42, NO. 3, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Breakthrough curves of the 1.9 µm, 1.9 × 2.8 µm, and 2.8 µm colloids for experiments with the (A) 0.78 mm, (B) 0.33 mm, (C) 0.14 mm, and (D) 0.12 mm sands. Symbols and lines represent observed and model-computed concentrations, respectively. compute the particle orientation angle (θ) as a function of dimensionless distance, x′. It should be noted that the dynamics of particle orientation depend only on the aspect ratio of the colloid (a) and the contraction ratio H/r. The actual velocity is not a factor provided the flow is still Stokesian (i.e., Reynolds Number 4.0 µm), where colloid straining was found to be the greatest. The concentrations of strained colloids exhibited small variability over the length of the column (see Figure S2, Supporting Information), but differed between particle treatments. In the experiments with the 0.14 mm sand, for example, the depthaveraged concentrations of the 4.3 × 6.1 µm particles differed from those of the 4.0 µm microspheres by only 11%, but

FIGURE 4. Breakthrough curves of 4.0 µm, 4.3 × 6.1 µm, 5.1 µm, and 6.1 µm colloids for experiments with the (A) 0.78 mm, (B) 0.33 mm, (C) 0.14 mm, and (D) 0.12 mm sands. Symbols and lines represent observed and model-computed concentrations, respectively. were 45% and 91% lower than the concentrations of strained 5.1 and 6.1 µm colloids, respectively. These observations are consistent with the colloid breakthrough results, which suggest that the straining of the 4.3 × 6.1 µm peanut-shaped colloids resembles that of 4.0 um spherical colloids. 3.2. Comparison of Experimental and Modeled Results. The mathematical model for coupled particle transport and straining (governed by eqs 1 and 2) was applied in inverse mode to determine the best-fit values of clean-bed straining rate coefficient (ko) and the parameter λ. The good agreement between measured and modeled breakthrough concentrations suggests that the form of eq 2 is appropriate for capturing the kinetics of particle retention over the range of conditions evaluated in this study (Figures 3 and 4). Model calculations that used the best-fit estimates of ko and λ also mimicked the depth profiles of retained particle concentrations (S(x)) measured at the end of the column experiments (see Figure S2, Supporting Information). The best-fit values of ko for the microspheres (i.e., spherical colloids) vary from 0 h-1 to 32.8 h-1 and in a discernible fashion with the ratio of particle diameter (dp) to sand-grain diameter (dg). That is, estimates of ko for the microspheres increase linearly with dp/dg for dp/dg > 0.0083 and are negligible below this threshold dp/dg value (Figure 5A). Xu et al. (15) reported a nearly identical relationship between ko and dp/dg for column experiments that were conducted with the same porous medium and pore-water composition as described here, but that used carboxylate-modified (instead of sulfate-modified) polystyrene latex microspheres as the particles (Figure 5A). The relationship is also applicable for the nonspherical particles provided that the minor-axis lengths of the nonspherical particles are used to define dp (Figure 5A, closed triangles). More than 94% of the variation

in the observations from both studies can be quantified by the relationship ko ) 746.5 dp/dg - 6.2 (for dp/dg > 0.0083). Accumulation of colloids in straining pores slows colloid straining in an exponential manner (eq 2). The impact of colloid accumulation on straining kinetics is quantified in the model by the parameter λ. The best-fit values of λ depend on particle size and sand-grain size, and a linear relationship exists between λ and dp/dg (i.e., λ ) 1.54dp/dg - 0.0015) provided dp is used to define the diameter of the microspheres and the minor-axis length of the peanut-shaped particles (Figure 5B). 3.3. Model Simulations of Particle-Orientation Kinetics. Comparison of the values of ko indicates that the clean-bed straining rates of the peanut-shaped particles nearly matched those of microspheres with diameters equal to the minoraxis length of the peanut-shaped particles. This behavior is observed with both the 1.9 × 2.8 µm and 4.3 × 6.1 µm colloids and is consistent across the four grain-size treatments tested. In light of these results, we conclude that the minor-axis length of spheroidal particles regulates straining kinetics. We also infer that the orientation of spheroidal particles entering pore-space constrictions is not random, but that the particles adopt a preferred orientation with their major axis parallel to the local flow direction. We tested this inference with the pore-scale model for particle orientation (see eqs 3–11) by examining how particles with different initial orientation angles (θ0) change their orientation as they move through the pore-space constriction. For this analysis, we have assumed that the contraction ratio (H/r) equals the ratio of the grain radius to the minor semiaxis length of the spheroidal particles (see Figure 2). We present results for the 1.9 × 2.8 µm colloids (r ) 0.95 µm) and for 120 µm sand (H ) 60 µm), as the final particle orientation angles VOL. 42, NO. 3, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 6. Kinetics of the orientation angle of a 1.9 × 2.8 µm particle in a converging flow with the contraction ratio H/r ) 60/0.95. Each line represents results corresponding to one initial orientation angle (θ0). The particle’s aspect ratio (a) is 2.8/1.9. The solution of eqs 3–11 is inadequate for describing particle orientation for x′ ) x/L > 0.6 (i.e., the region to the right of the vertical dashed line). Inferences on changes in particle orientation for x′ g 0.6 are made from force-balance calculations (see Figure 7).

FIGURE 5. Relationships between the best-fit values of the parameters governing straining kinetics and the ratio of particle size (dp) to sand-grain diameter (dg): (A) k0 versus dp/dg and (B) λ versus dp/dg. The particle size, dp, is equal to the diameter of the microspheres and to the minor-axis length of the peanut-shaped colloids. Error bars denote standard deviations for duplicate experiments. The equations for the regression lines are provided in the text. for this case are greater than any other colloid-sand combination examined in this study. For all values of θ0 tested, the particle orientation angle (θ) decreases asymptotically with increasing x′ (Figure 6), indicating that the spheroidal particle reorients its major axis in the direction of flow as it moves toward the pore throat. The extent of particle realignment can be considerable, with θ0/θ (x′ ) 0.6) ranging from 2.3 to 8.0 depending upon θ0. A particle with an initial orientation of 85°, for example, will rotate 48° and assume an orientation of 37° by the time it reaches x ) 0.6, which, in this simulation, is 24 µm upstream from the narrowest part of the pore constriction (Figure 6). Near the narrowest part of the pore constriction (i.e., forx′ > 0.6, the presence of the particle perturbs the flow field in complex ways that are not accounted for by the model and hence eqs 3–11 are inappropriate for describing particle rotation and displacement. We evaluated particle-orientation kinetics for 0.6 e x′ e 1 by numerically solving the full Navier–Stokes equation for flow within the pore throat and by using the simulated velocity and pressure fields to compute the forces exerted on the spheroidal particle. In these simulations, the flow velocity at the pore inlet was set at 140 µm s-1, which matches the average linear porewater velocity (w) of the column experiments, and the velocity of the colloid was specified as a model parameter. We systematically adjusted the x and y components of the colloid’s translational velocity and the colloid’s angular speed to 776

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minimize both the sum of the forces and their moments on the spheroidal colloid. A spheroidal particle located at x′ ) 0.8 with an orientation angle (θ) of 40° exerts a significant perturbation on the flow field that stretches over the width of the pore throat (Figure 7a and b). Within this flow field, pressure and viscous shear forces govern particle-orientation kinetics. Analysis of the Navier–Stokes solution indicates that the moment of the pressure forces is negative (clockwise), which tends to align the particle’s major axis parallel to the local streamline, while the moment of the viscous shear force is positive (counterclockwise). Because the pressure force is greater in magnitude than the viscous force, the spheroidal particle will rotate clockwise at an angular speed of -11.4°/ms. This rotation rate is 19 times greater than the particle rotation rate at x′ ) 0.6, where the particle-induced disturbance in the flow field is small in relationship to the width of the pore space (Figure 7c). Assuming a constant angular speed of -11.4°/ ms (a conservative estimate given that the clockwise rotation rate increases with x′), the particle orientation angle will decline from 40° at x′ ) 0.8 to 8° at x′ ) 1. At this low orientation angle, the straining of the spheroidal particle will be determined by the dimensions of its minor axis. This result is consistent with our experimental findings that a relationship between straining rates and dp/dg derived for spherical particles can be applied to quantify straining of peanut-shaped particles provided that dp is taken as the minor-axis length of the peanut-shaped particles. 3.4. Implications and Future Applications. Similar to our peanut-shaped particles, some pathogenic bacteria exhibit elongated shapes (13). Rod-shaped Escherichia coli, for example, measures 0.5 µm in diameter and 2 µm length, and Legionella measures 0.3–0.9 µm in width and 2-20 µm in length (13). The aspect ratios of these microbes exceed 4, more than twice that of the peanut-shaped particles. Porescale simulation results indicate that tendency of a nonspherical particle to align with its major axis parallel to the local flow direction increases with aspect ratio. For instance, a particle with an aspect ratio (a) of 4 and an initial orientation angle (θ0) of 85° will rotate to 1° when it reaches x′ ) 0.6 compared to 37° for a 1.9 × 2.8 particle (a ) 1.5). Based on these results, we conclude that quantitative inferences on

Supporting Information Available Particle electrophoretic mobilities and energy barrier values between particles and the 0.78 mm sand (Table S1); data from experiments with bromide, microspheres, and peanutshaped particles (Figures S1 and S2). This material is available free of charge via the Internet at http://pubs.acs.org.

Literature Cited

FIGURE 7. Fluid pressure fields (colors) and velocity fields (arrows) computed by solving the two-dimensional form of the Navier–Stokes equation for flow within a pore-space constriction formed by adjacent mineral grains (dg ) 120 µm): (a) flow field without colloid; (b) flow field with a 1.9 × 2.8 µm colloid at x′ ) x/L ) 0.8; and (c) flow field with a 1.9 × 2.8 µm colloid at x′ ) x/L ) 0.6, where both the Navier–Stokes equations and eqs 3–11 are appropriate for quantifying particle orientation kinetics. The particle-orientation angle in (b) and (c) equals 40°. The computational fluid dynamics software, Fluent, was used to solve the Navier–Stokes equation. the straining of nonspherical bacteria, such as Escherichia coli and Legionella, should be made on the basis of measurements of their minor-axis dimensions. In this research, we used cleaned quartz sand to minimize physicochemical deposition in order to evaluate straining in an unambiguous way. In natural geologic environments, reactive coatings on mineral-grain surfaces serve as favorable sites for the adhesion of microscopic particles (2, 21–26) and thus physiochemical deposition, in addition to straining, will contribute to the filtration of inorganic colloids and colloidsized microbes within groundwater aquifers. Weiss et al. (27) observed that the transport of a variety of bacteria in porous media was a function of their aspect ratio. Salerno et al. (28) reported that physicochemical deposition rates are sensitive to changes in colloid aspect ratio and suggest that the orientation of nonspherical particles may affect both the frequency of particle-collector collisions and the probability of particle attachment. In light of this colloid-shape effect, our findings and pore-scale modeling approach may also be useful in advancing understanding of physicochemical deposition of nonspherical particles.

Acknowledgments This work was supported by the National Science Foundation (EAR-0409174) and the Department of Energy (DE-FG0702ER63492). We thank four reviewers for their helpful comments.

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