Environ. Sci. Technol. 2006, 40, 6336-6340
Transport of Rodlike Colloids through Packed Beds MICHAEL B. SALERNO,† MATT FLAMM,‡ BRUCE E. LOGAN,§ AND D A R R E L L V E L E G O L * ,‡ Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, and Department of Civil and Environmental Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
The effect of colloid shape on filtration rates in porous media was examined by constructing particles with different aspect ratios and measuring their retention in packed beds. Spherical polystyrene latex microspheres (1.0-µm diameter) were heated, stretched to the desired aspect ratio (2:1 and 3:1, with a 1:1 control), and quickly cooled. These particles were injected into minicolumns containing glass beads (40-µm diameter) in solutions at two different ionic strengths (IS ) 1 and 100 mM). The measured retentions increased with aspect ratio in both IS solutions. The ζ-potentials for all three aspect ratios were indistinguishable, and no charge nonuniformity was measured for any of the samples. Thus, the data support that changes in retention resulted from the different aspect ratios rather than from different surface chemistries. Interpretation of the retention data in terms of a collision efficiency (R) showed an increase with aspect ratio in both IS solutions, and for 1 mM the R increased from 0.011 (1:1) to 0.095 (2:1) to 0.26 (3: 1). These results demonstrate for the first time the direct impact of particle shape on retention in porous media. Our findings have important implications for the transport of particles with high aspect ratios, such as rod-shaped bacteria, and for the modeling of such transport.
Introduction Colloid filtration rates in porous media are often modeled using semiempirical solutions to hydrodynamic equations that predict the frequency of collisions between spherical particles and spherical collectors (1, 2). Accurate prediction of the collision frequency, η, between the particle and the collector is essential in order to calculate the collision efficiency for the particle (R; the probability of attachment for a particle that strikes a collector). For given retention data, any inaccuracy in the prediction of η will result in an error in the fit for R. Collision frequencies between very small particles and much larger collectors is dominated by particle diffusion coefficients, while at other size ratios collisions can be due to interception, gravitational settling, and interparticle forces (i.e., van der Waals forces, electrostatic forces, etc.). * Corresponding author phone: (814)865-8739; fax: (814)865-7846; e-mail:
[email protected]. † Current address: Biodesign Institute, Center for Environmental Biotechnology, Arizona State University, Tempe, AZ 85287-5701. ‡ Department of Chemical Engineering, The Pennsylvania State University. § Department of Civil and Environmental Engineering, The Pennsylvania State University. 6336
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The hydrodynamic flow around a single collector, according to the Happel model (3), is constrained to be a shell of fluid around a spherical particle. Limitations of the Happel flow cell are well recognized (4) for predicting collision frequencies, as shown by measured values of R that exceed unity based on the η model of Rajagopolan and Tien (5, 6). Reexamination of collision frequencies by Tufeniki and Elimelech provided improved predictions of collision frequencies under some conditions, but the RT and TE models are identical when collisions are dominated by diffusion (7). One source of error in predicting collision frequencies is the shape of the collector. Irregularly shaped collector particles, such as quartz, produce higher values of R than some other materials under conditions which are expected to completely destabilize particles (i.e., high ionic strength). For example, a collision efficiency of R ) 0.19 was found for adhesion of Alcaligenes paradoxus to glass beads, but R ) 1.58 was found using cleaned quartz (6). Using a porous medium with a wide particle-size distribution can also affect R. For example, mixing quartz media wet-sieved to produce a bimodal size distribution resulted in values of much larger than unity, depending on the “single collector” size used to characterize the bimodal distribution of quartz particles. Collision efficiencies ranged from 0.26 e R e 1 based on number distribution, and 0.74 e R e 1.9 for a volume distribution of quartz particle sizes (5). The effect of the shape of the colloid being transported in filtration experiments has received considerably less attention than that of the collector, and therefore it is not well-understood. Particle shape could be very important for understanding bacterial filtration rates in porous media, since many bacteria have rodlike and not spherical shapes. Bacteria can vary widely in terms of hydrophobicity (8), surface charge, and motility, making it difficult to compare filtration rates on the basis of their shape. Even bacteria with similar bulk chemical surface properties can vary widely in terms of their collision efficiencies, presumably due to differences in their surface chemistry, but also perhaps due to shape. It is perhaps impossible to vary the shape of a bacterium while holding all other chemical properties of the bacteria constant. Therefore, the effect of shape on bacterial adhesion rates has only been previously inferred in studies using different strains of bacteria (9). In one comparison of filtration rates of bacteria with different shapes under otherwise identical solution chemistry and column packing, it was found that rod-shaped bacteria were more likely to have higher filtration rates than spherical bacteria (9). However, differences in surfaces between these different strains of bacteria could have been an equally important factor in this finding. The properties of spheroidal versus spherical particles have been compared within various physical environments and are well-known to be important. For example, spheroidal and spherical particles have been characterized by their rotational diffusion (10), deposition rates in turbulent duct flows (11, 12), electrophoretic motion (13), and forces experienced in a linear flow field (14). Researchers have provided evidence that the DLVO theory can be used to model nonspherical particles with high aspect ratios (15), but they have not examined the impact of shape within the context of colloid transport through porous media. In order to directly measure the effect of colloid shape on filtration rates, we increased the aspect ratio of spherical colloids (latex microspheres) while holding constant the particle surface chemistry and volume. To determine the effect of shape on filtration rate, we compared the column retention data of these particles with different aspect ratios 10.1021/es0614565 CCC: $33.50
2006 American Chemical Society Published on Web 09/16/2006
TABLE 1. Calculated and Measured Values for Each Aspect Ratio of Particlea
a
particle characteristic
1:1
2:1
3:1
actual aspect ratio surface area (µm2) main axis (c; µm) secondary axis (a; µm) ellipticity (e) effective radius (aeff; µm) ζ-potential (mV) fraction retained (R) at 1 mM fraction retained (R) at 100 mM collector efficiency (η) R, IS ) 1 mM R, IS ) 100 mM
1.0:1 3.14 0.50 0.50 0 0.50 -18.8 ( 2.5 0.020 ( 0.003 0.052 ( 0.004 0.0140 0.011 ( 0.002 0.036 ( 0.005
2.2:1 3.45 0.85 0.38 0.89 0.52 -16.3 ( 0.7 0.13 ( 0.012 0.19 ( 0.04 0.0145 0.095 ( 0.01 0.14 ( 0.03
3.1:1 3.74 1.06 0.34 0.95 0.55 -15.1 ( 5.7 0.30 ( 0.064 0.82 ( 0.04 0.0155 0.26 ( 0.07 1.2 ( 0.17
Uncertainties shown for ζ-potential, fraction retained (R), and collision efficiency (R) values are 95% confidence intervals (n g 3).
in columns packed with spherical glass beads, at two different ionic strengths, under conditions where collisions were primarily due to diffusion. On the basis of these experiments with colloids, we can predict the effect of shape on the filtration rates for nonspherical particles, or even bacteria.
Materials and Methods Colloid Preparation. Spheroidal particles were synthesized using the method of Ho et al. (16, 17). The method is based on heating polymer particles above their glass transition temperature (roughly 95 °C for polystyrene), then stretching them in a defined manner to a set aspect ratio. This process yields very reproducible, monodisperse particles that can then be used for experiments. Fluorescent carboxylated latex microspheres (1.0-µm diameter, Polysciences, Inc.) were stretched to the desired aspect ratio (2:1 and 3:1). This stretching was accomplished by dispersing particles in a poly(vinyl alcohol) (PVA) solution in a Petri dish and allowing the solution to air-dry, resulting in a PVA film containing suspended particles. Drying required up to one week, depending on the relative humidity and room temperature. Once the film was dry, it was heated to 200 °C (beyond the glass transition temperature of the polystyrene beads) using an oil bath, and then it was immediately placed on a stretching apparatus (constructed by our machine shop, and consisting of two parallel bars that slide on rails) and stretched to the appropriate aspect ratio. The film was allowed to cool for several seconds while being held at the proper aspect ratio. The center section of the film was then cut out, the PVA dissolved in de-ionized (DI) water (Milli-Q System, Millipore), and the stretched particles recovered and purified by washing and centrifugation. For the control (the original spheres at 1:1 ratio) all the steps outlined in the above methodology were taken, except no stretching was performed to retain their original spherical shape. Ho et al. performed electrophoresis on spheroidal latex particles, concluding that the electrophoretic mobilities of the particles change as the aspect ratio increases (18). However, a closer inspection of their data reveals that the ζ-potentials changed with aspect ratio only for the smallest particles (possibly a finite Debye layer effect), or when they compared untreated to treated particles. That is, when they compared treated spherical colloids to treated stretched colloids for diameters greater than 500 nm, the electrophoretic mobilities were the same. Ho et al. also analyzed the charge distribution on the particles by adsorbing nanoparticles to the spheroids and observing their spatial distribution (19). They concluded that the stretching procedure did not induce any surface charge nonuniformity on the particles. Packed Column Experiments. Collision efficiencies were calculated on the basis of particle retention measured in
minicolumns as described previously (20). Briefly, the columns are 8-mm-i.d. plastic Luer Lok syringes packed with glass beads (40-µm diameter, soda lime, Polysciences, Inc, Warrington, PA) cleaned by agitation in 10% v/v sulfuric acid (3 h) and then copiously rinsed with de-ionized (DI) water prior to use (21). Columns were rinsed with 10 mL (∼20 pore volumes) of DI water, followed by 10 mL of a salt solution (1 or 100 mM KCl) using vacuum filtration. A 2-mL sample of the colloids was then pulled through the column, followed by a 6-mL rinse of the background solution. The top layer (0.3-0.6 cm, ∼10-20% of the total packing) of the packing material (the glass beads) was extruded from the column, sliced off, and analyzed for the number of retained particles. There is some variation in the amount removed for any given experiment, since the removal is done by hand, but the experiments are done in triplicate to reduce any errors. Particles were extracted by washing glass beads with a nonionic surfactant (0.1% v/v Tween 80, Fisher Scientific) three times, followed by vacuum filtration of the solution onto black filters (Whatman, 0.22-µm pore diameter). Particles were then enumerated by fluorescence microscopy. On the basis of the number of particles retained by the slice, we calculated the fraction of particles retained in the slice (R). The collision efficiency (R) was calculated according to the Rajagopalan-Tien (RT) model (22) as
R)
-4ac ln(1 - R)
(1)
3(1 - θ)ηL
where ac is the radius of the glass beads (20 µm), θ ) 0.46 is the packed bed porosity, η is the collector efficiency (calculated for each experiment, but varying only slightly from 0.0140 for 1:1 particles to 0.0155 for 3:1 particles; see Table 1), and L is the length of the slice of the column extruded (0.3-0.5 cm). Particle Characterization. ζ-Potentials were obtained using a ZetaPALS analyzer (Brookhaven Instruments Corporation, Holtzville, NY). Measurements were made for 5 samples with 20 cycles for each analysis. Samples were analyzed only in 1 mM KCl, as measurements are more accurate in low-IS water (solution conductivity of ∼150 µS/ cm). Precise differences in ζ-potentials between different ratio particles were measured using differential electrophoresis (23, 24) using an optical microscope, since ζpotential differences can be measured much more accurately than absolute values. Particle charge uniformity was analyzed for each type of particle using charge nonuniformity light scattering (CNLS), which consists of a light-scattering apparatus fitted with an electrophoresis cell (25). Particles were observed using both optical microscopy and scanning electron microscopy (SEM; JEOL model JSM5400). Samples were sputter-coated (Bal-tec SCD-050 VOL. 40, NO. 20, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. The fraction of particles retained in packed columns as a function of aspect ratio and ionic strength. (Error bars represent 95% confidence intervals with n g 3).
FIGURE 2. Collision efficiencies (r’s) of particles based on measured retention in columns using an effective particle radius as defined in eq 4. (Error bars represent 95% confidence intervals for n g 3).
Sputter Coater) with a gold/platinum mixture to a depth of 10 nm, and images were obtained at 20 keV in order to quantify aspect ratios as described below. SEM images were analyzed using image analysis software (Scion Image, Scion Corp.) to determine major and minor axes. The total surface area of the spheroids was calculated as (26)
S ) 2πa2 +
2πac -1 sin e e
(2)
where a is the minor-axis radius, c is the major-axis radius, and e is the ellipticity, defined as (27-29)
e≡
x
1-
a2 c2
(3)
There are several ways to estimate an effective radius aeff of the particles. For constant-volume particles, one approach based on the equivalent orientation-averaged hydrodynamic radius is aeff ) ap(f/f0), where ap is the original particle radius (0.5 µm) and f/f0 is 1.0 for c/a ) 1, 1.04 for c/a ) 2, 1.10 for c/a ) 3, and 1.18 for c/a ) 4 (30). Thus, 1:1 spherical particles have aeff ) 0.50 µm, 2:1 particles have aeff ) 0.52 µm, and 3:1 particles have aeff ) 0.55 µm. An alternative approach is to set aeff equal to the radius of a sphere that would have the same surface area as the spheroids, or
aeff )
x4πS
(4)
That is, as the particle is stretched, the volume is conserved and the surface area is increased, and thus aeff increases. For our stretch ratios, the hydrodynamic method and the surface area method give the same results. The calculated effective radii (aeff) (see Table 1) were the values used in the RT filtration model to determine collision efficiencies.
Results Packed Column Experiments. The fraction retained (R) of spheroidal particles in minicolumn tests increased with aspect ratio (Figure 1). The 3:1 ratio particles had the largest fraction retention values of 0.30 and 0.82, while the 1:1 ratio particles had the lowest fraction retained values of 0.02 and 0.05 in 1 and 100 mM IS solutions, respectively. On the basis of the collision frequencies estimated using “equivalent sphere” sizes (eq 4), the collision efficiencies (R) increased significantly with aspect ratio in both IS solutions (Figure 2). The value of R increased by 8.6 times when the aspect ratio was increased from 1:1 to 2:1, and 24 times when the aspect ratio was increased from 1:1 to 3:1 in the 1 mM IS solution. In the 100 mM solution, R increased 3.9 times between 1:1 6338
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FIGURE 3. Optical (top) and scanning electron microscope (SEM, bottom) images of particles with aspect ratios of 1:1 (control), 2:1, and 3:1.
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and 2:1, and 33 times between 1:1 and 3:1. All differences between R were statistically significant. SEM and Geometry Calculations. SEM images (Figure 3) confirmed the aspect ratio of the original particles was 1:1 (1.0:1 ( 0.1, 95% confidence interval, n ) 5). For particles designated as 2:1, the measured ratio was 2.2:1, and for the 3:1 particles the ratio was 3.1:1 (both (0.2, 95% confidence interval, n ) 5). The major and minor axes were 0.5 × 0.5 µm (1:1), 0.85 × 0.38 µm (2:1), and 1.06 × 0.34 µm (3:1). For the stretched particles, the minor axis becomes smaller due to conservation of volume of the particles. ζ-Potentials and Charge Nonuniformity. There was no significant difference in ζ-potentials of the particles with the three different aspect ratios (Table 1), with values ranging from -15.1 to -18.8 mV. Moreover, the differences between ζ-potentials determined by differential electrophoresis confirmed negligible differences in the ζ-potentials of the particles at an applied electric field of 2 V/cm (uncertainties of less than 0.2 mV). Charge nonuniformity light-scattering (CNLS) measurements indicated no particle rotation (i.e., no charge nonuniformity) (31), further demonstrating that there were no changes in the uniformity of the surfaces of the particles introduced by particle stretching.
Discussion The retentions (R) and collision efficiencies (R) of the three different types of particles significantly increased in proportion to their aspect ratios (1:1, 2:1, 3:1), demonstrating that rodlike particles are preferentially retained in comparison to spherical particles. In tests with 14 different strains of bacteria, Weiss et al. (9) found that there was preferential retention of cells with higher aspect ratios (quantified in their study in terms of ratio of cell length to width). However, their results were not conclusive as cells differed in other surface properties, and it was noted that cells with the highest adhesion rates were rods with low water-contact angles. In
our study, however, all particles had the same ζ-potentials and volume, and they had uniform charge distributions. The changes we observed in the magnitude of R cannot be due to changes produced in the collision efficiency (η) as a result of changes in equivalent particle radius with particle shape (Table 1). Slight increases in aeff, and therefore η, should lead to lower values of R and not the increased values we observed. Our data suggest that equations for η must be reformulated for nonspherical particles such as rodlike colloidal particles. We note that if we assume that R were held constant at each ionic strength, then the values of η for 1 mM IS would be 0.014 (1:1), 0.125 (2:1), and 0.366 (3:1), and for 100 mM they would be 0.014 (1:1), 0.0563 (2:1), and 0.517 (3:1). It is important to note that while the spherical 1:1 ratio particles should behave as predicted by the RT filtration model, the 3:1 ratio particles will not. Their collision efficiency might be lower than expected (e.g., if the rodshaped particles align with the streamlines and interact less with the collector beads) or higher than expected (e.g., blocking in some paths through the column (32), such as by a percolation mechanism). Our data raise questions for the hydrodynamic modeling of spheroids through porous media. Solution chemistry was an important factor in particle retention, with a greater increase in the collision efficiency noted for the higher IS solution. Increasing the IS from 1 to 100 mM increased colloidal adhesion (Figure 2), consistent with previous findings for colloidal retention on glass beads (33-35). On the basis of DLVO (Derjaguin-Landau-VerweyOverbeek) theory between a plate (i.e., a large collector is like a plate) and a sphere of radius 0.50 µm, and using the Ohshima et al. theory for electrostatics (36) and Lifshitz theory for van der Waals forces (37), the energy for attaching a colloid via a primary minimum was 42 kT in IS ) 1 mM; there was no secondary minimum. At 100 mM there is no barrier to aggregation in the primary minimum. These calculations use the parameters listed in Table 1. One complication in this analysis with spheroidal particles is the interaction area assumed for particle-surface interactions. The exposed surface area for the particle-packed bead interaction increases or decreases for prolate spheroids, depending on side or tip interactions, respectively, compared to that for spherical colloids. In IS ) 100 mM, the interaction will always be attractive and short-range, and so the role of the surface area is likely not as important. Calculations for a 3:1 aspect ratio (constant volume) reveal that the effective end-on interaction area decreases such that the interaction energy should be about 20 kT, still large enough to prohibit contact, although adhesion still occurs. This calculation was estimated using the minor axis as the radius of a sphere interacting with a plate. The large increase in the retention and collision efficiency with increased aspect ratio of the particle may help to explain, in part, high sticking coefficients measured in bacterial transport experiments. Collision efficiencies should be less than or equal to unity, but values larger than this have been observed in several bacterial transport tests, particularly those packed with media having a highly irregular shape such as quartz and soils (5, 6). While the irregular shape of the column packing is certainly an important factor in adhesion results, it is clear from results presented here that the nonspherical shape of the particle can also contribute to underestimation of collision frequencies, and therefore overestimation of R.
Acknowledgments This research was funded by the National Science Foundation through the CRAEMS program (Grant CHE-0089156) and NIRT Grant CCR-0303976. This research was also funded in part by the Penn State Biogeochemical Research Initiative for Education (BRIE) (NSF IGERT Grant DGE-9972759).
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Received for review June 19, 2006. Revised manuscript received August 3, 2006. Accepted August 15, 2006. ES0614565
