Environ. Sci. Technol. 2000, 34, 3969-3976
Characterization of Alum Floc by Image Analysis RAJAT K. CHAKRABORTI,* JOSEPH F. ATKINSON, AND JOHN E. VAN BENSCHOTEN Department of Civil, Structural and Environmental Engineering, State University of New York at Buffalo, Buffalo, New York 14260
In-situ monitoring of particle characteristics is of general interest for both natural and engineered aquatic systems and of particular interest in studying the fragile floc that typically is formed by the addition of chemical coagulants. A nonintrusive photographic technique coupled with digital image processing for in-situ analysis of aggregates formed by the addition of alum [Al2(SO4)3‚18H2O] to lake water and a montmorillonite clay suspension is described. The technique is unique in that there is no need for sample collection and handling. The analysis method is used to test the hypothesis that charge-neutralization and sweep-floc mechanisms produce fundamentally different particle characteristics, including differences in fractal dimension. For comparative purposes, particle characteristics prior to coagulant addition also are reported. It is found that fractal dimension is lower for sweep-floc coagulation where larger and more irregular aggregates are produced. The results presented here provide insight to jar test data and help explain why better settling often is observed in practice for sweep-floc coagulation as compared to floc produced by a charge-neutralization mechanism.
Introduction Particle aggregation is an important process affecting the fate of particles in both engineered and natural environments. In water and wastewater treatment plants, for example, particle aggregation is necessary prior to particle removal by solid-liquid separation processes. Altering the mass, surface area, and number concentration of particles substantially affects their removal by gravity sedimentation and deposition in packed-bed filters (1, 2). In addition to size, particle shape affects the behavior of aggregated particles, particularly with regard to collision efficiency (3, 4) and settling rates (5-9). In recent years, irregular aggregate shapes have been described in terms of fractal geometry concepts, and complete characterization of a particle suspension should include a description of the fractal dimension of the aggregates (3, 6-8). The need for measurements of in-situ size distribution and geometry of particles has long been recognized in the chemical, biological, and other process industries, but often it is difficult to measure these properties accurately using existing technologies. Use of the Coulter principle or the electrical sensing zone method, for instance, requires samples to be withdrawn and the particles to be passed through a small orifice, which may cause the flocs to break apart (10). Dilution * Corresponding author fax: acsu.buffalo.edu. 10.1021/es990818o CCC: $19.00 Published on Web 08/09/2000
(716)645-3667; e-mail:
2000 American Chemical Society
rkc@
or other processing may be required prior to measurement, which can alter particle surface chemistry and aggregation kinetics. In-situ or optical techniques avoid these problems. In addition, modern advances in rapid computerized data acquisition and storage capabilities make imaging techniques particularly attractive for the in-situ study of dynamic systems. Summarized in Table 1 are studies that have utilized image-based techniques for analyzing particulate matter in various types of suspensions. The list is not exhaustive but is meant to be representative of the range of imaging methods used and the types of systems to which they have been applied. It is apparent that a variety of digital imaging methods coupled with image analysis systems has been used in recent years. Fewer studies involve in-situ methods where the particle suspension has not been subject to sampling, dilution, or other handling. The range of suspension types is quite broad, and only a few studies have used common coagulants such as alum. The work of Tambo and Hozumi (17) combined an in-situ photographic method with the use of alum to promote particle destabilization and floc formation, although relatively small numbers of particles were actually photographed and analyzed. The use of in-situ techniques for the study of alum floc is important due to the extremely fragile nature of these aggregates. One aim of the present study is to provide additional information on the structure of alum floc using an in-situ image-based system. Traditionally, study of alum coagulation focuses on particle surface charge and solid/liquid separation efficiency. Far fewer studies of suspensions destabilized using alum have provided insights to particle characteristics, including the fractal dimension. Fractal geometry concepts are useful in describing the rugged surface of large, irregular, porous aggregates that are not well defined by Euclidean geometry. In fractal geometry, area and volume are not necessarily calculated by raising a standard characteristic length of an object to an integer power. Heterogeneously (nonuniformly) packed objects with irregular boundaries can be defined by nonlinear relationships where the properties of the object scale with a characteristic length dimension raised to a power called the fractal dimension (3, 4, 11, 18-20). For example, the two-dimensional fractal dimension is defined by a power law relation between projected area (As) and the characteristic length of the aggregates, l. It may be calculated from refs 3, 5, 6, 11, 18, and 19:
A s ∼ lD 2
(1)
where D2 is the two-dimensional fractal dimension. The coalesced sphere assumption corresponds to D2 ) 2 in Euclidean geometry, which always expresses area as a linear measure raised to the power 2 regardless of specific shape (5, 18, 20, 21). Densely packed aggregates have a high fractal dimension (D2 = 2), while lower fractal dimensions result from large, highly branched and loosely bound structures (20). Similar to eq 1, the three-dimensional fractal dimension (D3) can be calculated from a power law relationship between the volume of the aggregates and the characteristic length raised to the power, D3. In Euclidean geometry, D3 ) 3 (6, 18-20). Fractal dimensions can be derived on the basis of power law relationships related to measured aggregate properties (e.g., eq 1), from settling velocity relationships, or from particle size spectra (18). A fractal dimension can be derived for a single aggregate or from a population of aggregates. In the case of the latter, the basic length scale can be taken as the shortest, longest, geometric mean, or equivalent radius (based on area) (18). At present there is no VOL. 34, NO. 18, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 1. Studies of Particle Suspensions Using Image-Based Methods ref
imaging method
11
14 15
CCD camera, digitized with frame grabber, processed by a program underwater video-microscope photographic negatives analyzed by microscope and with BIOQUANT IV imaging method videocamera and VCR attachment image captured by CCD videocamera floc camera assembly where photos are analyzed on Leitz TAS plus image system endoscopic snapshot connected with imaging method plankton camera
16
imaging method attached with microscope
17
photographic method: distance and time of floc in a settling column recorded
12 5 7 6 13
consensus on which approach yields the most accurate estimates of fractal dimension. Gorczyca and Ganczarczyk (5) reported fractal dimensions for inorganic suspensions of illite, montmorillonite, calcite, and silt using alum and a polymeric coagulant aid (Purifloc A-23, Dow Chemical). A dose of 4.5 mg/L alum was used along with 1 mg/L polymer. Although particle charge was not measured, final pH of 5.3-6.3 suggests a chargeneutralization mechanism (22). The two- and three-dimensional fractal dimensions (D2 and D3) for the suspensions were as follows: illite, D2 ) 1.71, D3 ) 1.49; montmorillonite, D2 ) 1.86, D3 ) 1.79; calcite, D2 ) 1.97, D3 ) 1.65; silt, D2 ) 1.80, D3 ) 1.37. Li and Ganczarczyk (21) analyzed data on kaolinite destabilized by alum as reported by Tambo and Watanabe (23). Values of D3 from 1.6 to 2 were reported. Coagulation was carried out at pH 7.5, suggesting a sweepfloc mechanism. In charge neutralization, particles are destabilized by soluble aluminum species, while in sweep floc, particles are enmeshed in Al(OH)3(s) and “swept” from suspension (22). Because of these differences in aluminum chemistry, differences in particle characteristics are expected. The relevance of the fractal dimension to engineered processes includes effects on the properties of the aggregates formed and the coagulation rate. It is desirable to have rapid coagulation rates and also to produce floc with properties that result in efficient solid/liquid separation. As noted by Jiang and Logan (6), however, the fractal dimension may vary in a manner that favors only one of these outcomes. Coagulation rates are reported to be inversely proportional to D3 (18, 20), while settling velocity, ws is proportional to a characteristic length of the aggregate, l, raised to a power that depends on various fractal dimensions (3, 6, 7, 18, 19):
ws ∼ l(D3-D2+1)
(2)
Thus, for rapid coagulation, particles with small D3 may be desirable while for gravity settling a large D3 is preferred. Recently, fractal concepts have been used to explain higher observed settling velocities for large aggregates, relative to Stoke’s settling (7). As indicated in eq 2, both aggregate size and fractal dimensions are important in settling. The objectives of the present study are 2-fold: (i) to develop an improved procedure for measuring floc characteristics, one that avoids disturbing the flow or possibly damaging the floc structure through sampling; and (ii) to apply the method in the context of an aggregation experiment using alum and gain insight to particle characteristics for two common coagulation mechanisms. It is hypothesized that charge-neutralization and sweep-floc coagulation mech3970
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in-situ/ ex-situ
suspension type
ex-situ
activated sludge floc
none
in-situ ex-situ
glass beads and quartz sand inorganic minerals
none alum and coagulant aid
ex-situ ex-situ in-situ
latex microsphere polystyrene microsphere marine snow
NaCl NaCl none
in-situ in-situ
none none
ex-situ
natural water natural water, marine environment kaolinite clay
in-situ
kaolinite clay
coagulant added
alum, ferric sulfate, and cationic polymer alum and coagulant aid
FIGURE 1. Experimental setup consisting of stroboscopic light, CCD camera attached to a computer, and the suspended sample in a mixing jar. anisms produce fundamentally different particle characteristics, including differences in fractal dimension. Two water types were used in the experiments: a lake water and suspension of montmorillonite clay. Analyses were conducted at constant pH for (i) the initial suspension before addition of coagulant; (ii) a coagulant dose causing a local turbidity minimum (near charge neutralization or zero ζ-potential); and (iii) a higher coagulant dose resulting in a sweep-floc mechanism. Particle size distributions and morphology were measured, and different geometrical characteristics including two- and three-dimensional fractal dimensions were calculated.
Methods and Experimental Procedures Jar Tests. Jar tests were performed using 2-L floc jars and 6-place paddle mixer (Phipps and Bird Stirrer, Richmond, VA). The main function of these tests was to determine the proper alum doses to achieve the three stages of coagulation described previously. The jar test procedure consisted of an initial period of rapid mix for 1 min at a mixing speed of 100 rpm, followed by 15-20 min of slow mixing at 25-35 rpm. After slow mixing, the floc was allowed to settle for 30 min, after which time measurements of ζ-potential and turbidity were taken. Samples collected from just below the water surface were analyzed for turbidity using a turbidimeter (HACH Ratio Turbidimeter, Loveland, CO). In addition, ζ-potential was measured using a zeta meter (Zeta Meter Inc., Staunton, VA). The pH was monitored continuously and maintained at pH 6.5 by manual addition of acid or base as required. Image Acquisition and Processing. The main components of the image processing system (Figure 1) include a computer-controlled digital CCD camera, lighting provided by a stroboscopic lamp, image acquisition, and image analysis
software (24). The strobe light was placed on the opposite side of the jar from the camera to provide back-lighting, which produces particle images as shadows. The stroboscope emits a diffuse, but still high intensity, adjustable-duration flash of light. Depending on the particle concentration, the flash rate was adjusted to between 420 and 510 flashes min-1. To minimize noise in image quality due to other light sources, the experiments were conducted in a darkened room. A highresolution digital camera (Kodak MegaPlus model 1.4) was used to record the images. The shutter opening was synchronized with the strobe pulses using the camera control software of a standard particle image velocimeter (PIV) system (TSI Inc., St. Paul, MN). Typically, a shutter exposure of 147.1 ms was found to provide good results for image analysis. The camera has a sensor matrix consisting of 1320 (horizontal) × 1035 (vertical) pixels. Each pixel is recorded using 8-bit resolution, i.e., there are 256 gray levels for each image pixel. An image resolution of 540 pixels mm-1 was achieved for the present set of experiments. The PIV software was used to manage the image acquisition and storage procedures. All data were recorded on the hard drive of a PC and a public domain software package, NIH-Image (National Institutes of Health, Bethesda, MD), was used to analyze the captured images. This software has been widely used in many recent research and engineering applications. To interpret image sizes correctly, a graduated microscale was photographed to determine the number of pixels corresponding to a given standard length for each set of experiments. Before processing a particular image to determine size distribution and geometrical characteristics, each image was treated using contrast enhancement in order to produce the clearest possible particle images prior to thresholding. If the images are not sharp and well contrasted from the background, there is a possibility of oversizing due to fuzziness at the edges of the particle (25). The operation of thresholding provides a sort of filtering of the image and renders it binary, so those particles not in good focus are not analyzed. This may lead to loss of some objects from the real image as the resolution and clarity are somewhat variable in different parts of the image. However, the advantages of better image resolution are thought to outweigh this potential problem. These procedures also are related to the field of focus, which depends on the lens and aperture setting of the camera. The filtering ability of the software takes care of some of the natural variations inherent in the images, but this also may introduce undersizing of particles (25, 26). A number of tests were performed with the NIH software (27) to determine the best settings for processing the images. In general, it was found that the image processing results were not significantly sensitive to minor changes in these settings. For each coagulation mechanism, multiple digital images were recorded at the end of the slow stirring period when the aggregates started to settle by gravity sedimentation. Slight adjustments were made in lens focal length so the multiple images correspond to views of particles at different planes within the jar. Multiple images were desired to increase the overall sample size and thus minimize errors in undersizing caused when a particle is randomly oriented parallel to the viewing direction so as to obscure its longest dimension. For example, an ellipsoid viewed from the end may appear as a sphere. Particle distributions were created by sorting particles according to size. Their corresponding geometrical properties (see below) were averaged for similar size particles within an image and across the multiple images. Thus, the final data sets used for plotting size distributions and determining fractal dimensions included averaged properties for many aggregates. For the lake water, for example, the total number of aggregates captured in four images was 537, 286, and 106 for the initial suspension, charge neutralization, and sweep
floc, respectively. The smaller numbers for stages 2 and 3 reflect the fact that particles had aggregated into floc. Geometric Parameters. Geometric characteristics were derived for the images collected for the three coagulation stages. Unlike spherical particles that can be described by a single parameter of diameter only, nonspherical particles can be characterized in many ways (26, 28). The NIH-Image software (27) analyzes various particle attributes based on the fundamental measurement of the number of pixels passing the threshold criterion (as explained above) which essentially defines the outline of the particle or aggregate. The software then determines the area, perimeter, and the second-order moments of the image for each aggregate. An ellipse is fitted to the aggregate image such that the moment of inertia of the ellipse and the image are equal, with the resulting area of the fitted ellipse within about 4% of the image area (27). Finally, the image software scales the major and minor axes of the ellipse so it has the same area as the image. The major and minor axes of the fitted ellipse are used in this paper as the basic length scales characterizing the particles. The distributions of the projected area, elongation ratio, and the major and minor axes of the fitted ellipse were obtained using the image processing software at each stage of coagulation for both the lake water and clay suspensions. Fractal Geometry. The two-dimensional fractal dimension was calculated by regression analysis of the logarithm of the projected area versus the logarithm of the characteristic length as suggested by eq 1. In this work, the long axis of the fitted ellipse was taken as the characteristic length. The threedimensional fractal dimension cannot be calculated in a similar manner as D2 since aggregate volume cannot be measured directly with the present apparatus. However, volume can be estimated by assuming thickness in the direction normal to the viewing direction. As the majority of particles tended to be elongated, the volume of the aggregates based on the assumption of spherical shape is not valid. For purposes of illustration, an encased volume (solid volume plus pore volume (3)) was defined by an ellipsoid shape. The volume was calculated based on the long and short dimensions of the fitted ellipse obtained from the two-dimensional images. In other words, the volume was defined by rotating the fitted ellipse about its major axis. It can easily be shown that, for a circle and an ellipse having the same area, the volume of a sphere obtained by rotating the circle is always greater than the volume of the corresponding ellipsoid. Thus, using equivalent spheres will overestimate aggregate volume. Once volumes were calculated, D3 was obtained from regression analysis of volume versus characteristic length, similar to the procedure for D2. This method of calculating D3 essentially represents a hypothesis that information on three-dimensional characteristics can be extracted from a two-dimensional image. Materials. Lake water was collected from Lake LaSalle, a shallow lake located on the campus of the State University at Buffalo, NY. The lake has an average depth of 3 m, with maximum depth of 8 m, and a total area of 243 000 m2. The water was collected on July 14, 1998. Average temperature was 22 °C, and wind speed was 16 km/h (National Climatic Data Center, Buffalo, NY). Given these conditions, a reasonable level of particle suspension was expected. The clay suspension was prepared by dissolving montmorillonite fine clay powder (K-10) in deionized water to produce a sample with a solids concentration of 100 mg/L. Montmorillonite is an aluminum hydrosilicate where the ratio between SiO2 and Al2O3 is approximately 4:1. It has a bulk density of 370 gm/L, surface area of 240 m2/gm, and pH 3.2 observed at 10% suspension (Fluka Chemicals, Buchs, Switzerland). For coagulant, a stock solution of alum was prepared by dissolving Al2(SO4)3‚18 H2O (Fisher Scientific, VOL. 34, NO. 18, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. ζ-potential and residual turbidity as a function of alum dose: (a) lake water and (b) montmorillonite clay suspension. Pittsburgh, PA) in deionized water to a concentration of 0.1 M (0.2 M as aluminum).
Results and Discussion Selection of Coagulant Doses. Identification of coagulant doses resulting in charge-neutralization and sweep-floc mechanisms was made from measurements of turbidity and ζ-potential. Figure 2a shows the change in residual turbidity with increasing alum dose for the lake water. This plot illustrates (i) the initial suspension, (ii) charge neutralization as defined by a local turbidity minimum, and (iii) a coagulant dose resulting in a sweep-floc mechanism. It may be noted that turbidity continues to decrease with higher doses beyond dose 3 identified in Figure 2. Therefore, the specific location for stage 3 is somewhat arbitrary but was chosen to be in that part of the turbidity vs dose curve where sweep floc is generally thought to occur. The residual turbidity plot captures the classic steps of charge neutralization and charge restabilization, followed by sweep floc at gradually higher alum doses where precipitation of Al(OH)3(s) is expected. Figure 2b shows the three coagulation stages for montmorillonite suspensions. The plot is similar to that of the lake water samples. In Figure 2a,b, the alum doses corresponding to the three coagulation stages are marked with arrows. Images. Representative images for the three stages of coagulation are shown in Figure 3 for the lake water 3972
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suspension. The images were obtained from an interrogation window of about 2 mm × 2 mm with a resolution of 540 pixels mm-1 as noted previously. The initial particle image (stage 1) displays heterodispersity in the suspension (Figure 3a). For charge neutralization (stage 2), several small flocs are evident (Figure 3b). At this stage, there is more irregularity than observed at stage 1. Figure 2c shows an image taken at stage 3, corresponding to sweep-floc coagulation. Large aggregates comprised of many primary particles have formed, surrounded by the gel-like alum floc. Compared to the stage 1 and 2 images, the image at stage 3 shows fewer but much larger, highly irregular and permeable aggregates. Qualitatively at least, this supports the characterization of aggregates in terms of fractal geometry. Images taken at the three stages of coagulation for the montmorillonite clay suspension (not shown) were similar to the lake water samples. Shape Characteristics. To demonstrate the shape characteristics of the flocs, the distribution of elongation ratio (ratio of long to short dimension) of the lake water suspensions for each of the three aggregation stages is plotted in Figure 4a. Similar calculations for the clay samples are shown in Figure 4b. These plots show that the particle lengths are much larger than the respective widths, particularly for the higher coagulant doses when the aggregates are elongated and slender and comprise many primary particles. The distributions of elongation ratio show that the majority of the particles, approximately 80%, possessed ratios in the range between 1.2 and 2.2, particularly for the clay samples (Figure
FIGURE 3. Images of lake water taken at three stages of coagulation: (a) stage 1, (b) stage 2, and (c) stage 3.
TABLE 2. Two- and Three-Dimensional Fractal Dimensions for Lake Water and Montmorillonite-Clay Samples fractal dimensions sample lake water montmorillonite
coagulation stages 1 2 3 1 2 3
two-dimensional D2 r2 1.96 ( 0.09 1.84 ( 0.09 1.65 ( 0.10 1.89 ( 0.09 1.81 ( 0.09 1.77 ( 0.10
4b). It is interesting to note that some of the primary particles also exhibit an elongated shape with ratios up to 3 to 4, indicating highly nonspherical shape. Values for measured perimeter (P) generally are greater than the perimeter calculated from P ) πDA, where DA is the projected area equivalent circular diameter. The difference between measured and fitted perimeters is greater for the larger flocs and is a further indication of the complicated morphology of the aggregates and their deviation from spherical form. Various additional calculations were performed, concerning the “roughness” of the boundaries or the “roundness” of the flocs. These all revealed consistent results, showing a high degree of irregularity for the aggregate shapes. Particle Size Analysis. Particle size distributions based on the long axis of the fitted ellipse at the three coagulation stages are plotted in Figure 5a,b for the lake water and clay suspension, respectively. The gradual movement of the peak of the distribution toward larger size with higher dose is easily seen. For the lake water, the primary particle size (stage 1) ranges from about 7 to 100 µm, with the peak observed at about 10 µm. At stage 2, there is a peak at 30-50 µm. At this stage, the turbidity is reduced (Figure 2). At a higher alum dose (stage III), the peak occurs at about 200 µm. At high alum dose, it is seen that small particles are trapped in gellike flocs (Figure 3c), leading to the sweep-floc mechanism.
0.93 0.96 0.93 0.95 0.97 0.95
three-dimensional D3 r2 2.93 ( 0.20 2.57 ( 0.20 2.12 ( 0.50 2.71 ( 0.20 2.51 ( 0.20 2.39 ( 0.30
0.81 0.88 0.70 0.86 0.90 0.82
n 69 45 21 58 49 38
The clay samples show a similar progression in the peak size distribution with increasing alum dose (Figure 5b), but compared with the lake water sample, the distributions are more closely spaced. For stages 2 and 3, it is difficult to compare the two suspensions directly since different alum doses were used and the ζ-potentials for the two suspensions at stage 2 are different (Figure 2). What is consistent between the suspensions is that sweep-floc coagulation produces larger particles than coagulation by charge neutralization. Fractal Dimension. As suggested in eq 1, when area or volume is plotted on a log-log scale against l, the slope of a line fitted to the data is equal to the corresponding fractal dimension (D2 for area, D3 for volume). Values for D2 for the three aggregation stages are listed in Table 2, which also includes the correlation coefficients (r2) and the number of data points (n) used in the regression. For the regression analysis, n is the number of size classes where each size class contained the mean values of particle properties derived from multiple photographic images. It should be noted that the approach used here to calculate D2 or D3 does not measure the fractal dimension for a single particle. Instead, it is a fitting parameter that resolves observed properties (size and mass) for an entire distribution VOL. 34, NO. 18, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 4. Elongation ratio at three stages of coagulation: (a) lake water and (b) montmorillonite clay suspension. of suspended particles. In a sense, this gives an averaged fractal dimension for the whole population of aggregates in a particular sample. From Table 2, there is a clear trend of decreasing values for D2 and D3 for both the lake water and the clay suspensions, as particle size increases with each successive stage of coagulation. This trend is consistent with images of particles as shown in Figure 2, with fewer primary particles per unit volume in larger aggregates. For all three stages of coagulation, the data are highly correlated, especially for D2 values, with r 2 ranging from 0.93 to 0.97. The differences in fractal dimensions between stages 2 and 3 for clay samples are not as pronounced as with the lake water. Apparently, the clay particles do not form the large and “fluffy” flocs as found in the lake water samples. The data for D3 are not as highly correlated as D2, possibly due to the approximation made in calculating aggregate volumes. Direct three-dimensional measurements would be needed for calculating D3. The fractal dimensions (D2) calculated for aggregates in this study for three stages of coagulation were in the range from 1.65 to 1.96 for lake water and from 1.77 to 1.89 for montmorillonite clay suspension. Values for D3 ranged from 2.12 to 2.93 for lake water and from 2.39 to 2.71 for the montmorillonite suspension. The values of D2 reported here are in good agreement with D2 values reported in the literature for inorganic suspensions destabilized using alum (5), polystyrene microspheres destabilized by sodium chloride (6), and marine snow (29). The corresponding D3 values reported in these studies are somewhat lower (range from 1.4 to 2) than the D3 values calculated in this study. Overestimates of D3 may result if the calculated aggregate volume (based on the volume of the fitted ellipsoid) is too large. However, the 3974
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derived value of D3 ) 2.12 for stage 3 of the lake water (Figure 3), for example, appears quite reasonable as compared to aggregates of similar fractal dimension produced in clustercluster model simulations (30-32). Theoretical simulations of the aggregation process vary somewhat depending on the aggregation mechanism (reaction limited vs diffusion limited), but aggregates with D3 < 2 appear to possess a significantly more branched structure than the aggregates observed in stage 3 for the lake water. Settling Velocity. An additional parameter of some interest is the settling velocity, ws, which is calculated from a force balance applied to an aggregate settling at a constant rate. Using eq 2, ws ∼ l1.96 for stage 1, ws ∼ l1.73 for stage 2, and ws ∼ l1.47 for stage 3 for the lake water samples; ws ∼ l1.82 for stage 1, ws ∼ l1.70 for stage 2, and ws ∼ l1.62 for stage 3 for the montmorillonite suspensions. Although the exponent in these results becomes smaller for stages of higher alum dose, l also increases with each successive coagulation stage, suggesting more rapid collision of aggregates (33). If median particle size from each of the particle size distributions from Figure 5 is used as the characteristic length, the ratios of lD3-D2+1 for stages 1-3 is 1:1.3:5.3, respectively, for lake water and 1:3:2.6, respectively, for the clay suspension. Thus, larger particle size offsets the effect of lower fractal dimension for the lake water and helps to explain the common observation from water treatment practice that sweep coagulation results in better settling floc than charge neutralization (see Figure 2). It is interesting to note that, for the clay suspension, the scaling relationship for settling velocity suggests little difference between stage 2 and stage 3. This result is in general agreement with jar test turbidity data (Figure 2) where the difference in final turbidity between stage 2 and stage 3 is
FIGURE 5. Particle size distribution at three stages of coagulation: (a) lake water and (b) montmorillonite clay suspension. much more pronounced for the lake water than for the clay suspension. It would be of interest to compare settling velocity estimates with Stoke’s law, but the density of the aggregates is not well-known.
Acknowledgments We gratefully acknowledge the advice and thoughtful suggestions of Prof. K. H. Gardner, University of North Hampshire, and Prof. Robert Botet, University of Paris-South, Orsay, France. The New York Sea Grant Institute also is gratefully acknowledged for partial support of the project under Grant R/CTP-21. The American Water Works Association Research Foundation provided funding for initial development of the imaging system.
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(27) NIH-Image Manual; http://rsb.info.nih.gov/nih-image/manual/ contents.html. (28) Zhang, Y.; Talley, D. G. In Liquid Particle Size Measurement Techniques, Vol. II; Hirleman, E. D., Bachalo, W. D., Felton, P. G., Eds.; 1990; pp 128-141. (29) Kilps, J. R.; Logan, B. E.; Alldredge, A. L. Deep-Sea Res. 1994, 41, 1159-1169. (30) Meakin, P. Adv. Colloid Interface Sci. 1988, 28, 249-331. (31) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Nature 1989, 339, 360-362.
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(32) Vicsek, T. Fractal growth phenomena; World Scientific: River Edge, NJ, 1992; p 488. (33) Serra, T.; Logan, B. E. Environ. Sci. Technol. 1999, 33, 22472251.
Received for review July 19, 1999. Revised manuscript received June 12, 2000. Accepted June 21, 2000. ES990818O
