Environ. Sci. Technol. 1989, 23, 1385-1389
(11) Calvert, J.; Pit@ J. N. Photochemistry; Wiley: New York, 1966; pp 783-786. (12) Abel, M.; Giger, W. Anal. Chem. 1985, 57, 2584. (13) Snider, L. R.; Kirkland,J. J. Introduction to Modem Liquid Chromatography, 2nd ed.; Wiley: New York, 1979; p 675. (14) See for example: Homogeneous and Heterogeneous Photocatalysis; Pelizzetti, E., Serpone, N., Eds.; Reidel: Dordrecht, The Netherlands, 1986. Photocatalysis and Environment; Schiavello,M., Ed.;Reidel: Dordrecht, The Netherlands, 1988. (15) Buxton, G. V.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. J . Phys. Chem. Ref. Data 1988, 17, 513. (16) Christensen, H.C.;Sehested,K.; Hurst, E. J. J. Phys. Chem. 1973, 77, 983. (17) Sehested, K.; Corfitzen, H.;Christen, H.C.; Hart,E. J. J . Phys. Chem. 1975, 79,310. (18) O'Neill, P.; Steenken, S.; Schulte-Frohlinde, D. J . Phys. Chem. 1975, 79, 2773. (19) Neta, P.; Dorfman, L. D. Adv. Chem. Ser. 1968,81, 222. (20) Neta, P.; Hoffman, M. Z.; Simic, M. J . Phys. Chem. 1972, 76, 847. (21) Behur, D.; Rabani, S. J . Phys. Chem. 1988,92, 5288. (22) Eiben, K.; Fessenden, R. W. J. Phys. Chem. 1971, 75,1186. (23) Augugliaro, V.; Palmisano, L.; Sclafani, A,; Minero, C.; Pelizzetti, E. Toxicol. Environ. Chem. 1988, 16, 375. (24) Minero, C.; Maurino, V.; Pelizzetti, E. work in preparation. Supplementary material for Igepal CO-210 and CO-520 degradations is available from the authors; the details of the kinetic analysis and the implementation of eq 3 in Basic or Fortran languages are available from C.M. (25) Anbar, M.; Meyerstein, D.; Neta, P. J . Phys. Chem. 1966, 70, 2260. (26) Adams, G. E.; Michael, B. D.; Trans. Faraday SOC.1967, 63, 1171.
hydroxyl radical attack on the ethoxylated chain and on the benzene ring. The rate per monomer of the two processes differs by approximately 1order of magnitude and is dependent on the adsorption on the photocatalyst surface, but the operating mechanism leads to a faster disappearance of long ethoxylated chains. Further oxidation yields lower molecular weight products, such as acidic compounds, polyethylene glycols, ethylene glycols, and finally a virtually quantitative conversion to COz: this is sustained from simultaneous disappearance of POC and DOC content. It is also interesting to note that 4-nonylphenol, a stable and even more toxic compound, is quantitatively mineralized, and that the photocatalytic degradation of related compounds does not lead to its formation. Clearly then, photocatalytic processes could also be applied, together with other treatment of wastes (2), to ensure final disposal of these nondesirable products. Literature Cited Bock, K. J.; Stache, H.In The Handbook of Environmental Chemistry; Hutzinger, O., Ed.; Springer Verlag: Berlin, 1982; Vol. 3B, p 163. Swisher, R. D., Ed.Surfactant Biodegradation; M. Dekker: New York, 1986. Abel, M.; Giger, W.; Koch, M. In Organic Micropollutants in the Aquatic Environment; Bjorseth, A., Angeletti, G., Eds.; Reidel: Dordrecht, The Netherlands, 1986; p 414. Rudling, L.; Solyom, P. Water Res. 1974, 8, 115. Stephanon, E.; Giger, W. Environ. Sci. Technol. 1982,16, 800. Reinhard, M.; Goodman, N.; Mortelmans, K. E. Environ. Sci. Technol. 1982, 16, 351. Ahel, M.; Conrad, T.;Giger, W. Environ. Sci. Technol. 1987, 21, 697. Giger, W.; Brunner, P. H.; Schaffner,C. Science 1984,225, 623. Bringmann, G.; Kuhn, R. 2.Wasser Abwasser Forsch. 1982, 15, 1. Hidaka, H.;Ihara, K.; Fujita, Y.; Yamada, S.; Pelizzetti, E.; Serpone, N. J . Photochem. Photobiol. 1988, 42, 375.
Received for review December 7,1988. Accepted May 30,1989. This research has received generous support from the following agencies: CNR, MPI, Eniricerche, Regione Piemonte, E.S.O. under Contract DAJA 45-85-C-0023. Partial support from the European Economic Community (EEC)under Contract EV4V0068-C(CD) is kindly acknowledged.
Fractal Geometry of Particle Aggregates Generated in Water and Wastewater Treatment Processes Da-hong Li and Jerry Ganczarczyk'
Department of Civil Engineering, University of Toronto, Toronto, Canada, M5S 1A4
A fractal is a mathematical description of highly irregular geometric shapes. It is demonstrated that particle aggregates generated in water and wastewater treatment processes possess fractal features. The fractal dimension for the structure of the aggregates, determined in this work, ranged from 1.4 to 2.8. The concept of the fractal dimension is found applicable in the characterization of the aggregates' geometry, in substrate transfer to biological aggregates, and in the process of aggregation. Introduction
The geometric characteristics of particle aggregates generated in water and wastewater treatment processes are difficult to describe because of their highly irregular and disordered nature. The literal phrases (e.g., ref 1and 2) used to match the shapes and morphology of the aggregates frequently appear either far-fetched, simplified, or ambiguous. Attempts to apply quantitative techniques such as shape factors (3) and the signature wave form (4) 0013-936X/89/0923-1385$01.50/0
seem equally unsuccessful. The former is too much an approximation to the complex reality while the latter is tedious and, sometimes, indeterminate. Moreover, the existing quantitative techniques, as well Q the literal description, are limited by their inability to characterize the spatial structure of the aggregates. The fractal theory, developed by Mandelbrot (5),provides a completely new approach to the characterization of many natural and engineered systems that have no definite form or regularity. The most important numerical parameter in fractal theory is the Hausdorff or fractal dimension. As an extension and generalization of the classical concept of Euclidean dimensions, the fractal dimension preserves the fundamental dimension roles in the measurements where the ordinary dimensions are used as exponents. For example, the mass M of a fractal with fractal dimension D is proportional to its size R raised to power D:
0 1989 American Chemical Society
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Table I. Size-Density Fractal Dimensions of the Aggregates type of aggregates activated sludge flocs ferric aggregates alum aggregates alum aggregates activated sludge flocs clay-iron flow clay-magnesium flocs activated sludge flocs activated sludge flocs Darticles in trickling filter effluent
C or equiv
source of data (ref)
fractal dimens D by this study
0.55-1.0 0.19-0.39 0.6764.668 1.03-1.41 1.6 1.08 1.09 1.51-1.56 0.93-1.30 1.27
Li and Ganczarczyk (8) Lagvankar and Gemmell(7) Boadway (10) Tambo and Watanabe (9) Tambo and Watanabe (9) Tambo and Watanabe (9) Tambo and Watanabe (9) Magara et al. (10) Mitani et al. (11) Zahid (13)
1.45-2.0 2.61-2.85 2.302-2.324 1.59-1.97 1.4 1.92 1.91 1.44-1.49 1.70-2.07 1.73
5
20
longest dimension (mm)
I
30
l
l
40 50
I I I I 1 100 200 300 400503 Characteristic Size (urn)
lo00
Flgure 2. Effective density as a function of aggregate size.
Figure 1. Settling velocity of activated sludge flocs.
Equation 1differs from an ordinary mass-size relationship only in that the power coefficient D is no longer limited to integers. In this work, selected data on geometry and some other features of the particle aggregates were processed in terms of the fractal theory.
Characterization of Particle Aggregates by Fractals Unexpected Phenomena and Fractal Nature. Several studies of particle aggregates generated in water and wastewater treatment processes have revealed a number of unexpected phenomena that diverge from well-established principles. Considering typical results of a settling test (Figure 1)for activated sludge flocs (6),the velocitysize functions shown as the solid curves in Figure 1 can be expressed as
R'
(2) where u is settling velocity, R is a characteristic size, and C is an exponential constant. Values of C = 0.55 or 1, instead of the value of 2 (the dashed line) predicted by Stokes' law, were found to best fit the points in Figure 1 because of their higher correlation coefficients of 0.90 and 0.88, respectively, as compared to only 0.78 for C value of 2. Assuming the general validity of Stokes' law, such unusual behavior of the aggregates would result in an unexpected property of the aggregate density, which can be expressed as p a v / R 2 = RC-2 (3) u
0:
where p is buoyant or effective density of the aggregates. This simple power-law behavior was obtained, based mainly on interpretations of the settling tests, for ferric and alum aggregates (7-9),clay flocs (9),activated sludge flocs ($121, and particles of trickling filter effluent (13). In a double logarithmicplot, buoyant density of aggregates 1386
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will be a linear function of the size, as shown in Figure 2 for a few documented examples. This finding conflicts with the basic concept of density, which does not depend on size for the same substance. Further analysis along the same approach may be pursued by breaking density into its component parameters, mass and volume. On the basis of eq 3, if the space occupied by the aggregates remains three-dimensional, the buoyant mass of the aggregates would be M 0: RC+'. For C < 2, this mass-ize relationship disagrees with the conventional wisdom on the subject, which always suggests 3 to be the power coefficient. A possible explanation of these phenomena is that the studied aggregates are fractals or, at least, are objects possessing fractal attributes. Clearly, the above mass-size equation becomes identical to eq 1,if D = C + 1. Also, with the fractal mass-size formula (eq 1)and Stokes' law, the settling velocity of the aggregates can be expressed as eq 2 with C C 2. In other words, all these unexpected phenomena are expected in the fractal theory. The exponential constant C is significant in that it contains information on the fractal dimension. It should be noted that if the space occupied by the aggregates were fractally expressed, the density calculated accordingly would be independent of aggregate size. This kind of substance was called fractally homogeneous (5). Table I presents a list of the fractal dimensions of the aggregates calculated here on the basis of the reported data of settling tests and size-density relationships. Computer Simulation. In early models of computersimulated aggregates, the aggregation process was proposed as a series of successive random additions of primary particles to the growing aggregates (14). Accordingly, the number of the primary particles was found to be a function of aggregate size R: N ( R ) RD (4) where D is a constant of less than 3. Later models as-
Circumference (mm) n p u r 4 . fleIaWMlpbaweencroswectionalareaanddrcunta; enca of pure cultue lbcs of Z m g b "&a. ~
i FIpn 3. a M (b) mlddb. (c) bottom.
of "aid &Ige fioc sectbm. (a)Top.
suming various mechaniims for aggregate formation also
predicted D < 3 for three-dimensional aggregate models (9,15,16). It can be readily shown that if primary particles are uniformly arranged in the space of an aggregate the D value would be 3, the Euclidean dimension. This divergence was not fully explained by the investigators (9) who originally developed the relationship of the size and the number of primary particles. With the fractal theory, however, the fact that D < 3 in eq 4 for the simulated aggregates can be explained by
considering the aggregate as being of a fractal structure and D the fractal dimension. The number of particles in a space of an aggregate is just another measure that can be made by generalizing the Euclidean dimension to the fractal dimension. One can now interpret the result of the computer simulation as a confirmation of the fractal nature of the aggregates. Fractal dimensions of the model aggregates calculated in this work ranged from 1.85 to 2.1. These values were in agreement with the fractal dimensions based on experimental resulk of inorganic aggregates presented in Table I. Self-Similarity. Evidence supporting the bctal nature of the biological aggregates was observed directly in our earlier study of the internal structure of activated sludge flocs (17). In the study, stabilized flocswere sliced by a microtome and were stained to show locations of microbial cells and extracellular polymers. The microphotograph of the floc sections in Figure 3 demonstrate that the unstained areas of the flocs range in scale from a whole floc section down to almost a single cell, indicating a lack of a characteristic length that may represent the nonstained gaps in the section. Moreover, although Figure 3b is a part of Figure 3a and Figure 3c is, in turn, a part of Figure 3b after magnification, there appears among them a broad geometric resemblance in general appearance. This implies a self-similar structure at least within a limited scale range, although it may not be as systematic as those computer-generated structures presented by Mandelbrot (5). Cross-Sectional Geometry of the Aggregates. In Euclidean geometry, the area of a planar object is always expressed as a linear measure raised to the power 2, regardless of specific shapes. However, the cross-sectional properties of the projection of the aggregates are 80 unusual that this elementary geometric equation is not valid. For example, it was found that the experimental data were best fit when area was expressed as the longest dimension raised to the power 1.8 for particles in trickling Nter effluent (13). By use of the data presented in a study on pure culture flocs of Zoogloea ramigera (ref 18 Table 1 of average values and Figure 9 of values of experiment 9).a regression analysis made in this study specified the relationship b e tween cross-sectional area (A) and circumference (or perimeter P) of the flocs. AS shown in Figure 4, the cross-sectional area was proportional to circumference raised to powers much less than 2. This phenomenon cannot be simply explained by noncircle shapes. In contrast, the area-length relationship derived for fractals provides a different expression (5): area 0: length2/" (5) where D is the b c t a l dimension of the length. If the shape Envlron. Sci. Tecmol.. Vol. 23. No. 11. 1989 1387
"
o
l
lo'! 10 -I
I
the relative pen tip size (-)
1
Flgure 5. Perimeter as a function of the relative pen tip size of an image analysis process.
is regular, D will equal 1 in this case and the power coefficient reduces to the Euclidean dimension. For 2 / D = 1.8 of the particle aggregates in trickling filter effluent (13),the fractal dimension of the aggregates was calculated as 1.1. Similarly, the fractal dimensions of circumference of the Zoogloea flocs have been calculated to be 1.89 (from the exponential value of 1.06) for experiment 9 and 1.65 (from the exponential value of 1.21) for the average data (Figure 4). There is also a different approach to the fractal nature and the fractal dimension of the aggregate perimeter. In our earlier study of microtome sections of activated sludge flocs (In,a light pen of an image analysis system (3) was used to trace the sectional contour of the aggregates for the measurement of area and perimeter. When a higher magnification was employed, the size of the light pen tip became smaller in relation to the magnified images and more details became visible and could be measured. Consequently, the section perimeter increased with the decrease of the relative tip size. As seen in Figure 5 , the perimeter-size function was a straight line in a double logarithmic plot with a negative slope. Theoretically, the extension of the straight line toward the left side (corresponding to higher magnifications) would lead the perimeter of a fixed area to infinity, a contention analogous to that of the length of coastline in Mandelbrot's example (5). This is an indication that the value of 1 is not an appropriate dimension for the perimeters of the sections. The fractally-featured perimeters have effective dimensions of 1plus a fraction, which is the absolute value of the slope. From the few examples shown in Figure 5, the fractal dimensions for the sectional perimeter were in the range from 1.13 to 1.22. Discussion of Possible Applications
The spatial structure of a fractal object can be described with fractal dimensions, which may be reflected not only in geometric forms but also in some other physical phenomenon such as aggregate density. This allows the study of spatial properties of the irregular aggregates without the generation of three-dimensional images. In addition, the solid-liquid interface area and perimeter of the projected images are likely to possess fractal features, implying that several fractal dimensions may be available for an irregular aggregate. Thus, the fractal dimension can be a competitive alternative to the simplified standard shapes and shape factors used previously. Variation in fractal dimensions makes it possible to differentiate aggregates generated in varied conditions in a more elaborate manner than the literal description. Fractal dimensions correspond to the degree of irregularity 1388 Environ. Sci. Technol., Vol. 23, No. 11, 1989
and complexity or the space-filling capacity of an object. For instance, a rugged curve has a higher space-filling capacity than a smooth curve, which, in turn, has a higher space-filling capacity than a disconnected smooth curve. The respective fractal dimensions vary in the same order; despite that these figures are all one-dimensional in classical geometry. The observation that the fractal dimension of the three-dimensional structure was sometimes leas than 2, the Euclidean dimension of surface, strongly implied a disconnected structure with extremely low space-filling capacity. Theoretically, the solid portion in such a structure is so low that it would not fill completely its own projected area. This implication by the fractal dimension of the aggregates is in qualitative agreement with the high porosity of the aggregates reported (6). The internal gaps, shown on the microphotographs of biological aggregate sections, were usually assumed to be uniformly distributed in most of the substrate-transfer studies whether the mechanism proposed was molecular diffusion (e.g., ref 19) or advective transport by flow through the aggregates (20,21). Direct observation of the internal fine structure of activated sludge flocs (17) and the fractal nature of the flocs concluded in this study indicated that the assumption of uniformity was not realistic. The fractal nature of activated sludge flocs suggests that the flocs may be filled by gaps of all sizes. Furthermore, it seems possible to quantitatively characterize the gaps in the flocs by using fractal theory, once the fractal dimension of a sample of activated sludge flocs is determined. Extensive research on aggregation of particles similar to those found in water and wastewater treatment processes, such as gold and silica colloids (2%24), showed that aggregation by primary particle addition might result in a relatively uniform structure. This may correspond to an affinity between fractal and Euclidean dimensions. According to these findings, the aggregates discussed in this work are most likely formed by the process of cluster to cluster collision or combined collisions, because of their low fractal dimensions. This approach to the study on the process of aggregation has been applied without the knowledge of fractals. Several investigators observed that there was a transition point in the size-density function of various flocs (7,9,1I). Smaller than this point, density varied at a reduced slope in the double logarithmic coordinates. Based on the current study, this was an indication that different mechanisms might principally act in the formation of small and large flocs. The higher fractal dimension determined from the reduced slope implied that small flocs were formed by a process more similar to the particle addition and were more compact than the larger ones. In fact, by use of the same principle, it can be further predicted that there will be another transition point in the relationship discussed above, by which the straight line will be leveled off. This would be the point where the size of the aggregate reaches that of the primary particles, which have a constant density. Because fractal dimension may vary with the aggregates generated under different conditions, it can be used to study the factors that affect the process of aggregation. Tambo and Watanabe (9) demonstrated that an increasing aluminum ion concentration dose to suspended particle concentration ratio considerably increased the absolute value of the exponential constant (C-2). This influence can now be interpreted in terms of the size-density fractal dimension, which links the affecting factor directly to the process of aggregation and the structure of the aggregates.
Environ. Sci. Technol. lQ89, 23,1389-1395
Conclusions It has been demonstrated that particle aggregates generated in the flocculation/coagulation process, the activated sludge process and the particles washout from trickling filter biofilm, possess some fractal features. Several morphological properties of these aggregates can be characterized by fractal dimensions. The fractal nature of the aggregates was also observed in the computer-simulated models of the aggregates. The fractal theory can be used for analysis of the geometric characteristics of the aggregates, substrate transfer in biological flocs, and the process of flocculation. Literature Cited (1) Maxham, J. V.;Hickman, H. J. Theor. Biol. 1978, 43, 229-239. (2) U.S. Environmental Protection Agency. The Causes and Control of Activated Sludge Bulking and Foaming. Cincinnati, OH, EPA/6251-97/012, 1987. (3) Li, D.-H.; Ganczarczyk, J. Water Pollut. Control J . Can. 1986,21, 130-140. (4) Kaye, B. M. Am. Lab. (Fairfield, Conn.) 1986, 55-63. ( 5 ) Mandelbrot, B. B. The Fractal Geometry of Nature; W. H. Freeman and Co.: New York, 1983. (6) Li, D.-H.; Ganczarczyk, J. Water Res. 1987,21, 257-262. (7) Lagvankar, A. L.; Gemmell, R. S. J.-Am. Water Works Assoc. 1968,60, 1040-1046.
(8) Boadway, J. D. J. Environ. Eng. Diu. (Am. SOC.Civ. Eng.) 1978,104,901-915. (9) Tambo, N.; Watanabe, Y. Water Res. 1979,13,409-419. (10) Magara, Y.; Nambu, S.; Utosaw, K. Water Res. 1976,10, 71-77. (11) Mitani, T.; Unno, H.; Akekata, T. Jpn. Water Res. (in Japanese) 1983, 6, 69-75. (12) Li, D.-H. Master's Thesis, Department of Civil Engineering, University of Toronto, Toronto, Canada, 1985. (13) Zahid, W. Master's "hais,Department of Civil Engineering, University of Toronto, Toronto, Canada, 1987. (14) Vold, M. J. Colloid Sci. 1963, 18, 684-695. (15) Sutherland, D. N.; Goodarz-Nia, I. Chem. Eng. Sci. 1971, 26,2071-2085. (16) Goodarz-Nia, I. J. Colloid Interface Sci. 1977,62,131-141. (17) Li, D.-H.; Ganczarczyk, J. Structure of Activated Sludge Flocs. Biotechnol. Bioeng., in press. (18) Mueller, J. A.; Morand, J.; Boyle, W. C. Appl. Microbiol. 1967,15, 125-134. (19) Baillod, C. R.;Boyle, W. C. J . Sanit. Eng. Diu., Am. SOC. Cio. Eng. 1970,96, 525-545. (20) Logan, B.; Hunt, J. R. Biotechnol. Bioeng. 1988,31,91-101. (21) Li, D.-H.; Ganczarczyk, J. Water Res. 1988,22, 789-792. (22) Witten, T. A.; Cates, M. E. Science 1986,232,1607-1612. (23) Schaefer,D. W.; Martin, J. E.; Wiltzius, P. W.; Cannell, D. S . Phys. Rev. Lett. 1984,52, 2371-2374. (24) Meakin, P.; Ado. Colloid Interface Sci. 1988,243,249-331.
Received for review March 16, 1989. Accepted May 30,1989.
Polychlorinated Dibenzo-p-dioxins and Dibenzofurans in the Ambient Atmosphere of Bloomington, Indiana Brian D. Eltzert and Ronald A. Hltes" School of Public and Environmental Affairs and Department of Chemistry, Indiana University, Bloomington, Indiana 47405
A long-term study of polychlorinated dibenzo-p-dioxins (PCDD) and dibenzofurans (PCDF) in the ambient atmosphere of Bloomington, IN, has been completed. Methods capable of measuring individual PCDD/F (Le., PCDD + PCDF) at ambient concentrations (as low as 1 fg/m3) were developed. PCDD/F were measured in both the vapor and particle-bound phases. In Bloomington, the total concentrations of these compounds were found to vary by a factor of 10, but generally they remained between 1 and 4 pg/m3. Vapor-to-particle ratios for individual PCDD F ranged from 0.01 to 30 and were found to be depen ent on the compound's vapor pressure and the ambient temperature. Heats of adsorption were estimated to range from 11 to 32 kd/mol. These data should prove useful in the determination of the sources of these compounds to the atmosphere and their ultimate environmental fates.
I
Introduction Polychlorinated dibenzo-p-dioxins (PCDD) and polychlorinated dibenzofurans (PCDF) are injected into the atmosphere by various combustion processes and dispersed throughout the environment by atmospheric transport (1). These combustion processes include the incineration of municipal wastes (2-14) and the combustion of automotive fuels (15);these processes generate complex mixtures of PCDD/F (i-e.,PCDD + PCDF) with varying numbers of 'Current address: Connecticut Agricultural Experiment Station, 123 Huntington St., New Haven, CT 06504. 0013-936X/89/0923-1389$01.50/0
chlorine atoms and with varying sites of chlorine substitution, depending on fuel composition and combustion temperature. Because of the varying toxicities of PCDD/F, it is important to understand the processes and parameters that control the rate at which individual compounds undergo transformations while in the atmosphere. For example, could toxic PCDD/F photodegrade a t a faster rate than nontoxic ones? As a first step in obtaining this understanding, it is important to measure the concentrations of PCDD/F in the ambient atmosphere. We chose Bloomington, IN, because of the proposed construction of an incinerator that could burn PCB-contaminated material along with the town's municipal waste. Given previous evidence on the production of PCDD/F in municipal incinerators (2-14) and in PCB fires (9, IO),this proposed incinerator could have a significant impact on Bloomington's air quality. Thus, this study was undertaken to provide base-line data against which the impact of this incinerator on local PCDD/F concentrations could be judged. Examination of several locations over a 3-year period allows small-scale local effects to be minimized and the primary sources of variability in the data to be determined. Although there have been a few recent reports of PCDD/F in ambient atmospheric samples (16-21),there has been no long-term study of these compounds in the atmosphere at a single location. Furthermore, none of these studies examined the vapor-phase to particle-bound partitioning process. We felt that it was important to study this process if we are to understand the variability in PCDD/F atmospheric concentrations. Therefore, we
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