Environ. Sci. Technol. 2005, 39, 2731-2735
Determination of the Fractal Dimension of Microbial Flocs from the Change in Their Size Distribution after Breakage XIAO-YAN LI* AND RUBY P. C. LEUNG Environmental Engineering Research Center, Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China
The fractal dimension is of ultimate importance in the description of the properties and behavior of microbial flocs in biological wastewater treatment systems. However, the methods for the measurement of the fractal dimension have not been well-established. In this study, a new method is developed to determine the fractal dimension of biological flocs in activated sludge (AS) suspensions. The new method utilizes the particle size distribution (PSD) of the sludge flocs measured by image processing under a microscope. Mechanical breakage is conducted for the sludge sample to create a change in the PSD. On the basis of the self-similarity of fractal aggregates, the fractal dimension of the AS flocs can be calculated from a comparison between the original PSD and the altered PSD by breakage. It is determined that the sludge flocs grown in laboratory bioreactors with sludge ages of 5, 10, and 20 days have fractal dimensions of 2.07, 2.21, and 2.36. The sludge collected from a full-scale AS treatment plant has a fractal dimension of 1.99. This new method overcomes the deficiencies of other existing methods. It is easier to use and provides more reliable results in the determination of the fractal dimension of biological flocs and other similar aggregate samples.
Introduction Microorganisms in the sludge suspension of biological wastewater treatment reactors are in the form of aggregated flocs that are known to be highly fractal (1-3). Small aggregates of colloids generated by Brownian motion share a similar and well-defined fractal dimension (1, 4). No such universality in the magnitude of the fractal dimension can be applied to large particle aggregates, including microbial flocs. The value of the fractal dimension depends on the surface property of the primary particles, the type of floc, the hydrodynamic conditions, and the mechanism of floc formation (5-8). Theoretical descriptions of the flocculation process and the aggregate structure have been greatly improved with the application of fractal geometry. It has been demonstrated that the fractal dimension has a profound impact on the properties and behavior of particle flocs, such as density, porosity, settling velocity, permeability, strength, and mass transport rate (3, 8-12). The coagulation theory has also been modified to incorporate the fractal feature of particles in their interaction and attachment (13-16). * Corresponding author phone: (852) 2859-2659; fax: (852) 25595337; e-mail:
[email protected]. 10.1021/es049177+ CCC: $30.25 Published on Web 02/23/2005
2005 American Chemical Society
Despite the ultimate importance of the fractal dimension, methods for its determination are not well-established, particularly for microbial aggregates that are highly porous and fragile and cover a wide size range. Deficiencies in the methods proposed in recent years can be readily identified. The fractal dimension can be estimated by the analysis of particle size distributions (PSD) (3, 17, 18). However, the PSD-based methods assume that the PSD can be fitted by a power law function, which may not hold for most particle systems in engineered facilities (16, 19, 20). The particle concentration technique (PCT) has been used to calculate the fractal dimension of particles based on their mass-size relationship extracted from both PSDs in terms of the actual (visual) size and the solid volume (21). The PCT does not require a power law function for the PSD, but it does need a PSD to be measured by an electronic particle counter (e.g., a Coulter counter (21)). Biological aggregates in wastewater treatment are usually too large and too fragile to be measured by such counting instruments (22). For large biosludge flocs, the fractal feature has been characterized from the measurement of such parameters as mass (8, 23), settling velocity (24-26), and solid fraction (27, 28) in relation to size for a number of selected individual flocs. However, the fractal dimension obtained may not be representative of the entire population of particle flocs over a wider size range. In the present study, a new method that uses imagebased PSD is developed for the determination of the fractal dimension of microbial flocs produced in activated sludge (AS) reactors. Breakage by shear turbulence is conducted on the sludge sample to create a change in PSD. On the basis of the self-similarity of fractal aggregates, the fractal dimension of the AS flocs can be determined by a comparison of the original PSD with the altered PSD after breakage. The new method is easy to use and produces reliable and accurate results in the measurement of the fractal dimension of microbial flocs and other similar samples.
Materials and Methods Theoretical Section. A population of particles in water can be described with a continuous size distribution, such as N(l) that is the cumulative number concentration of particles of size l or larger (16, 21, 29). The size distribution may also be presented in a discrete form using the differential size density function n(l), defined by n(l) ) - dN(l)/dl (7). Hence, the number of particles within a size interval ∆l is
∆N(l) ) n(l)∆l
(1)
The mass concentration of the particles between sizes l1 and l2 can be written as C ) ∫l1l2mln(l)dl, where ml is the mass of the particles of size l (7). In practice, particle size distributions are often acquired by counting particles against a finite number of size intervals (14, 16, 21). Thus, the mass concentration of particles in the size range concerned can be approximated by t
C)
∑m ∆N(l ) i
(2)
i
i)1
where i signifies the size intervals from 1 up to t. For fractal particles such as AS flocs, the mass can be related to the size (length) by
ml ) alD VOL. 39, NO. 8, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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where a is an empirical constant and D is the fractal dimension of the particle flocs (1, 3, 8, 23). Assuming an average D for the AS flocs of all sizes, the mass concentration of the biosludge measured by the suspended solids (SS) or the volatile suspended solids (VSS) can then be written as t
C)a
∑l
D i
∆N(li)
(4)
i)1
Breakage of the particle flocs by enhanced turbulence can transform large flocs into smaller particles and hence alter the PSD (e.g., from the original N1(l) to the new N2(l)). However, owing to the self-similarity of fractal aggregates (1, 3, 30), their fractal structure will not be affected by breakage, and the same value of D will be maintained. The sample after breakage can be related to the original sample by t
C1
∑l
D i
∆N1(li)
i)1
)
C2
(5)
t
∑l
D i
∆N2(li)
i)1
If D is an unknown, and the biomasses C1 with a PSD of N1(l) for the original sludge and C2 with a PSD of N2(l) for the breakage-treated sludge are determined, then a new parameter as a function of D can be defined here as
(∑ (∑
) )
t
Γ(D) )
liD∆N1(li) /C1
i)1 t
(6)
liD∆N2(li) /C2
i)1
The ratio N(l)/C is actually a mass-based PSD, N′(l) ) N(l)/C, with a unit such as no./mg. Substitution with N′(l) in eq 6 produces t
∑l Γ(D) )
D i
∆N′1(li)
i)1
(7)
t
∑l
D i
∆N′2(li)
i)1
A comparison of eqs 6 and 7 with eq 5 suggests that the D value giving Γ(D) ) 1 is the fractal dimension of the microbial flocs of the sludge sample, assuming that the size intervals from 1 to t include all the mass of particles and flocs in the sample. Moreover, if C1 and C2 are identical, then eq 6 becomes t
∑l Γ(D) )
D i
∆N1(li)
i)1
(8)
t
∑l
D i
∆N2(li)
i)1
Experimental Section Activated Sludge Aggregates of Different Sludge Ages. Microbial aggregates were generated in three 2 L beakers used as activated sludge reactors that were placed on a paddle mixer (PB-700, Phipps and Bird, Richmond, VA). Each reactor contained a sludge suspension of 1.6 L. The AS reactors and their operations have been described in previous studies (8, 23). In brief, the reactors were seeded with the activated 2732
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sludge collected from the Stanley Sewage Treatment Works (STW) in Hong Kong. The sludge in the reactors was wellsuspended by the paddles mixing at 10 rpm and by the continuous aeration from the bottom. The AS reactors were fed once a day with starch-based synthetic wastewater (8). Three different sludge wastage ratios were used for the three AS reactors, resulting in the different sludge retention times (SRTs) of 5, 10, and 20 days. During the steady-state operation that lasted for a period of more than 3 months, the three bioreactors had food/microorganism (F/M) ratios of about 0.35, 0.25, and 0.15 g BOD5/g VSS-d, resulting in sludge concentrations in MLSS of around 1400, 1200, and 1100 mg/ L. In addition to the sludge grown in the laboratory, fresh activated sludge obtained from the Stanley STW was also analyzed. The STW uses a conventional AS system for the treatment of domestic wastewater at an SRT of approximately 15 days. Immediately after collection, the fresh sludge mixture was diluted to about 1200 mg/L and was also placed in a 2 L beaker on the jar-test paddle mixer with aeration and mixing before the sludge characterization. Sludge Breakage. A sludge sample of 1 mL was gently withdrawn from a reactor and transferred into a 50 mL test tube. Before being sampled, aeration of the sludge suspension was briefly stopped for 10 min to allow more flocculation. To stain the biomass, 100 µL of 0.1% (w/v) acridine orange was added into the test tube. After 5 min of staining, 19 mL of deionized (DI) water was slowly added to the test tube to dilute the sludge to a level at which individual AS flocs could be easily observed. Half of the sludge suspension (10 mL) was then transferred into another 50 mL test tube, using a 5 mL pipet with the tip cut for a larger opening. Subsequently, breakage of the sludge aggregates was conducted vigorously with the pipet by sucking in and pumping out the sludge solution rapidly about 15 times. Both the tube holding the original sludge without breakage and the tube holding the treated sludge that had undergone breakage were filled up with DI water to 20 mL. Afterward, 5 mL of the well-mixed sludge solution was withdrawn from each tube and placed gently into a Petri dish (47 mm diameter, Millipore, Billerica, MA). The samples were left in quiescence for 3 h or longer to allow all the biomass to settle on the bottom of the dishes. PSD Measurement and Fractal Dimension Determination. The size distribution of the sludge flocs in a Petri dish was determined under a microscope (BX60, Olympus, Tokyo, Japan) equipped with a digital camera (DP10, Olympus) and a computer-based image analysis system (Scion Image, Frederick, MD). The AS biomass stained by the acridine orange was well-illuminated by the fluorescent blue light (420-480 nm) of the microscope (Figure 1). Projected images of the sludge flocs were analyzed by the image software for particle sizing and counting, following the procedures detailed elsewhere (16, 21). The enclosed area of a particle image, A, was converted to the equivalent diameter using l ) (4A/π)1/2. Fifty fields were scanned at 50× for each sludge sample to obtain its PSD within a size range of 3-1280 µm, which was wide enough to cover all the flocs observed. After the PSD measurement, all the sludge mass in the Petri dish was collected by filtration on a preweighted 0.4 µm (pore diameter) polycarbonate membrane filter (25 mm diameter, Osmonics, Minnetonka, MN). The dry mass of the sludge on the filter was measured using an electronic microbalance (AEM-5200, Shimadzu, Kyoto, Japan) (8, 23); hence, the massbased PSD, N′(l), could be calculated. Eventually, two sets of mass-based PSDs were obtained for a sludge sample, one for the original sludge and the other for the sludge that had undergone breakage. Using eq 7 and plotting Γ(D) as a function of D, the fractal dimension of the AS aggregate could thus be determined.
FIGURE 1. Representative images of the sludge flocs before and after breakage: (A1) and (A2) activated sludge produced in a laboratory bioreactor with a sludge retention time of 10 days, and (B1) and (B2) AS sample collected from a wastewater treatment plant. Each picture combines the photos of four view fields.
Results and Discussion At least 1000 particle flocs were counted to produce the particle size distribution for an AS sample. All size distributions followed the previously reported general PSD shape, which features many more small particles than large particles (19-21, 29). After log-log transformation, portions of linear correlation could be identified in the mass-based cumulative PSD (Figure 2). However, there is no single straight line that can be applied to an entire size distribution, and a bended curve is more typical for larger particles. In agreement with the measurements and simulations of previous studies (8, 16, 20), the curved PSD lines indicated the effect of particle breakage by stirring and aeration in the AS reactors. Because of the fact that no slope can be derived for the entire PSD of a sludge sample, its fractal dimension cannot be estimated using the PSD slope-based approach because it requires a power law PSD function. Enhanced breakage in the test tubes significantly changed the size distributions of the AS flocs for all the sludge samples (Figure 2). Aggregates of larger sizes were broken by vigorous fluid shear, transforming the sludge mass to the size range of smaller particles. As a result, the treated sludge had more small particles and less large particles than the original sludge. Thus, the breakage applied was adequate to shift the sludge PSD, allowing the further characterization of the fractal dimension of the AS flocs. The ratio factors defined in eq 7 can be computed as a function of the fractal dimension for all sludge samples based on the PSD and biomass measurements (Figure 3). As derived previously, the D value corresponding to Γ(D) ) 1 is the fractal dimension of a sludge sample. The AS flocs produced in the bioreactors with SRTs of 5, 10, and 20 days had fractal dimensions of 2.07, 2.21, and 2.36, respectively. The fractal dimension of the AS flocs appeared to increase with the sludge age. In other words, a longer SRT resulted in a more tightly
packed aggregate structure with a higher fractal dimension. The actual sludge collected from the full-scale AS treatment plant had a fractal dimension of 1.99 (Figure 3). The fractal dimensions of activated sludge determined from the change in PSD after breakage using the new method compared reasonably well with previously reported values (8). On the basis of the direct relationship between dry mass and size for a number of individual large flocs, sludges generated under similar conditions to those in the present study with SRTs of 5, 10, and 20 days were found to have average fractal dimensions of 2.10, 2.34, and 2.30. However, these D values were calculated for only a small number (200 µm) and may not be applicable to the majority of the sludge particles. By contrast, the results obtained here are the average D values for the sludge flocs of all sizes (3-1280 µm) and are more representative of the entire population of AS flocs. The D values determined for activated sludge were within the range indicated for aggregates formed through clustercluster flocculation other than those formed through particlecluster attachment (1, 31). In addition to flocculation, particle breakage and restructuring in the AS reactors could also affect the structure feature of the sludge flocs, resulting in an increase in the fractal dimension (1, 8, 30). Specifically, there was stronger turbulence, brought about by mixing and aeration, in the small bench bioreactors than was observed in the actual AS aeration basins. The sludge produced in the bioreactors had been extensively restructured; hence, its fractal dimensions were higher than those of the fresh sludge collected from the actual AS treatment system. In addition, the biomass with a short sludge age (5 days) was likely to yield more extracellular polymeric substances (EPS) (8, 15, 32). An abundance of EPS could prevent bacterial cells from close contact, resulting in a more porous structure with a lower D value. In contrast, in the biomasses with longer sludge VOL. 39, NO. 8, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Accumulative particle size distributions before and after breakage as determined by imaging analysis for sludge flocs produced in laboratory bioreactors with sludge retention times of (A) 5 days, (B) 10 days, and (C) 20 days and for (D) the AS sample collected from the wastewater treatment plant.
days appeared to be less fractal (with higher fractal dimensions) than the sludge with an SRT of 5 days. The AS flocs examined in the present study had fractal dimensions in the range expected for biological aggregates (2), although the different methods employed for fractal characterization may undermine the significance of a direct comparison of the D values reported in different studies. Most studies have found values of D > 2 for flocs produced in bioreactors. For example, the activated sludge collected from full-scale wastewater treatment plants has been reported to have D ) 2.24 for small flocs (25) and D ) 2.26 for large flocs (21), and activated sludge flocs produced in laboratory reactors were found to range from D ) 2.10-2.34 for sludge ages in the range of 5-20 days (8). A somewhat lower value of D ) 2.09 was found for the bacterial flocs produced in a laboratory sequencing batch reactor that treated synthetic wastewater (23). Anaerobic flocs have been reported with a fractal dimension of around 2.0 (34), and aggregates of yeast formed in rotating test tubes were found to have a higher fractal dimension of D ) 2.66 (5). Biofilms in rotating biological contactors were found to have higher fractal dimensions, with values ranging from D ) 2.1-2.8 (6). The method developed here for the determination of D is an improvement on the existing methods. In comparison to the PSD slope-based methods (3, 18), the new method does not require a power law function for size distributions. Compared to the particle concentration technique (PCT) (21), the new method does not need the PSD to be measured by a (Coulter) particle counter in terms of the solid volume. In actuality, microbial flocs are highly porous and fragile; thus, the PSD given by a Coulter counter can be rather questionable (22). The fractal dimensions of a number of selected large AS flocs have been estimated in other studies based on the settling velocity distribution (24, 26) and the mass-size relationship (8, 23). However, as discussed, the D results may not be applicable to the entire population of sludge flocs over a wide size range. Direct observation of thin microtome sections of an object fixed in paraffin (27, 28) is another possible method of fractal analysis. However, the applicability of this sectioning method has not been examined for the characterization of highly fragile AS flocs because they could easily become compressed during a few steps of dehydration and other treatments involved in this method. Thus, in addition to its theoretical soundness, the new method is easier to use and produces more reliable results than other existing methods.
Acknowledgments This research was supported by Grants HKU7100/99E and HKU7114/04E from the Research Grants Council of the Hong Kong SAR, China. The technical assistance of Mr. K. C. H. Wong is highly appreciated.
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FIGURE 3. Ratio factor Γ(D) defined in eq 7 as a function of the fractal dimension for the laboratory sludge flocs produced at sludge retention times of 5, 10, and 20 days and the AS sample collected from the wastewater treatment plant. ages, the EPS production would be lower (20, 32, 33), which could allow close contact between cells through floc restructuring. Therefore, the AS flocs with SRTs of 10 and 20 2734
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Received for review June 3, 2004. Revised manuscript received December 18, 2004. Accepted January 18, 2005. ES049177+
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