Environ. Sci. Technol. 2002, 36, 387-393
Collision Frequencies of Microbial Aggregates with Small Particles by Differential Sedimentation XIAO-YAN LI* AND YUAN YUAN Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China
Collision and coagulation rates between microbial aggregates and small particles were measured for individual aggregates (1.0-2.5 mm) that settled through a suspension of fluorescent yellow-green (YG) particles (2.83 µm) placed in a settling column. The microbial aggregates, with an average fractal dimension of 2.26, were generated in a lab-scale sequencing batch reactor (SBR) and also collected from a full-scale activated sludge (AS) treatment system. As calculated from comparisons between the settling velocities observed and those predicted by Stokes’ law for impermeable particles, the average fluid collection efficiencies were 0.08 for the SBR aggregates and 0.14 for the AS flocs, which were much lower than those previously reported for nonbiological aggregates of latex microspheres. The collision frequency functions between microbial aggregates and small YG particles were 2 orders of magnitude lower than predicted by the rectilinear model but 1 order of magnitude greater than predicted by a curvilinear model. The overall scavenging efficiencies of suspended particles by the falling microbial aggregates compared well with those observed for the nonbiological aggregates, while the particle removal efficiencies from the flow internal to the microbial aggregates were 1 order of magnitude higher than those of the nonbiological aggregates. It is argued that the permeability of microbial aggregates could be reduced by exopolymeric material clogging the pores within the aggregates. The internal permeation through a bioaggregate thus may not be significant enough to be included in the calculation of its settling velocity; however, the intra-aggregate flow cannot be simply neglected where coagulation is concerned. Streamlines still can penetrate the interior of microbial aggregates, allowing greater collision frequencies with other particles than predicted by the curvilinear model. The narrow and convoluted internal flow passages resulting from the collection of extracellular polymeric substances may also contribute to the higher interior particle removal efficiencies of microbial aggregates than those of more permeable, nonbiological aggregates.
Introduction Particle coagulation and consequent sedimentation are important processes regulating the transport and removal of particulate matter in both natural waters and engineered treatment systems. The downward flux of organic carbon in * Corresponding author phone: +852-2859-2659; fax: +852-25595337; e-mail:
[email protected]. 10.1021/es010681d CCC: $22.00 Published on Web 01/04/2002
2002 American Chemical Society
the ocean, which is an important component of the global carbon cycle, mainly occurs through sedimentation of large aggregates of bacteria and phytoplankton (1, 2). During settling, marine aggregates continue to scavenge colloidal material and particles and thus increase the overall mass transport throughout the water column (3, 4). In engineered water and wastewater treatment processes, flocculant sedimentation is commonly used for removing particulate impurities and biomass. For example, bio-aggregates formed in activated sludge aeration tanks are separated from effluent in secondary clarifiers. Coagulation between falling flocs and suspended small particles plays an important role in controlling the effluent quality as well as the sludge flux in the clarifiers. Despite its practical importance, the kinetics of particle coagulation induced by differential sedimentation has not been well-described. While the conventional rectilinear model is known to overpredict particle collision frequencies (5-7), curvilinear models may underestimate the coagulation rates for large aggregates (2, 8-10). Particle aggregates in aqueous systems are not usually solid spheres but rather are highly amorphous, porous, and fractal (11-14). During settling, the open structure of fractal aggregates could allow a significant flow through the aggregates (15-17), resulting in higher collision frequencies between the aggregates and other particles than those predicted by curvilinear models for impermeable spheres (9, 10, 18). In a recent study, the coagulation between settling fractal aggregates (200-1000 µm) and suspended small particles (1.48 µm) was examined (9). The aggregates were produced from latex microspheres (2.84 µm) in a paddle mixer filled with a NaCl solution for particle destabilization. It was observed that these nonbiological aggregates were highly permeable, with an average fluid collection efficiency of around 0.5, and that they settled 2-3 times faster than predicated by Stokes’ law for impermeable but identical spheres. These microsphere aggregates had collision frequency functions more than 2 orders of magnitude lower than predicted from the rectilinear model but 1 order of magnitude higher than predicted using the curvilinear model of Han and Lawler (5). It is unclear, however, if these findings in terms of aggregate permeability and collision frequency function can be generalized to other types of fractal aggregates, such as the important microbial aggregates. The exopolymeric substances yielded by the microorganisms within bio-aggregates could fill in the pores of the aggregates, altering their internal permeation and associated particle capture efficiency. In a sheared fluid, bacterial fractal aggregates formed in the laboratory have been found to collide with small particles much faster than the curvilinear model would predict (2), behaving in a manner similar to that previously determined for nonbiological fractal aggregates (10). In the present study, using a quiescent settling column, we measured the collision frequencies between individual settling microbial aggregates and suspended small particles. The microbial aggregates were collected from a laboratory sequencing batch reactor and a full-scale activated sludge treatment process. The results in permeability and collision frequency function of the microbial aggregates were compared with those obtained for nonbiological microsphere aggregates by means of a similar experimental approach (9).
Methods Theoretical Section. Calculation of Collision Frequency Function. During free settling of a large aggregate, the rate VOL. 36, NO. 3, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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at which coagulation occurs between the aggregate, a, and smaller particles, p, can be written (9) as
Rc ) R(a,p)β(a,p)Np
(1)
where β(a,p) is the collision frequency function between the aggregate and small particles, R(a,p) is the corresponding collision efficiency, and Np is the number concentration of small particles. Several models have been developed to describe the collision frequency function with different levels of accuracy. The rectilinear model assumes that all small particles in the fluid approaching an aggregate will collide with it. According to this model, the collision frequency function between a large, fast-settling aggregate and much smaller, slow-settling particles can be calculated by
π βrec ) d2aU 4
(dp , da)
(2)
where da is the diameter of the aggregate and U is its settling velocity. In addition to the collisions induced by differential sedimentation, Brownian motion can also produce contacts between particles, particularly small ones. However, in the case of the present study, it has been found that Brownian motion could contribute to less than 1% of the total collisions between a settling aggregate and small particles examined, and the inclusion of Brownian motion has little effect on the calculation of the collision frequency function. The curvilinear collision model takes into account the hydrodynamic interactions and short-range forces between approaching particles, resulting in fewer collisions than predicted by the rectilinear model. The curvilinear βcur can be related to the well-defined βrec by a reduction factor, ecur, i.e.
βcur ) ecurβrec
(3)
Analytical solutions for ecur are not readily available. Using the numerical approach, Han and Lawler (5) proposed
ecur ) 10(a+bλ+cλ +dλ ) 2
3
(4)
where λ(e1) is the size ratio between the small and large particles concerned; coefficients a-d are the functions of a single dimensionless number, Ng ) 8A/(3πµd2aU), where A is the Hamaker constant, assumed here to be 4 × 10-20 J, and µ ) 0.0095 g cm-1 s-1 is the fluid viscosity. With a given Ng, coefficients a-d are similar to each other in magnitude. Thus, for collisions between large and small particles, e.g., λ < 0.1, eq 4 may be approximated to ecur ) 10a. On the basis of Han and Lawler’s numerical solutions for Ng < 0.01, the regression result gives a ) -1.45 + 0.268 log(Ng). Thus, it can be derived that
ecur ) 5.6 × 10-5(d2aU)-0.268
(5)
Substituting eq 5 in eq 3 produces
βcur ) 4.4 × 10-5(d2aU)0.732
(6)
Stokes’ Law for Impermeable Biological Aggregates. The terminal settling velocity, Us, of a single impermeable particle aggregate can be calculated using a generalization of Stokes’ law (13, 19) below for a wide range of Reynolds number:
[
]
4g(Fa - Fl)da Us ) 3FlCd
1/2
(7)
where Fa and Fl are the densities of the aggregate and liquid, respectively; g is the gravitational constant; and Cd is the 388
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empirical drag coefficient. The calculation of Cd may be obtained from Cd ) 24/Re + 6/(1 + xRe) + 0.4, where the Reynolds number Re ) FlUda/µ (15, 20). It is rather difficult to measure Fa of an individual aggregate in water. However, the dry mass of a large aggregate, Wd, can be measured directly by sophisticated instruments, such as the microbalance used in the present study. Assuming that the bacterial cells making up an aggregate have a (wet) density of Fc and a ratio factor of f between dry mass and wet mass, the actual volume of the cells within the aggregate is Wd/ (fFc). Thus, the porosity of the microbial aggregate becomes
)1-
6Wd
(8)
πfFcd3a
The overall density of the aggregate is a function of its porosity according to Fa ) Fl + (1 - )(Fc - Fl) (15). Substituting this correlation and eq 8 into eq 7, the settling velocity of the bio-aggregate predicted from Stokes’ law can be written as
Us )
[
(
)
1 Wd 8g 1 πf Fl Fc C d2 d a
]
1/2
(9)
It has been determined in a separate experiment that f ) 0.296 and Fc ) 1.06 g/cm3 for the bacteria composing the microbial aggregates (21, 22). Using these values, it can be calculated that activated sludge has a dry density of 1.25 g/cm3. All these figures are consistent with the data reported for the sludge flocs in activated sludge systems (23-25). Fractal and Permeable Aggregates. Biological aggregates are fractal (14, 26, 27), with their wet (cell) mass, Wc, scaling with size by a fractal dimension, D, through a formula Wc ) Wd/f∼dD a . The fractal dimension of aggregates can therefore be determined from the slope of a log-log plot of the paired values of dry mass and size. Fractal aggregates have D < 3 and a porosity increasing with size, in accordance with the relationship given in eq 8, i.e., 1 - ∼dD-3 . Internal flow a through the porous structure of fractal aggregates could reduce the drag force exerted on the aggregates, resulting in faster settling velocities relative to those predicted by Stokes’ law for impermeable particles. The aggregate permeability can be estimated from a comparison of the actual settling velocity measured, U, to that predicated by Stokes’ law, Us, using the correlation (9, 28-30)
U ξ 3 ) + Us ξ - tanh(ξ) 2ξ2
(10)
where the dimensionless permeability factor, ξ, is related to the aggregate permeability, κ, by ξ ) da/(2κ1/2) (17, 31). More directly, the extent of the permeability of an aggregate may be better indicated by its fluid collection efficiency, ef, defined as the ratio of the interior flow passing through the aggregate to the flow approaching it. The fluid collection efficiency is a solo function of ξ and can be calculated (9, 17, 18, 32) by
ef )
9(ξ - tanh(ξ)) 3
2ξ + 3(ξ - tanh(ξ))
(11)
Combining eqs 10 and 11 produces
ef )
9Us 2ξ2U
(12)
Flow through a porous fractal aggregate can increase its collision frequencies with suspended small particles as compared to those calculated using the curvilinear model for impermeable spheres. However, not all particles in the
fluid entering an aggregate will collide and attach to the aggregate. Defining ep as the removal efficiency of the particles from the intra-aggregate flow, the actual collision frequency function of the aggregate with small particles can be related to the rectilinear collision kernel (9) by
β)
efep β R rec
(13)
The product E ) efep is termed here as the aggregate’s overall small particle capture efficiency, which is the ratio of the particles scavenged by a settling aggregate to the particles approaching it based on the total volume of water swept out by the aggregate. There is no analytical solution of ep for particle aggregates. Conceptually, a model describing particle filtration by a porous medium can be used to analyze the attachment of small particles in the internal flow on the aggregate. According to the one-dimensional filtration equation of Yao et al. (33), the fraction of mono-sized small particles captured from the interior flow by the aggregate (3, 9) is
ep ) 1 - exp[-Rk(1 - )da]
(14)
where k is a filtration coefficient that relates to the aggregate structure and the transport process of the small particles concerned within the aggregate. The particle removal efficiency of the aggregate increases with the coefficient, k. Derivation of this coefficient is available in detail elsewhere (34, 35). Experimental Section. Microbial Aggregates. A laboratory sequencing batch reactor (SBR) 3.9 L in volume was used to generate SBR aggregates. The reactor was fed with an artificial wastewater with a BOD5 ∼160 mg/L containing nutrients from glucose and inorganic salts. During stationary operation, the SBR had a cycling time of 6 h and a sludge retention time (SRT) of around 15 days. Samples of biological aggregates were also collected from a full-scale activated sludge (AS) treatment plant. The AS system had an influent of domestic wastewater with a BOD5 ∼230 mg/L, a hydraulic retention time (HRT) of 12 h, and a SRT of approximately 15 days. As a pretreatment, flocculation of the diluted sludge sample was carried out in a paddle mixer (PB-700, Phipps & Bird) to form large aggregates. Detailed descriptions of the generation, collection, and handling of the microbial aggregates can be found elsewhere (21, 36). Settling-Coagulation Experiments. The experimental apparatus was made of glass and consisted of a settling column of 250 mm in height and 40 mm i.d., two valves, and a collector. The apparatus was assembled to form a concentric tube, while two valves, top and bottom, with opening holes of 6 mm in diameter were used to seal the column and prevent the convection of fluid in the column. During each run of the settling-coagulation experiments, an aggregate was introduced into the top of the column, which was filled with a suspension of small particles. Each valve was opened when the aggregate approached it to allow passage of the aggregate. A small cylinder collector 8 mm in diameter was inserted below the bottom valve for recovering the aggregate. YG fluorescent latex microspheres 2.833 µm in diameter with carboxylate surface groups (Polysciences) were used to make the diluted particle suspension. The concentrations of the YG beads, Np, were 6 × 104/mL for the experiments with the SBR aggregates and 4.6 × 104/mL for the AS aggregates. These latex beads had a density of 1.05 g/cm3 and a settling velocity in water as slow as 1 mm/h, much slower than those of the microbial aggregates. Thus, the small beads’ settling was negligible, and the particle solution was considered stable during the experimental period-usually less than 4 h, after which the solution was discharged and replaced.
After the settling apparatus was carefully assembled and filled with the particle suspension, one aggregate at a time was gently transferred to the top of the settling column using a rubber dropper bulb with a 1-mL pipet tip cut midway to provide a larger opening. The aggregate’s settling velocity within the 10 cm lower portion of the column was then measured. The aggregate, with the YG fluorescent beads attached, eventually fell into the bottom collector and was removed for subsequent analysis. To ensure that the free water within the bio-aggregates was exactly the same in density as that of the bead solution, prior to being introduced into the settling column, the aggregates were transferred in series through two beakers of water identical to that used for making the bead solution placed in the column. Aggregates that broke up during any transfer step were discarded. Aggregate Characterization. The technique for characterizing each recovered aggregate was similar to that detailed in Li and Logan (9), Yuan (21), and Yuan and Li (36). Briefly, the equivalent (projected area) diameter of the aggregate placed in the collector was measured using a microscope (BX60, Olympus) and an image analysis system (HLImage98, Imagraph). The number of YG fluorescent beads captured by the aggregate, Pc, was then counted under a fluorescent blue light. Following procedures similar to the measurement of suspended solids, the dry mass of the aggregate was determined using a microbalance (AEM-5200, Shimadzu) after the aggregate had been transferred on a polycarbonate membrane filter and dried completely. In addition to the dry weight of cells, this dry mass likely included the dry materials of exopolymeric substances bound with the cells and other particulate matter within the aggregate. Collision Frequency Function. The collision frequency function between the settling aggregate and small latex particles can be calculated (9) using
β)
P cU RHNp
(15)
where the effective coagulation length H ) 40 cm. Drawing on previous investigations (2, 37), R ) 0.5 was assumed here for the coagulation between the bacterial aggregates and YG microspheres. The overall small particle capture efficiency of the settling aggregates is
E)
Pc (π/4)d2aHNp
(16)
Results Fractal Dimensions of Microbial Aggregates. A total of 48 microbial aggregates generated in the lab SBR were successfully recovered during the settling-coagulation experiments and analyzed. The SBR aggregates varied in size from 1.0 to 2.5 mm, with the dry mass ranging from 6 to 59 µg (Figure 1). On the basis of the slope of the logarithmic relationship between dry mass and size, the SBR aggregates had an average fractal dimension D ) 2.26 ( 0.30 (the correlation coefficient r ) 0.83), indicating the fractal nature of microbial aggregates. The porosities of the SBR aggregates, ranging from 0.93 to 0.98, increased with the size of aggregates (Figure 1). In the case of the actual activated sludge collected from the treatment plant, 51 aggregates were recovered and analyzed. The AS aggregates were in the size range from 1.3 to 2.4 mm, with the dry mass ranging from 7 to 42 µg (Figure 1). They were porous and fractal with a fractal dimension D ) 2.26 ( 0.47 (r ) 0.73), which happened to be the same as that of the SBR aggregates. The aggregate porosities increased with size from 0.87 to 0.99. Permeabilities and Fluid Collection Efficiencies. The SBR aggregates had settling velocities in water varying from 0.16 VOL. 36, NO. 3, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Dry mass and average porosity as a function of size for the SBR and AS aggregates.
FIGURE 3. (A) Number of YG fluorescent beads captured by individual settling aggregates. (B) PcU/HNp as a function of the size of microbial aggregates.
FIGURE 2. (A) Settling velocities of microbial aggregates vs the predictions of Stokes’ law. (B) Fluid collection efficiencies calculated from measured settling velocities. to 0.49 cm/s (Figure 2A), while the corresponding Reynolds numbers were 1.9-12.3. The slope of the settling velocity related to the size after log-log transformation was 0.85 (r ) 0.71). The observed settling velocities were only slightly faster than those predicted for porous but impermeable particles using Stokes’ law for Re > 1. The AS aggregates’ settling velocities varied from 0.17 to 0.42 cm/s, with Reynolds numbers from 2.4 to 8.8. The slope of the settling velocity vs size was 0.94 (r ) 0.62). These aggregates settled in water just marginally faster than predicted by Stokes’ law (Figure 2A). The average ratios between observed and predicted settling velocities were 1.19 ( 0.18 for the SBR aggregates and 1.31 ( 0.20 for the AS flocs; both were much lower than the values previously reported for nonbiological aggregates (9, 15). The discrepancy between the observed settling velocities and those predicted from Stokes’ law did not appear to be significant for microbial aggregates. By comparing the actual settling velocity of an aggregate to the velocity predicted by Stokes’ law, the permeability of each individual aggregate can be estimated, using eq 10. As a more direct indication of permeability, the aggregate’s fluid collection efficiency was calculated (Figure 2B). The SBR aggregates had fluid collection efficiencies varying from 0 to 0.25 with an average of 0.08 ( 0.07. Slightly higher fluid 390
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collection efficiencies, ranging from 0 to 0.32 with an average of 0.14 ( 0.09, were observed for the AS aggregates. Both SBR and AS aggregates appeared to have their fluid collection efficiencies scattered over a wide range. However, considering the fact that actual bio-sludge aggregates were examined in the present study, the variation of data observed here was fairly acceptable. These bio-aggregates were not perfect selfsimilar fractals. The structure and hydrodynamic behavior may vary to a certain extent from one aggregate to another. Some aggregates could be more permeable than other similarly sized aggregates. In general, the fluid collection efficiencies of microbial aggregates did not change significantly with their size. Compared to nonbiological fractal aggregates (9, 15, 17), microbial aggregates were considerably lower in fluid collection efficiency. The settling behavior of the microbial aggregates apparently was not affected significantly by their internal permeation. It has been argued that extracellular materials produced by microorganisms could fill in the pores within microbial aggregates, resulting in a largely reduced permeability (38, 39). However, even limited intra-aggregate flow could still result in small particles being drawn into the aggregates, producing more particle collisions and attachment than predicted for impermeable spheres. Collision Frequency Functions. The number of small YG beads captured by the falling aggregates generally increased with the size of aggregates (Figure 3A). As the concentration of YG beads for the SBR aggregates (Np ) 6 × 104/mL) was 23% higher than that for the AS aggregates (Np ) 4.6 × 104/ mL), more YG beads were captured by the SBR aggregates than by the similarly sized AS aggregates. However, the coagulation data in terms of PcU/HNp (eq 15), in which the assumed collision efficiency factor, R, was not included, were related to size in a quite similar manner for both types of microbial aggregates (r ) 0.89 for SBR aggregates and r ) 0.69 for AS aggregates in Figure 3B). The collision frequency functions calculated using R ) 0.5 between microbial aggregates and YG beads were 1 order of magnitude higher than predicted by the curvilinear collision model and about 2 orders of magnitude lower than
through the aggregate interior was considered, the particle removal efficiencies were in the range from 0.0036 to 0.076 (average ) 0.021 ( 0.020) for the SBR aggregates and from 0.002 to 0.087 (average ) 0.014 ( 0.017) for the AS aggregates (Figure 5B). The majority of YG beads in the internal flow through an aggregate did not successfully attach to the aggregate; however, the particle removal efficiencies determined here for the microbial aggregates were about 5 times higher than those previously estimated for the microsphere aggregates with a similar fractal dimension of D ) 2.33 (9).
Discussion
FIGURE 4. Collision frequency functions measured vs those predicted by the rectilinear and curvilinear models for the microbial SBR and AS aggregates as compared to the previous results of Li and Logan (9) for the nonbiological aggregates of latex microspheres.
FIGURE 5. (A) Overall capture efficiencies of YG beads by the two groups of settling microbial aggregates. (B) YG bead removal efficiencies by the aggregates from the flow through the aggregate interior. predicted by the rectilinear model (Figure 4). Values of the collision frequency functions, ranging from 4 × 10-6 to 5 × 10-5 cm3/s, were fairly consistent for both SBR and AS aggregates (r ) 0.88 for SBR aggregates and r ) 0.69 for AS aggregates). Data obtained here for larger microbial aggregates compared well with the results of Li and Logan (9) for nonbiological aggregates of microspheres in the size range of 200-1000 µm. As anticipated, the rectilinear model overpredicts β, while the curvilinear model underestimates collisions since it does not include a mechanism for flow through the aggregate interior. Overall Particle Capture Efficiencies of Settling Microbial Aggregates. Overall capture efficiencies of the YG beads by microbial aggregates, based on the total volume of liquid swept out by a settling aggregate, varied from 0.0006 to 0.0028 (Figure 5A). The overall particle capture efficiencies decreased with the size of aggregates and showed no difference for the two groups of aggregates. These efficiencies were close in magnitude to those previously measured for nonbiological microsphere aggregates (9). When only the internal flow
Both the lab SBR aggregates and actual AS flocs had similar collision frequencies with suspended small particles. Measured collision frequency functions between microbial aggregates and YG beads increased with the size of the aggregates, as predicted by the rectilinear model and curvilinear model. However, the collision frequency functions were 1 order of magnitude greater than those predicted by the curvilinear model for impermeable particles. A small degree of intra-aggregate flow allowed by the microbial aggregates would bring small particles into the interior of aggregates, permitting internal as well as external collisions. In addition, the fractal nature of microbial aggregates resulted in a larger surface area per projected area than that of a sphere of corresponding size. The larger and rough surface area, combined with the internal permeation, produced more attachments of small particles on the microbial aggregates than predicted by the curvilinear model (2). The collision frequency functions determined for the microbial aggregates during settling compared well with the results reported by Li and Logan (9) for smaller aggregates (0.2-1.0 mm) of latex microspheres (Figure 4). Similar conclusions have been obtained by Serra and Logan (2) for the coagulation of bacterial aggregates with small beads in a sheared fluid as compared to the coagulation previously observed between nonbiological aggregates and small particles (10). The microbial aggregates, however, were in general not as permeable as the nonbiological microsphere aggregates. Those nonbiological aggregates, with a fractal dimension of D ) 2.33, had an average fluid collection efficiency of 0.46 in comparison to the efficiencies of 0.08 determined here for the SBR and 0.14 for the AS aggregates. Although microbial aggregates are highly porous and fractal, they probably have a more complex structure than that of the aggregates of latex microspheres. Extracellular polymeric substances produced by microorganisms could form a matrix frame for the bioaggregates and clog the large pores within the aggregates (38-41). This exopolymeric material has great surface tension for water retention, reducing to a large extent the permeability of microbial aggregates. Nonetheless, the limited permeability still allowed streamlines to penetrate the aggregates (2, 16, 42), promoting higher numbers of particle collisions than those predicted for impermeable objects. For the small YG beads in the intra-aggregate flow, the microbial aggregates had particle removal efficiencies (average ∼0.02) 1 order of magnitude higher than those previously determined for nonbiological aggregates (average ∼0.002). A higher collision efficiency of R ) 0.5 assumed here between the bacteria and the beads, compared to that of R ) 0.237 used previously for collisions between latex microspheres, could partially contribute to the higher particle removal efficiency from the internal flow by the microbial aggregates. More importantly, the difference in particle removal efficiency between the microbial aggregates and the nonbiological aggregates can be explained by the filtration process of internal flow through the aggregates. The nonbiological microsphere aggregates were more porous and permeable. Macropores formed within fractal aggregates can account for the greater fluid collection efficiency and internal flow VOL. 36, NO. 3, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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rate, but the large pore size means that most small particles in the intra-aggregate flow pass through the aggregates without contacting the material making up the aggregates. In the case of microbial aggregates, the pores may be filled by sticky polymeric material, resulting in a much lower fluid collection efficiency. However, the flow path for fluid passing through an aggregate may become narrow and winding, producing more contacts and attachments between the suspended particles in the internal flow and the microbial aggregates than occur with nonbiological aggregates. The filtration coefficient, k, used in the filtration model of eq 15 could be greater for microbial aggregates with a more complicated and less permeable interior structure than that of nonbiological aggregates, which results in a higher particle removal efficiency from the internal flow. In summary, microbial aggregates are highly porous and fractal. However, their fluid collection efficiencies were much lower than those determined for nonbiological fractal aggregates. The permeabilities of microbial aggregates were probably reduced by the exopolymeric material produced by microorganisms within the aggregates. However, the importance of internal permeation for particle coagulation cannot be simply neglected for microbial aggregates. Collision frequencies between settling microbial aggregates and suspended small particles were an order of magnitude greater than those predicted by a curvilinear model. Limited permeability still allows fluid to penetrate into bio-aggregates, producing higher particle collision and coagulation rates than those calculated for impermeable spheres. Therefore, the scavenging of suspended particles by settling microbial aggregates could play an important role in the vertical transport of particulate matter in both sedimentation tanks and natural water bodies.
Acknowledgments This research was supported by Grant HKU7010/97E from the Research Grants Council of Hong Kong SAR, China.
Notation R
collision efficiency
β
collision frequency function
βcur
collision frequency function predicted by a curvilinear model
βrec
collision frequency function predicted by a rectilinear model
λ
size ratio between two approaching particles
ξ
dimensionless permeability factor
κ
permeability
µ
fluid viscosity
aggregate porosity
Fa
density of an aggregate
Fc
wet density of individual cells
Fl
density of a liquid or water
A
projected area of an aggregate, Hamaker constant
Cd
empirical drag coefficient of a particle
D
fractal dimension
da
diameter of an aggregate
dp
diameter of a particle
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E
overall particle capture efficiency
ecur
curvilinear reduction factor relative to the rectilinear collision kernel
ef
fluid collection efficiency
ep
particle removal efficiency from the intraaggregate flow
f
ratio of dry mass to wet mass of bacterial cells
g
gravitational constant
k
filtration coefficient used in eq 14
Ng
dimensionless number used for the calculation of ecur in eq 4
Np
particle number concentration
Pc
number of small particles captured by an aggregate
r
correlation coefficient of a curve fit
Rc
coagulation rate between an aggregate and small particles
Re
Reynolds number
t
time
U
terminal settling velocity
Us
settling velocity predicted by Stokes’ law
Wc
(wet) cell mass within a microbial aggregate
Wd
dry mass of a microbial aggregate
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Received for review February 26, 2001. Revised manuscript received September 20, 2001. Accepted October 19, 2001. ES010681D
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