Efficiency of different shear devices on flocculation

Transcription

1 Available at journal homepage: Efficiency of different shear devices on flocculation Teresa Serra a,, Jordi Colomer a, Bruce E. Logan b a Department of Physics, University of Girona, Campus de Montilivi, Girona, Spain b Department of Civil and Environmental Engineering, Pennsylvania State University, University Park, PA 16802, USA article info Article history: Received 16 May 2007 Received in revised form 9 August 2007 Accepted 27 August 2007 Available online 7 September 2007 Keywords: Aggregation Shear Couette Paddle mixer Fractal dimension Oscillating grid abstract Various types of coagulation devices have been used to study aggregation, with the goal of understanding aggregation dynamics in natural and engineered systems. Three different devices were investigated here (paddle mixer, oscillating grid and Couette) to examine the effect of different laboratory devices on the particle size spectra over a wide range of shear range values (G ¼ s 1 ) at four different initial volume concentrations (f 0 ¼ , , and ). For each device there was maximum aggregate size produced at each shear rate, with three distinct zones observed depending on the magnitude of G. At low shear rates (Go20 s 1 ), mean particle diameter increased with G, showing that aggregation dominated over breakup. At intermediate shear rates (20 s 1 ogo30 s 1 ), flocculation rates were maximized, producing the largest flocs. At higher shear rates (G430 s 1 ), the dominant effect of breakup was shown through reduced maximum floc sizes with increasing shear rates. Fractal dimensions of aggregates from the paddle mixer and oscillating grid, calculated using cumulative size spectra and assuming pseudo-steady-state conditions, were typical of aggregates formed by reaction-limited conditions or those compacted by aggregate reformation (D ¼ ). Fractal dimensions for the Couette flow device were extremely low and less than unity (D ¼ ), indicating that this method of calculating D could not be used for conditions produced in this device. The paddle mixer and the oscillating grid produced almost identical maximum diameters of the suspension under pseudo-steady-state conditions for all initial volume fractions, but the Couette device consistently produced larger diameter flocs at the same average shear rates and the maximum size of the aggregates increased with the volume concentration. These results indicate that even at low shear rates aggregate formation was influenced by breakup. It is therefore concluded that the Couette device is the most useful method for forming aggregates that are least influenced by breakup processes during aggregate formation. & 2007 Elsevier Ltd. All rights reserved. 1. Introduction The removal of particles from a suspension by sedimentation following flocculation is a basic process for water treatment. Coagulation of small particles into larger aggregates requires increasing the collision frequency between particles and minimizing breakup. Particles formed by coagulation are not uniform in size, but rather can vary over a wide range. Maximizing the size of these particles is important to obtain fast-settling particles while at the same time minimizing hydraulic retention time. In natural systems (such as a lake, river or ocean), suspended particles like phytoplankton, marine snow or lake snow are also formed by differential settling and shear coagulation (such as wind, waves or Corresponding author. Fax: address: teresa.serra@udg.es (T. Serra) /$ - see front matter & 2007 Elsevier Ltd. All rights reserved. doi: /j.watres

2 1114 shearing layers), although mean shear rates are much lower than those in engineered systems. These large aggregates can settle out faster than the smaller particles they were formed from, enhancing the transport of carbon throughout the water column to the sediments. In addition, fast-settling aggregates can scavenge fine picoplankton cells (Waite et al., 2000), thus accelerating the rate of sedimentation of other particles in the water column. The first step in the coagulation process is dominated by a rapid initial growth rate in the mean diameter of the particles. During this initial time period, if particles are fully destabilized they aggregate as soon as they come into contact. As coagulation continues, aggregates become larger and have more tenuous and fragile structures that are susceptible to breakup by fluid shear. In this stage of the process, there are now fewer but larger particles, and the growth rate of particle size slows. Finally, the particle size distribution reaches a pseudo-steady state, where breakup balances aggregation, and size spectra is essentially constant (Oles, 1992; Spicer and Pratsinis, 1996; Serra et al., 1997). Serra et al. (1997), Oles (1992) and others have found that the larger the shear the smaller the average aggregate size (d ss ) under steady-state conditions. However, only shear rates above 25 s 1 were examined. At these shear rates, an increase in the shear rate breaks aggregates and gives a particle size distribution dominated by aggregates with smaller diameters. Colomer et al. (2005) used lower values of the shear rate (from 0.5 to 27 s 1 ) generated by both an oscillating grid and a flask on a shaker table. Under these conditions, they found that the larger the shear, the larger the value of d ss. This suggests that each device has a shear rate for which there is a transition from aggregation dominated conditions to breakup dominated conditions. It is not clear, however, when this transition occurs in different coagulation devices. Different types of shear devices have been used to study aggregation rates and the characteristics of aggregates formed during coagulation. Paddle mixer or jar test devices (Spicer and Pratsinis, 1996; Li and Logan, 1997; Serra and Logan, 1999) and Couette flow devices (Oles, 1992; Serra et al., 1997) are most commonly used. In the studies cited, only shear rates above G ¼ 25 s 1 were examined. Except for the study by Spicer et al. (1996) where the effect of different impellers were examined, there are few studies that have compared aggregates formed in different flocculation devices. Spicer et al. (1996) found only slight differences between aggregates obtained from different impellers. Logan and Kilps (1995) compared fractal dimensions of aggregates formed with a paddle mixer under a shear flow of G10 s 1 with aggregates formed in a rolling cylinder. They examined the fractal dimensions of the particles formed, not the sizes of particles formed, and concluded that the fractal dimensions were a function of the two different fluid mechanical environments and the method used to calculate the fractal dimension. Several studies (Hunt, 1980; Jackson et al., 1995; Li et al., 1998) have demonstrated that the particle size distribution may be fitted by a power law function, N(l)l b, where N(l) is the cumulative number concentration and b is the slope of the particle size distribution. The value of b varies over the range of 1.5 to 4.0 depending on the coagulation mechanism (Brownian, shear or differential sedimentation). In nature, environmental conditions may shift from one coagulation mechanism to another, which can affect the particle size distribution and the value of b. Numerical models that include the fractal structure of aggregates have been proposed in order to predict the evolution of a particle size distribution under different experimental conditions (Li et al., 2004; Zhang and Li, 2003). The purpose of this study was to examine particle coagulation in three different devices (paddle mixer, oscillating grid, and laminar shear in a Couette flow device), over the same range of shear rates, in order to evaluate coagulation efficiency in terms of size spectra and maximum particle sizes. We were particularly interested in determining how an increase in the shear rate affected mean particle size for the different devices. This topic has important implications for particle and sediment transport in aquatic systems. 2. Methods 2.1. Particles Suspensions of latex particles were prepared in 1.29 M NaCl solution in ultrapure water (Milli-Q-Water, Millipore, Bedford, MA) at different initial particle volume fractions, ranging from f 0 ¼ to , corresponding to a mass concentration from 21 to 105 mg L 1. Suspensions were sheared in the range of G ¼ s 1. Ranges of both G and f 0 were chosen to be as wide as possible, within the limits of the lower limit of the speed of the rotating motor and the maximum measurable particle concentrations of the laser analyzer. Latex particles were used having a diameter of mm (Interfacial Dynamics Corporation, Portland, OR). To avoid sedimentation in the reactors, the solution density was set at the same density as the latex particles (1.055 g cm 3 ). As a result of this salt addition, the electric double layer was highly reduced to an approximate value of the Debye Hückel length of 10 8 m, and thus particles were completely destabilized Experimental devices Under the conditions examined here, aggregate formation by Brownian motion was negligible. This is shown by a high Peclet number (20 474), where the Peclet number is the ratio of viscous to thermal forces or Pe ¼ 6pZGr 3 0 /KT, where Z is the dynamic viscosity of the fluid, r 0 the particle radius, K Boltzmann s constant and T the water temperature. A schematic of the oscillating grid system is shown in Fig. 1a. The oscillating grid device consisted of a PVC box of interior dimensions cm 3, with a plastic grid fitted at the bottom of the tank at a distance of 4.5 cm from the bottom. The grid was made of 1 cm thick square bars with a mesh spacing of size M ¼ 5 cm, and a porosity of 67% (based on area), with the stroke fixed at s ¼ 5 cm. With this set-up, the oscillating grid was always switched on with the grid situated at its lower position, 2 cm from the bottom tank, defined here as the virtual origin, z 0. The grid was set at an oscillation frequency of f ¼ Hz using a variable speed

3 1115 R 2 Controller motor S (rpm) R 1 h s z 0 Controler motor f (s -1 ) d p y Controller motor ω (s -1 ) r b Fig. 1 Schematic view of the shear devices used in this study: (a) the oscillating grid, where h is the height of the working fluid inside the system, s is the stroke of the grid situated at the bottom and f is the grid frequency. (b) A paddle mixer with a paddle of d p ¼ 75 mm and y ¼ 25 mm, where S p is the paddle rotation speed. (c) A Couette flow system with the outer cylinder rotating at a certain angular velocity (x). The radius of the inner cylinder is R 1 ¼ 41 mm and radius of the outer cylinder is R 2 ¼ 45 mm. motor. The depth of the working fluid (h) was considered to be from 15 to 28 cm. The rectilinear oscillating motion of the grid was ensured by constraining the connecting rods to move along a guide rail using precision bearings (Srdic et al., 1996). In the design of the apparatus, precautions were taken to minimize non-homogeneities and secondary circulation in the tank, as described in Fernando and DeSilva (1993) and Cheng and Law (2001). Also, the grid arrangement was further improved by designing its end as half of one of the squares, and in that situation the wall of the tank would be the position of the end of the square of the grid (i.e. the distance between the end of the grid and the wall of the tank is equal to half a square of the grid). With this set-up we effectively avoided unexpected secondary walls (Cheng and Law, 2001). The gap between the ends of the grid bars and the walls was set up as small as possible (2 3 mm) to further avoid undesirable influences of the end condition (E and Hopfinger, 1986; Cheng and Law, 2001). The fundamental theory of grid turbulence is based on measurements that consider a special decay of the horizontal root-mean-square (r.m.s.) turbulence velocity u of the form upz 1, where z is measured from z 0, which coincides with the grid mid-plane (Thompson and Turner, 1975; Hopfinger and Toly, 1976; E and Hopfinger, 1986). Variations in the horizontal and vertical r.m.s. velocities (u 0 and w 0, respectively) and the integral length scale l 0 of turbulence with distance z (measured from z 0 ) can be expressed as u 0 ¼ C 1 s 3=2 M 1=2 fz 1, (1) w 0 ¼ C 2 s 3=2 M 1=2 fz 1, (2) l 0 ¼ C 3 z, (3) where C 1 ¼ 0.22, C 2 ¼ 0.25 and C 3 ¼ 0.10 are constants (Hopfinger and Toly, 1976; DeSilva and Fernando, 1994). The subscript 0 is used to denote properties of stationary turbulence. The average volume turbulent parameters, i.e., energy dissipation rate e and velocity gradient G, are calculated (Tennekes and Lumley, 1972) as z ¼ g u03, (4) l rffiffi G z ¼, (5) n where g is generally taken equal to 0.8, l is the integral length scale with distance from the grid and u 0 is the integral velocity. Considering Eqs. (1) (3) and assuming that u 0 will be proportional to u 0, and that l will be proportional to l 0, Eq. (5) leads to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi G ¼ g C 3 s 9=2 M 3=2 f 3 2, nc 3 (6) z 4 which can be rewritten by substituting all the constants and using n ¼ m 2 s 1 and s ¼ M ¼ 5 cm: G ¼ 0:0458 f 3=2 z 2. (7) From this equation, we can estimate a maximum value of the shear of 410 s 1 at the center of the stroke, that is for z ¼ M/2 ¼ 2.5 cm. The mean shear rate in the fluid can be calculated taking the average of G (Eq. (7)) over the depth from z ¼ z 0 to h as follows: G ¼ 1 Z h 0:0458 f 3=2 z 2 dz ¼ 0:0458 f 3=2 ðhz 0 Þ 1. (8) h z 0 z 0

4 1116 Table 1 Ranges of G and Re for the three different devices For the f and h values considered, G was found to be in the range from 5 to 76 s 1. The Reynolds number of the grid can be estimated with Re G ¼ u 0 l 0 /n, and Eqs. (1) and (3) as Re G ¼ C 1C 3 s 3=2 M 1=2 f n ¼ 147:45f. (9) Thus, Re G is not a function of the distance from the grid to the bottom of the tank, and Re G ranges from 74 to 737 depending on the value of f, corresponding in all the cases to the turbulent regime. The paddle mixer consisted of a 1 L beaker and a single rectangular stirring paddle of 75 mm 25 mm (Fig. 1b). The beaker was filled with 800 ml of water. The average shear rate was calculated using the correlation of Li and Logan (1997) developed for the same conditions, of log G ¼ log S p, where S p is the paddle rotation speed in rpm. S p ranged from 12 to 123 rpm, producing shear rates of s 1. The Reynolds number for the paddle is Re p ¼ S p d p 2 /n (see Table 1 for values), where d p ¼ 75 mm is the paddle diameter, and S p is in rad/s, producing values of Re p in the range of ,700, corresponding to turbulent mixing. The Couette flow device consisted of two concentric cylinders (Fig. 1c) as previously described by Jiang and Logan (1996), with an inner cylinder radius of R 1 ¼ 41 mm and an outer cylinder radius of R 2 ¼ 45 mm, and a cylinder height of 153 mm. The outer cylinder was rotated at an angular velocity o that ranged from 0.9 to 9.3 rad s 1. The average shear rate for this system (Oles, 1992; Serra et al., 1997) is G ¼ 2oR 1R 2 R 2 2 (10) R2 1 producing shear rates of s 1. The Reynolds number is calculated as Re C ¼ or 1 (R 2 R 1 )/n (Peters and Redondo, 1997), which produces here Re C ¼ 176o or Re C X132 (see Table 1), indicating turbulent flow (Tritton, 1988) Measuring technique G (s 1 ) Couette flow Paddle mixer ,700 Oscillating grid Each experiment was run for a period larger than t* ¼ tgf 0 ¼ 25. After this time we assumed that the system had reached a pseudo-steady state (Spicer and Pratsinis, 1996; Serra et al., 1997; Colomer et al., 2005). At this time, 10 samples (5 ml each) were taken using a pipet tip cut at midlength (to provide a larger opening to avoid aggregate disruption) and analyzed using a laser particle size analyzer (Cis-1, Galai Industrial zone 10, 500 Migdal Haemek, Israel). The particle size analyzer uses a measuring cell stirred with a small magnetic stirrer situated at the bottom to homogenize Re the sample and maintain particles in suspension. The magnetic stirrer has three different speeds. Different measurements of the same sample were done over time to determine if stirring disrupted aggregates. For the two slowest speeds we did not observe any changes over time, indicating that detectable particle breakup was not occurring as a result of stirring the sample. All measurements were done at the slowest speed of the stirrer. To measure the particle sizes the device uses a rotating laser that scans the samples: the interaction of the laser and the particle gives a pulse with a width proportional to the particle size. This scattering technique only affects the pulse amplitude and therefore it is not necessary to know the refractive index or the particle s light absorption characteristics. This is an advantage compared with other techniques that use diffraction analysis. Aggregates formed with an initial particle volume concentration larger than could not be measured because the solution was opaque to the laser beam. When the suspension of particles to be measured is below this maximum concentration, the instrument keeps measuring particles until a 95% confidence level is achieved. The median particle size, obtained from a volume-based size distribution, was considered to be the characteristic diameter of the aggregates Aggregate fractal dimensions The fractal dimension (D) of aggregates provides information on the relative compactness of the structure, with nearly spherical objects having values typically greater than 2.5 and more tenuous-shaped objects with values of Do2 (Lick and Lick, 1988; Spicer et al., 1996). In this study, D was calculated using a steady-state size distribution method developed by Jiang and Logan (1991). When shear coagulation dominates particle aggregation, the particle size distribution scales with n(l) (the number of aggregates of length l per unit volume) scales, with l according to nðlþl ðdþ5þ=2. (11) Alternatively, the size distribution can be described using a cumulative size distribution where N(l) (the cumulative number of particles larger than l) scales with l according to NðlÞl b l ðdþ3þ=2. (12) Thus, D can be calculated from the slope of a plot of log n(l) or N(l) versus log l. Eq. (12) was used here for the calculation of D as this method uses a slope with less data scatter due to particle concentrations that are substantially different in adjacent size intervals (Logan, 1999) Floc strength The relative cohesiveness of the particles, or the floc strength, was evaluated using the method of Jarvis et al. (2005). The diameter of the aggregates under steady-state conditions (d ss ) is normalized by the diameter of the primary particles (d 0 ) and plotted as a function of G, ord ss /d 0 ¼ CG g. The exponent g is the stable floc size exponent and C is the floc strength coefficient (Jarvis et al., 2005). The steeper the slope, the

5 1117 greater the reduction in the floc size, and therefore g can be used as a measure of the floc strength. 3. Results The diameter of the aggregates formed under steady-state conditions (d ss ), normalized by the diameter of the particles forming the aggregate (d 0 ), was measured for the various initial concentrations (f 0 ) and shear rates (G). For all three types of flocculators, the dimensionless particle diameter (d ss /d 0 ) increased with G up to 20 s 1 (Fig. 2). For shear rate values between 20 and 30 s 1, d ss /d 0 reached a maximum, and at higher shear rates the maximum particle size decreased. Based on these results we defined three ranges: an optimum flocculation range of s 1 (rapid flocculation and minimum breakup); a breakup dominated range for G430 s 1 ; and an aggregation dominated range for Go20 s 1. In contrast to the results found with the other devices, the oscillating grid seemed to require a minimum shear rate (G416 s 1 )above which flocculation became important (Fig. 2a). Below this critical value of G, aggregation was minimal. In addition, experiments performed at different f 0 values with both the oscillating grid and the paddle mixer did not show appreciable differences in the values of d ss /d 0 for the same G. In contrast, with the Couette flow system an increase in f 0 resulted in increased values of d ss /d 0 at all values of G. There was a maximum of d ss under steady-state conditions (Md ss ) for all conditions examined. This maximum value was always observed at shear rates of G ¼ s 1. In some experiments Md ss was a function of f 0 (Fig. 3). For the oscillating grid and paddle mixer, Md ss had values between 15 and 20 d 0 (Fig. 3). In contrast, for the Couette flow system, Md ss increased with f 0, producing values of Md ss ranging from 20 to 35 d 0. The slope of Md ss versus f 0 is for the results obtained with the Couette flow system, which indicated a considerable increase of Md ss with f 0. The results from the curves shown in Fig. 2 also indicated that there are two possible values of the shear rate (one situated at each side of the maximum of the curve) that can give the same value of d ss. Since the value of d ss comes from the median of the particle size distribution, we expect to find similar particle size distributions associated with these shear rates. This fact can be easily seen in Fig. 4. Fig. 4a represents the particle size distribution in the steady state attained with different shear rates (G ¼ 20 and 35 s 1 ) with the paddle mixer device for f 0 ¼ Similar particle size distributions Fig. 2 Non-dimensional sizes of the particle size distribution (d ss /d 0 ) versus the shear rate under pseudosteady-state conditions for different values of the initial particle volume concentration (/ 0 ) attained with (a) the oscillating grid, (b) the paddle mixer and (c) the Couette flow system. Fig. 3 Maximum values of d ss (Md ss ) from the curves in Fig. 3 for each value of / 0 and for each flocculator.

6 1118 Fig. 5 Log log plot of N(l) versus l for the experiments carried out with the oscillating grid, paddle mixer, and the Couette flow device. Dots represent the average over all the experiments performed with each flocculator. Error bars represent the standard deviation of each point. Fig. 4 Particle size distributions under pseudo-steady-state conditions with different shear rates and with similar values of d ss. (a) Particle size distributions for / 0 ¼ and for G ¼ 20 and 35 s 1 with d ss ¼ 27.7 and 23.7 lm, respectively, both experiments were performed with the paddle mixer. (b) Particle size distributions for / 0 ¼ and for G ¼ 14 and 48 s 1 with d ss ¼ 40.0 and 40.8 lm, respectively, both experiments were performed with the paddle mixer. have also been obtained for G ¼ 14 and 48 s 1 for f 0 ¼ with the Couette device (Fig. 4b). From plots of N(l) versus l, the slope of the particle size distribution was for both aggregates in the paddle mixer and the oscillating grid, and for the Couette flow system. From this slope, fractal dimensions of D ¼ were obtained for the paddle mixer and oscillating grid, and D ¼ for the Couette device (Fig. 5). Data for particles less than l ¼ 6 mm were omitted due to the sharp change in slope observed in Fig. 5, and the relatively small aggregate size relative to the primary particle size (i.e. l/l 0 ¼ 3). 4. Discussion Coagulation experiments demonstrate that there were three different ranges for particle formation: low shear (Go20 s 1 ), which was the aggregation-dominated range; mean shear (G ¼ s 1 ), where flocculation rates were maximized and breakup minimized; and G430 s 1, where particle breakup dominated. In the aggregation-dominated range, aggregates size increased in proportion to the shear rate, but resulted in particle sizes that were limited by low particle collision rates of larger particles with other particles. Although breakup was probably occurring, it can be considered relatively unimportant to the overall aggregate sizes. In the breakup-dominated size range, there were sufficient collisions to make larger particles, but these particles were not stable due to breakup. The maximum size of the aggregates produced in these experiments depended on f 0 and the type of device. Both the paddle mixer and grid devices produced maximum particle sizes (Md ss ) nearly independent of f 0, while the Couette device produced the largest aggregates and aggregates that increased in size with f 0. The reasons for these differences can be found in the hydrodynamics of the flow in each system. Coufort et al. (2005) evaluated the hydrodynamics of the paddle mixer and Couette systems. They found that the mean size of the Kolmogorov microscale (Z) was smaller in the paddle mixer than in the Couette device for all the shear rates (see data from Tables 1 and 2 in Coufort et al., 2005 plotted in Fig. 6). Coufort et al. (2005) stated that the flow in the paddle mixer was non-uniform, and that in the impeller zone the turbulent kinetic energy was highly dissipated, while outside this zone the turbulent kinetic energy was found to be smaller. This produced a bimodal distribution of the turbulent kinetic energy in the reactor. In contrast, Coufort et al. (2005) claimed that in the Couette flow system, the distribution of the turbulent kinetic energy was relatively uniform throughout the system, with the largest values found only in a small region (1 mm thick) near the wall of the rotating cylinder. Their results reveal that low values of Z are less probable for the Couette system than for the paddle mixer. Furthermore, results from Coufort et al. (2005) indicated that for a certain shear rate (i.e. for a certain value

7 1119 Fig. 6 Values of the mean size of the eddy distribution found by Coufort et al. (2005) compared with values obtained here with the paddle mixer and the Couette flow systems. of the dissipation rate, e) different distributions of Z can result when using different shear devices, giving also different mean values of Z. Thus, we can expect that the final particle size spectra will be determined by the distribution of Z in different mixing devices. The slopes of the particle size distributions ( 2.6 for the paddle mixer and the oscillating grid and 1.9 for the Couette device) observed here were in a range similar to those reported by others (from 1.5 to 4.0; Jackson et al., 1995; Li et al., 1998) for aggregates generated in shear devices. A fractal dimension of D ¼ 2.2 was calculated for the aggregates produced in the paddle mixer and the oscillating grid system using b ¼ 2.6, which is similar to fractal dimensions reported by others in tests using paddle mixers. For example, a value of D ¼ 2.5 was reported by Spicer et al. (1998) for aggregates of polystyrene particles generated by a paddle stirrer. Oles (1992) reported the same value of the fractal dimension for the steady state of the aggregates obtained by a Couette flow system. However, the value of D ¼ 0.9 obtained for the Couette device is unreasonably low, and substantially lower than that reported by others. For example, Serra and Casamitjana (1998) found a value of D ¼ for aggregates of latex particles produced in a Couette flow device. However, both Serra and Casamitjana (1998) and Oles (1992) used only larger shear rates (above 25 s 1 ) than those examined here, and therefore they examined different particle sizes and likely more compact structures (i.e. larger D values due to the higher shear rates) than particles produced here. The very low value of D obtained using the Couette device suggests that the assumption of a pseudo-steady state (as it is defined for the approach of Jiang and Logan, 1991) was not valid for our experimental conditions with the Couette device. A much longer period of time was needed to obtain constant size spectra for the Couette device than for the other two systems. In addition, particles that settle out in the Couette device are not resuspended as they are in the other devices. Thus, while the particle size spectra may have reached a steady-state condition (i.e. time-invarient slopes), the assumptions needed to derive a fractal dimension from the slope of this spectrum were not met. In such cases where the steady-state assumption fails, other methods that do not require the assumption of steady-state conditions are needed to obtain D, such as the two-slope method. Logan and Kilps (1995) calculated the fractal dimensions of aggregates formed under a laminar shear (10 s 1 ) in a paddle mixer using both the steady-state and two-slope methods. They found that the steady-state method using aggregate size (l) in a cumulative size spectra produced a lower value of D ¼ 1.35 than the twoslope method which produced a value of D ¼ 1.92 for the paddle mixer. It is concluded from their results, and the values for D obtained here, that the steady-state method was not a reliable method to determine D here for conditions produced in the Couette device. Other methods to determine D, such as the two-slope method, could not be used as it requires additional data on aggregate mass that were not available here. Aggregates formed at a specific value of G in the Couette flow system were less subject to breakup than in the other two devices. The turbulence close to the paddle will be larger in the paddle mixer than the turbulence at any location in the Couette device. This is related to the fact that the smaller values of Z were found by Coufort et al. (2005) in the paddle mixer when compared with those found in the Couette device (Fig. 6). This will result in a stronger breakup of the aggregates Fig. 7 Non-dimensional size in the steady state (d ss /d 0 )asa function of G for the three different experimental devices used: the paddle mixer, the oscillating grid and Couette.

8 1120 Table 2 Values of C and c corresponding to the curves shown in Fig. 7 Coagulation device Log (C) g R 2 Paddle mixer Oscillating grid Couette flow (for f 0 ¼ ) The third column indicates the value of the correlation coefficient for each curve. in the paddle mixer than those in the Couette device. In the breakage-dominated region, d ss /d 0 can be compared with G to determine g. The results obtained here show the largest decrease of log(d ss /d 0 ) and log G for the oscillating grid and the smallest for the Couette device when using f 0 ¼ (Fig. 7). Values of g calculated with the adjustment between log(d ss /d 0 ) with log G are listed in Table 2. We can see that value of g for the paddle mixer is close to those values already found by other authors and summarized in the review of Jarvis et al. (2005). However, the value of g obtained for the oscillating grid were among the largest, showing the strong shear effect on the aggregates of an increase of G in such experimental configuration. Values of g are low for the Couette device, indicating that aggregates formed in this device are less subject to breakup than those in the other two systems. 5. Conclusions Coagulation experiments carried out under different initial particle volume concentrations (f 0 ) and under different shear rate values (G) by three different devices were investigated. The diameter of the particle size distribution at the steady state at each shear rate was investigated and three different zones were found depending on the G values. At low shear rates (Go20 s 1 ), the mean particle diameter increased with G; in this case the aggregation dominated over breakup. At intermediate shear rates (20 s 1 ogo30 s 1 ) flocculation rates were maximized, producing the largest flocs. For large shear rates (G430 s 1 ) breakup dominated over aggregation. In the last case, an increase in the shear rate caused a reduction in the mean particle size. Although the paddle mixer and the oscillating grid produced almost equal mean particle size diameters at the same shear rate values, the Couette device gave large aggregates. Therefore, the Couette device is the most efficient method for forming aggregates, which will be least influenced by breakup. Acknowledgments We would like to thank Guillem Ciurana for his technical support with the oscillating grid, and Marianna Soler, Florian Córdova and Mathieu Guerin for their help in taking some measurements during the experimental work Implications for particle formation in natural systems Contrary to the traditional acceptance that turbulence maintains particles in suspension in the water column, Ruiz et al. (2004) recently found that turbulence increases the average settling velocity of phytoplankton cells. From the results found in the present study, if phytoplankton cells aggregate under conditions of Go30 s 1 (or a value of the energy dissipation rate of e ¼ G 2 n ¼ m 2 s 3 ) an increase in G will form aggregates more rapidly, and produce aggregates with larger average sizes. The formation of larger aggregates will then increase the overall mass sedimentation rate. If G430 s 1, an increase in the shear will produce breakage and the size of the aggregates in the steady state will decrease, resulting in a reduction in the settling velocity. However, in lakes, e has values that range from 10 6 m 2 s 3 (i.e. G1s 1 ), indicating strong turbulence intensities, to 10 8 m 2 s 3 (i.e. G0.1 s 1 ), for low turbulence intensities (MacIntyre et al., 1999, 2002). Both of these are well below the value given above of m 2 s 3 (G30 s 1 ). Therefore, in natural systems, sheared flow with unstable suspensions of particles should always enhance the particle sedimentation through particle aggregation. In engineered water treatment systems, values of G above 40 s 1 are usually avoided to minimize breakage of particles and typical shear rates of s 1 in horizontal shaft turbines and of s 1 in vertical shaft turbines like paddle mixers are used (MWH et al., 2005), supporting the findings here of values needed to minimize breakup. R E F E R E N C E S Cheng, N.S., Law, A.W.K., Measurements of turbulence generated by oscillating grid. J. Hydraulic Eng. ASCE 127 (3), Colomer, J., Peters, F., Marrasé, C., Experimental analysis of coagulation of particles under low-shear flow. Water Res. 39 (13), Coufort, C., Bouyer, D., Line, A., Flocculation related to local hydrodynamics in a Taylor Couette reactor and in a jar. Chem. Eng. Sci. 60 (8 9), DeSilva, I.P.D., Fernando, H.J.S., Oscillating grids as a source of nearly isotropic turbulence. Phys. Fluids 6 (7), E, X.Q., Hopfinger, E.J., On mixing across an interface in stably stratified fluid. J. Fluid Mech. 166, Fernando, H.J.S., DeSilva, I.P.D., Note on secondary flows in oscillating-grid, mixing-box experiments. Phys. Fluids A Fluid Dynam. 5 (7), Hopfinger, E.J., Toly, J.A., Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78 (5 November), 155. Hunt, J.R., Prediction of oceanic particle size distributions from coagulation and sedimentation mechanisms. Advances in Chemical Series 189, Jackson, G.A., Logan, B.E., Alldredge, A.L., Dam, H.G., Combining particle size spectra from a mesocosm experiment measured using photographic and aperture impedance (Coulter and Elzone) techniques. Deep-Sea Res. II 42, Jarvis, P., Jefferson, B., Gregory, J., Parsons, S.A., A review of floc strength and breakage. Water Res. 39 (14), Jiang, Q., Logan, B.E., Fractal dimensions of aggregates determined from steady-state size distributions. Environ. Sci. Technol. 25 (12),

9 1121 Jiang, Q., Logan, B.E., Fractal dimensions of aggregates from shear devices. J. Am. Water Works Assoc. 88 (2), Li, X., Logan, B.E., Collision frequencies between fractal aggregates and small particles in a turbulently sheared fluid. Environ. Sci. Technol. 31 (4), Li, X.Y., Passow, U., Logan, B.E., Fractal dimension of small ( mm) particles in Eastern Pacific coastal waters. Deep- Sea Res. I 45, Li, X.Y., Zhang, J.J., Lee, J.H.W., Modelling particle size distribution dynamics in marine waters. Water Res. 38, Lick, W., Lick, J., Aggregation and disaggregation of finegrained sediments. J. Great Lakes Res. 14 (4), Logan, B.E., Environmental Transport Processes. Wiley, New York. Logan, B.E., Kilps, J.R., Fractal dimensions of aggregates formed in different fluid mechanical environments. Water Res. 29 (2), MacIntyre, S., Flynn, K.M., Jellision, R., Romero, J.R., Boundary mixing and nutrient fluxes in Mono Lake, California. Limnol. Oceanogr. 44 (3), MacIntyre, S., Romero, J.R., Kling, G.W., Spatial temporal variability in the surface layer deepening in an embayment of Lake Victoria, East Africa. Limnol. Oceanogr. 47 (3), Crittenden, J.C., Trussell, R.R., Hand, D.W., Howe, K.J., Tchobanoglous, G., MWH, Water Treatment: Principles and Design, second ed. Wiley, Hoboken, NJ. Oles, V., Shear-induced aggregation and breakup of polystyrene latex-particles. J. Colloid Interface Sci. 154 (2), Peters, F., Redondo, J.M., Turbulence generation and measurement: application to studies on plankton. Sci. Mar. 61, Ruiz, J., Macías, D., Peters, F., Turbulence increases the average settling velocity of phytoplankton cells. Proc. Natl. Acad. Sci. USA 101 (51), Serra, T., Casamitjana, X., Structure of the aggregates during the process of aggregation and breakup under a shear flow. J. Colloid Interface Sci. 206 (2), Serra, T., Logan, B.E., Collision frequencies of fractal bacterial aggregates with small particles in a sheared fluid. Environ. Sci. Technol. 33 (13), Serra, T., Colomer, J., Casamitjana, X., Aggregation and breakup of particles in a shear flow. J. Colloid Interface Sci. 187 (2), Spicer, P.T., Pratsinis, S.E., Shear-induced flocculation: the evolution of floc structure and the shape of the size distribution at steady state. Water Res. 30 (5), Spicer, P.T., Keller, W., Pratsinis, S.E., The effect of impeller type on floc size and structure during shear-induced flocculation. J. Colloid Interface Sci. 184 (1), Spicer, P.T., Pratsinis, S.E., Raper, J., Amal, R., Bushell, G., Meesters, G., Effect of shear schedule on particle size, density, and structure during flocculation in stirred tanks. Powder Technol. 97 (1), Srdic, A., Fernando, H.J.S., Montenegro, L., Generation of nearly isotropic turbulence using two oscillating grids. Exp. Fluids 20 (5), Tennekes, H., Lumley, J.L., A First Course in Turbulence. MIT Press, Cambridge, MA. Thompson, S.M., Turner, J.S., Mixing across an interface due to turbulence generated by an oscillating grid. J. Fluid Mech. 67, Tritton, D.J., Physical Fluid Dynamics. Oxford Science Publications. Waite, A.M., Safi, K.A., Hall, J.A., Nodder, S.D., Mass sedimentation of picoplankton embedded in organic aggregates. Limnol. Oceanogr. 45 (1), Zhang, J.J., Li, X.Y., Modeling particle-size distribution dynamics in a flocculation system. AIchE J. 49 (7),