Spatial and temporal evolution of floc size distribution in a stirred square tank investigated using PIV and image analysis

Chemical Engineering Science 61 (2006) 7651 – 7667 www.elsevier.com/locate/ces

Spatial and temporal evolution of floc size distribution in a stirred square tank investigated using PIV and image analysis J. Kilander, S. Blomström, A. Rasmuson ∗ Chemical Engineering Design, Department of Chemical and Biological Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden Received 22 September 2005; received in revised form 18 August 2006; accepted 2 September 2006 Available online 8 September 2006

Abstract In this study, non-intrusive measurements were performed in order to determine the spatial and temporal evolution of the floc size distribution in a square 7.3 L tank stirred with an A310 hydro foil impeller. The data was collected in situ using particle image velocimetry. The analysis of the data was done using a connected component labelling technique. It was found that the reproducibility of the system was adequate. The results show that there are large spatial differences in the mean size and the shape of the floc size distribution within the tank. It was found that steady-state was reached when stirrer speed was increased. It was also found that effects of the interaction between flocs and the water surface had substantial influence on the local size distribution. It was determined that the surface was more important for breakage of flocs than the impeller region. Results also showed clear number gradients in the tank. It is clear from this study that any population balance model developed in order to predict floc size distributions should incorporate spatial dependence. 䉷 2006 Elsevier Ltd. All rights reserved. Keywords: Mixing; Flocculation; Heterogeneous turbulence; Floc size distribution; Particle image velocimetry; Image analysis

1. Introduction Flocculation in stirred tanks is a common unit operation in wastewater management and has been studied extensively in the past (Koh et al., 1984; Casson and Lawler, 1990; Kramer and Clark, 1997; Ducoste and Clark, 1998; Pelin, 1999). The main focus of most studies has been on coupling turbulence with flocculation performance. This has traditionally been done using the average characteristic velocity gradient, G.
G=

N p
l N 3 D 5 V l

1/2 =

 1/2 ε¯ , 

(1)

where Np is the impeller power number,
l is the density of the liquid, N is the rotational speed, D is the impeller diameter, V is the volume of the vessel, l is the dynamic viscosity of the liquid,  is the kinematic viscosity of the liquid and ε¯ is the mean rate of energy dissipation. The use of G as a description of flow behaviour in a stirred tank is a rather crude tool since the ∗ Corresponding author. Tel.: +46 31 7722940; fax: +46 31 814620.

E-mail address: [email protected] (A. Rasmuson). 0009-2509/$ - see front matter 䉷 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2006.09.001

rate of energy dissipation, ε, is averaged over the entire volume. However, G has been used both as a design and operating parameter. It is well established that the turbulence quantities in a stirred tank differ between the mixing zone and the bulk (Zhou and Kresta, 1996). Recent investigations into the distribution of turbulence quantities by Kilander and Rasmuson (2005) using a large eddy particle image velocimetry (LE PIV) approach show that the rate of energy dissipation in the impeller area is as much as 100 times higher than in the bulk. Hence, the length scale of the smallest eddies are different in the impeller zone and in the bulk. Casson and Lawler (1990) have determined that flocculation is induced by eddies of the same size as the particles. Hopkins and Ducoste (2003) have found spatial variations in floc growth, steady-state size and steady-state variance between the impeller region and the bulk. Hopkins and Ducoste also found that the variances in floc size distribution decrease when the average characteristic velocity gradient, G, increases. With an increase in G they have also found, as previous studies have shown, that the floc growth increases and that the mean floc size decreases, regardless of particle concentration. Dyer and Manning (1999) have shown that the break-up of particles

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depend more on particle concentration than on the shear forces present in the tank. Spicer et al. (1996) have shown that the frequency of flocs in the impeller discharge zone is an important design parameter for maximizing floc size. Recent research points to the dependence of both tank size and impeller type on flocculation behaviour (Hopkins and Ducoste, 2003; Prat and Ducoste, 2006; Bouyer et al., 2001, 2004; Kemoun et al., 1997; Spicer et al., 1996). The influence of the impeller type on flocculation performance has been investigated by, e.g. Spicer et al. (1996) and Ducoste and Clark (1998). Spicer et al. (1996) have compared the effect of three different impeller types on floc size and structure during orthokinetic flocculation in a stirred baffled tank. The impellers that are compared in the study are the axial flow A310 hydro foil impeller, an intermediate 45◦ pitch-blade impeller and a Rushton turbine. Results show that for the same G-values, a steady-state floc size is first reached by the A310 hydro foil impeller. However, flocs formed by the A310 impeller are comparatively smaller. The reason for this is that higher mixing and circulation lead to an increase in the exposure of flocs to the impeller zone, and therefore higher shear forces and thus more breakage of flocs. However, if the tip speed of the different impellers is kept constant, the A310 produces the largest flocs, which is also confirmed by Ducoste (1996). These results show that the A310 is the best of the three impellers investigated to use for flocculation. Most studies of floc size distributions have been limited to local measurements using, e.g. photometric dispersion analyzer (PDA) (Dyer and Manning, 1999), photographic techniques limited in the placement of the measurement area (Ducoste and Clark, 1998) and laser sheeting techniques with limited spatial range (Pelin, 1999). Further, PDA only measures the relative change in the mean size of flocs. It is quite clear that the size distribution in, e.g. a stirred tank, has local deviations in space and time since net build-up and net break-up of flocs occur in different areas. Schuetz and Piesche (2002) have found that the assumption of using an ideally mixed reactor cannot be maintained for prediction of the floc size distribution. Data from non-intrusive measurements conducted in situ is critical for validation of e.g. population balance models that simulates spatially varied particle size distributions in heterogeneous systems. Any extraction of particles from the system is an intrusive action and influences particle size distributions and flow field. The fact that flocs are broken up by large shear forces is a well known phenomenon, but Yukselen and Gregory (2003) have also shown that flocculation is not a completely reversible mechanism for the system relevant for this study; the ability for flocs to grow large is lost with time. This is however not valid for polymer systems. It would be interesting to use images of flocs obtained in situ using PIV equipment, in combination with image analysis, to investigate how the size distribution of flocs evolves over space and time. This study will conduct PIV measurements in situ for a variety of areas, without disturbing the flow or the fragile flocs. The flocs are not mechanically stable and are disrupted by pressure and shear forces and, accordingly, the porosity and area of the flocs change. Local size distributions evolving over time

will be observed and commented. The mechanisms for death and birth of flocs and preferential concentration in space with respect to time will be investigated.

2. Particle characterization In order to compare experimental data with data calculated from, e.g. population balance models (PBM) we need some sort of characteristic parameter. Diameter is a natural choice for determining the size of particles. However, the irregular shape of flocs provides a problem and we need to define an equivalent length scale. The most common and the one used in this study is the equivalent sphere principle. Thus, it is assumed that the size of the flocs can be described by an equivalent diameter. The choice of characteristic length is also limited by the computational time required to analyse the images since the amount of data collected in the present study is large. This rules out other basic size measures, e.g. the perimeter of an object or coordinate-dependent measures in general. Perimeter measure is also highly erroneous depending on the discontinuities in digital images. The statistical diameter approach, e.g. the Feret diameter, is not a viable option here since there are not enough particles of the same shape to create the statistical data needed to make the measure meaningful (Wojnar, 1999). Flocs have an open structure and a porosity that changes with time and size of the flocs. This means that the volume of the flocs is not a function of the diameter powered to 3 but rather a fractal dimension, dF , somewhere in-between 1 and 3. Tambo and Watanabe (1979) have determined the fractal dimensions for clay–aluminium flocs from floc densities and have found dF to be in the range 1.6–2.0. Spicer et al. (1996) have shown that dF for polystyrene-alum flocs is somewhere between 2.1 and 2.5, depending on the size of the flocs. This means that we should see the flocs as a volume that is partly filled with the surrounding liquid. This constitutes a problem when comparing the results from a PBM since most models regarding flocculation assume compact flocs with geometric growth.

3. Image analysis—connected components labelling Connected components labelling is a widely used image analysis technique for determining the size of objects within a digital image. It works by scanning an image pixel by pixel from, e.g. the top left corner to the bottom right corner while determining if a pixel is connected to larger groups of pixels constituting an object in the image. Thus, the pixels that are connected are sorted and different labels are assigned depending on their connectivity. This means that the sizes of objects that can be determined are limited to the discrete number of pixels that make up the object, objects smaller than the size of a pixel are therefore inherently interpreted as being the size of the pixel. This means that accuracy is dependent on the relation between the sizes of the objects in the picture and the resolution of the image.

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In order to process the images, a thresholding operation is performed and a binary image is created according to BI (i, j ) = 1 BI (i, j ) = 0

for I (i, j )
T , for I (i, j ) T .

(2)

In Eq. (2), BI and I are the binary image and the original image matrices, respectively. T is the thresholding intensity that separates the intensity of the background from the intensity of the particles. The T value has to be determined for each set of images. In this work the appropriate value was found using histograms with the same amount of bins as the possible intensity values, in the present case 255. The histogram shows the bi-modal intensity distribution from particles and background noise. The background is represented by a log normal type distribution, Fig. 1. A pixel was considered to belong to a particle when its intensity value is represented by 3% or less of the number of pixels contained in the bin of the maximum

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represented intensity class. An example of the conversion from original image to binary image via the thresholding operation is shown in Fig. 2. The connected components labelling operator then scans the rows in the binary image, according to a set of rules. If a pixel, p, has intensity 1 then the operator examines the neighbours and the following procedure takes place: • if all neighbours have the intensity 0, then a new label is assigned to p; • if only one neighbour has the intensity 1, assign its label to p; • if one or more of the neighbours have the intensity 1, assign one of the labels to p and make note of the equivalence class. After a complete scan, the equivalent label pairs are sorted into equivalence classes and a label is given to each class. Then a second scan is performed and each label is replaced with a new label assigned to its equivalence class. The image then contains connected components of known number of pixels with unique labels. The size of the particle can then be estimated since the number of the same value can be counted. The size of the particle is proportional to the number of pixels of said value. If the pixel size is known, then particle size can be estimated.

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4. Optical issues in estimating particle size

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Intensity Fig. 1. Histogram of the intensity distribution.

The intensity of an illuminated particle is influenced by the location of the particle within the laser sheet. This is due to the Gaussian distribution of the intensity across the thickness of the laser sheet. The effect of intensity distribution on particle illumination is not symmetrical, because of the placement of the camera. Hence, the size of the particles in the low intensity region on the far side of the intensity maximum plane, with respect to the camera, will be underestimated more than the corresponding particles on the other side of the plane of maximum intensity. This effect is, however, negated by the

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Fig. 2. (a) Original image of flocs. (b) Binary image after thresholding operation.

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enlarging effects due to the defocus of off-centre particles. Hence, a blurring effect tends to increase the size estimates of particles away from the intensity maximum. Kadambi et al. (1998) have shown that a PIV system can be configured so that these two parameters cancel one another. The study also shows that a diameter calculated by finding the intensity weighted centroid and standard deviation of the particle is a better method for estimating the diameter than the extents diameter using binary edges, since the intensity weighted diameter is more independent on the location within the laser sheet, whereas the extents diameter tends to oscillate depending on position within the laser sheet. However, the standard deviation of the oscillation is small compared to the resolution of the images, and the calculation of the extents diameter requires less computational time. Therefore, the extents diameter is used in this study since the number of images required to follow the evolution of a size distribution in time in a flocculation system is very large. The relation between true physical size and size on the CCD array is determined in the calibration and does not need to be considered in the image analysis.

5. Experimental 5.1. Set-up A 7.3 L square glass tank filled with distilled water for flow field measurements and model water for the flocculation experiments was stirred with a hydro foil Lightnin A310 impeller. The diameter of the impeller was D = 64 mm, the water level and tank width was H = 194 mm. The impeller off bottom clearing was C = H /2. The impeller was inherently centered in the tank by the tank-motor set-up in the PIV experiments. The impeller was rotated clockwise at two different stirrer speeds, 199 and 227 rpm. The stirrer speed corresponds to an energy input of 1.72 and 2.55 W/m3 , in the text referred to as energy input 1 and energy input 2, respectively. The average velocity gradient for the lower energy input was 41.3 s−1 and for the higher energy, 50.4 s−1 . The tip speed for the two stirrer speeds was 0.67 and 0.76 m/s, respectively, and the Reynolds numbers were 13,520 and 15,420. The difference in stirrer speed was chosen in order to study the influence of energy input on flocculation behaviour. The power consumption per volume used in the higher energy input was the same as the one used in the dissipation study by Kilander and Rasmuson (2005). A PIV system with double 120mJ Nd:Yag lasers for stereoscopic 3D PIV (1008x1018 pixel CCD) was commercially obtained through LaVision GmbH. The software used for image analysis of the PIV images in order to obtain flow field was Davis 6.2 Kodak. The 3D stereoscopic PIV measurements were preceded by a 3D stereoscopic calibration. Two cameras were aimed and focused on a calibration plate situated in the area of interest in the water filled tank. The distance between the cameras was 0.7 m. The tank width as well as lab space available limited the distance between the cameras and the target to 2.4 m. One image was taken of the calibration plate by each of the cameras. The calibration target was then moved 1 mm away

Fig. 3. Areas investigated. The solid line boxes are areas where the flow field is investigated. The large dashed line box is investigated for the length scales in the impeller stream. The small dashed boxes denoted, UI for under impeller, LC for lower corner, UC for upper corner, OI for over impeller and B for the bulk, are investigated for flocs.

from the cameras using a micrometer screw and two new images were taken. The exact placement of the two calibration positions within the laser sheet is not of great importance since the calculated vectors are averaged over the thickness of the sheet. Of greater importance then is that the two calibration planes and the laser sheet are parallel since any skew will change the frame of reference for the calculated vectors in the area of interest. The four images of the calibration plate were then used to calculate the mapping function that determines the image relation between the two cameras and allows for elimination of the optical distortions created by the non-perpendicular, with respect to the calibration plate, set-up of the cameras. Seeding particles were used for the flow field investigations. The amount of seeding particles that was used in the tank in the PIV experiments was determined by allowing no less than 10 seeding particles to be present in the interrogation cell (IC). The seeding particles were hollow silver-coated glass spheres with a density of 1.6 g/cm3 and a mean diameter of 10
m. The size of the IC was 32×32 pixels with 75% overlap and was chosen in order to obtain good accuracy since displacement errors decrease with increasing IC. The size of the areas of interest was 60×60 mm2 located accordingly as in Fig. 3. This resulted in 15,750 vectors evenly distributed on a quadratic grid with a distance of 0.44 mm between the vectors. The size of a pixel is 60
m and is thus the resolution of the calculated size distributions. Also, this means that any particle smaller than 60
m that scatters light will be recorded as a 60
m particle. This means that size will be overrepresented in the current size distributions. The laser sheet had an estimated thickness of ∼1 mm. The time between the laser pulses was 200
s. The two resulting image pairs were then cross-correlated using a FFT-based method in order to produce 400 instantaneous vector fields from each measuring set. The PIV system in the present study works at 15 Hz, thus corresponding to roughly 30 s of data acquisition. The impeller position was not logged during the measurements. Missing

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5.2. Areas of investigation The areas that were investigated were the upper left corner, the lower left corner, directly over the impeller, directly under the impeller and in the impeller stream, see Fig. 3. The areas in the vicinity of the impeller region were placed in the middle of the tank, and in the corner, areas were located 1.5 cm behind the front wall. The distance to the wall was chosen after flow field experiments designed to locate the middle of the corner jet, as described by Kilander (2003). The areas within the solid line squares were investigated for the flow field and the area represented by the large dashed square was investigated for turbulent energy dissipation and length scales in the impeller stream. The areas that were investigated for floc size distribution are shown by the small dashed squares. The areas are all of equal size with a measuring area of 57,000 pixels corresponding to a physical area of 205.2 mm2 . The areas are denoted UC for upper corner, OI for over the impeller, UI for under the impeller, LC for lower corner and B for the bulk. The placement of the areas was determined in order to be able to follow floc growth from a mechanistic view point. It is assumed that the dominating mechanism for growth between areas UI and LC is turbulence controlled collisions induced by the impeller stream, also referred to as orthokinetic flocculation. It is also assumed that the dominating collision mechanism in the area between LC and UC is relative sedimentation as a result of different settling velocities for different sized flocs. Using the equations for collisions frequency, Eqs. (3) and (4), as suggested by e.g. Clark (1996), we can substantiate that this is indeed the case for the particle sizes studied here (
60
m), Fig. 4. (ri + rj )OF = 1.294(ri + rj )3 (ri + rj )DS =

 1/2 ε¯ , v

g (
−
l )(ri + rj )3 |ri − rj |, 9l F

(3)

(4)

where OF and DS are the collision frequency for orthokinetic flocculation and differential settling, respectively. The LC area was placed high enough so that the effect of the high strain zone in the corner, described by Kilander (2003), has already influenced the flocs thus isolating the differential settling mechanism between LC and UC. The areas OI and UI were placed so that breakage over the impeller could be studied more closely. The influence of the different mechanisms was expected to change

10-5

Collision frequency (m3/s)

vectors were filled in by interpolation based on numerical considerations. However, the percentage of missing vectors in each vector field was low ∼1–2%. All three velocity components calculated from the PIV experiments were used in order to evaluate the flow field in the tank and the dissipation in the vicinity of the impeller and impeller stream. The same procedure was used in order to calibrate the PIV system for the images of the flocs. The tank was, however, not seeded as this disturbed flocculation.

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Orthokinetic 199 rpm Orthokinetic 227 rpm Differential settling 10-10

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size (m) Fig. 4. Collision frequencies for different size particles in the current flocculation system.
F estimated at 2000 kg/m3 . Calculated for a 1
m floc.

as the mean size of the flocs grows during the experiment. This is also shown in Fig. 4. 5.3. Model flocculation system The model flocculation system was created using a solution of buffered water and kaolinite clay. Kaolinite clay (CAS Registry Number: 1332-58-7) is a hydrated aluminium silicate crystalline mineral. It is characterized by its fine particle size and chemical inertness. The kaolinite used in the experiments had a composition of 90% kaolinite, 9% mica and < 1% quartz. The specified density was 2.6 g/cm3 and the size distribution using an equivalent spherical diameter was: 0.2% is larger than 10
m and 80% is smaller than 1
m. The water was prepared by buffering distilled water adding sodium hydrogen carbonate to reach a concentration of 50 mg/dm3 . The buffered water was then left for 96 h in order to reach equilibrium. The buffered water had a pH of 7.85. The buffered water was then used to prepare a stock solution of kaolinite clay. The kaolinite clay was dried for 48 h at 100 ◦ C before a solution with the concentration 80 g/dm3 was prepared using the buffered water. The solution was kept under strong agitation for 48 h. The solution was then diluted, using buffered water, to a concentration of 0.80 g/dm3 . This stock solution was then agitated another 48 h before use in experiments. When the experiments were carried out, the stock solution was further diluted to a concentration of 0.024 g/dm3 . Fixed amounts of 10 mM HCl were added in order to reach pH 7.5 as this is favourable for flocculation in the current system. The flocculant was ferric (III) chloride and was prepared in order to mimic the commercial flocculant Ferriflock (CAS registry number 7705-08-0) that was used in the study by Pelin (1999). 10 g Fe3+ · 6H2 O was dissolved in 3.8 g distilled water and 55.2 g of 5 mM hydrochloric acid. The hydrochloric acid was added in order to avoid formation of iron complexes. The final flocculant solution had a concentration of 30 g Fe3+ per kg of solution. The concentration of Fe3+ ions in the flocculation experiments was 26.8
moles/dm3 as

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Pelin (1999) found this to be the optimal concentration. The addition of the ferric ions to the suspension leads to compression of the diffusive layer surrounding the kaolinite particles and neutralization of charges. Thus, the suspended kaolinite particles were destabilized, allowing the formation of hydroxides needed for the precipitation reaction. The precipitation of the ferric hydroxide, formed as a result of adsorption of ferric ions to the surface of the suspended kaolinite particles, enmeshed the particles into larger aggregates. Addition of ferric ions will also lead to a continuous reduction of pH as a result of hydroxide formation from the six water molecules surrounding the ferric ion, thus adding hydronium ions to the solution. 5.4. Experimental procedure The adsorption process of the flocculant to the surface of the particles is a very fast reaction. The flocculant should be distributed in a homogeneous fashion within 0.1 s. This was not possible with the tank volume used in this study since the mixing time, in practice, is much higher. In order to distribute the flocculant as evenly as possible, the addition was made just above the impeller. The clock started with addition of flocculant and 80 images were taken every 2 min for 40 min. The maximum number of images that could be taken was limited by the time it took to prepare the PIV system for the next set of images. 6. Results and discussion 6.1. Velocity magnitudes The magnitudes of the velocity in the areas of interest are presented in Fig. 5. It can be seen that the flow fields differ in magnitude but not in general structure. As expected, the velocities were the highest in the vicinity of the impeller with a maximum of the mean velocity of 0.19 m/s for energy input 1 and 0.22 m/s for energy input 2. The maximum mean velocities in the lower corner were 0.06 and 0.07 m/s, and in the upper corner 0.03 and 0.04 m/s for 199 and 227 rpm, respectively. 6.2. Stability of the flocculation system The validity of any conclusions drawn from this work is highly dependent on the stability of the flocculation system and the possibility of reproducing the same size flocs and the same flocculation dynamics in every experiment. Fig. 6 shows repeated experiments conducted at the area under the impeller, denoted UI, for the rotational speeds 199 and 227 rpm. As can be seen the experiments yield similar results. However, a complete statistical investigation to determine the standard deviation has not been made since the preparation and performance of the flocculation experiments is very time consuming. We see that the variance is larger in the 199 rpm case than in the 227 rpm case. This is in line with the observations made by Hopkins and Ducoste (2003).

6.3. Local size distributions The mechanisms governing the growth and death of flocs have different influences in different areas of the tank. The mean sizes of the flocs were obtained using number averaged particle diameter, according to Eq. (5). D¯ n =

J 

dj fn (dj ).

(5)

j =1

When examining Figs. 6–11, it is important to keep in mind that the mean sizes will be overestimated. This is because reflections from particles smaller than 60
m are inherently interpreted as 60
m since this is the resolution of the PIV system. However, the size estimates are adequate for comparisons between the different areas in the tank. Fig. 7 shows that the largest flocs can be found in the upper corner of the tank. This is to be expected, as there should be growth through orthokinetic flocculation between the areas just below the impeller and the lower corner and then growth through differential settling between the lower corner and the upper corner. The large difference between the upper corner and the area just above the impeller can be explained by effects of the water surface. This was observed visually during the experiments. Flocs tend to be captured in the boundary between water and air and then broken up by strong vortex motion on the water surface. The smaller pieces of the broken flocs were then reintroduced to the tank evenly across the water surface area. The effects of this will be commented on in the section on number concentration gradients, below. The spatial variance in floc growth decreases with higher energy input as can be seen in Fig. 7 and as found previously by Hopkins and Ducoste (2003). This is also true for the steadystate sizes and steady-state variance between the impeller region and the bulk. It is interesting to note that the difference in mean size between the area just below the impeller and the lower corner is much greater in the case with the lower energy input than in the case with a higher one. However, the growth between the lower corner and the upper corner is greater for the higher energy input. The lack of difference in the mean size between areas OI and UI is surprising, since we would expect noticeable floc breakage over the high shear impeller zone. To understand these phenomena fully we have to investigate changes that occur in each size class. This will be examined in greater detail below. 6.3.1. Size distributions and change of number fractions In Figs. 8–11 the size distribution is plotted as the number fraction versus the diameter. This allows for the study of the shape and evolution of the size distribution in time. The number fraction versus time is also plotted. This provides an opportunity to investigate in greater detail the individual changes with time that occur in each size class studied. Fig. 8 shows the size distribution and the change of number fraction with time for the area under the impeller, UI. The left column shows graphs for 199 rpm and the right shows graphs for 227 rpm. The top right graph of Fig. 8 shows that the amount

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Velocity impeller 7.3 L, energy input 2

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Fig. 6. Verification of the repeatability of the system. Mean size calculated for different flocculation experiments in the area under the impeller.

J. Kilander et al. / Chemical Engineering Science 61 (2006) 7651 – 7667

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Fig. 8. Size distributions and change of number fractions for the area denoted UI. Left graphs show the 199 rpm case, and the right graphs show the 227 rpm case.

of flocs of the smallest size decreases faster with increasing energy input. This can also be seen in the bottom right graph where the fraction of the largest investigated size class is higher for energy input 2 than for energy input 1. The rate of growth in the largest size classes is higher for the higher energy in-

put reaching an apparent steady-state after about 12–13 min, whereas the time needed to reach steady-state in the lower energy input case is about 18 min. However, it cannot be seen that steady-state is reached in the higher energy input case in the smallest size class within the experiment time. The shape of the

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Fig. 9. Size distributions and change of number fractions for the area denoted LC. Left graphs show the 199 rpm case and the right graphs show the 227 rpm case.

particle distribution curve and the size of the particles match results from Ducoste (2002) using alum to floc kaolin clay. Fig. 9 shows the size distribution and the change of number fraction with time for the area in the lower left corner of the tank, LC, at different impeller speeds. The left column shows the graphs for the 199 rpm case and the right column shows the graph for the 227 rpm case. In these graphs, we see the reverse effects of the UI area. The amount of the smallest size flocs decreases more rapidly in the lower energy input case. This is probably due to competing mechanisms and it should be stressed that the path between UI and LC is not closed (i.e., other streams contribute to LC) and mass is not conserved. We also see that after about 10 min, the amount of flocs of size 0.12 mm becomes the most abundant size class. It is also worth noting that, in this case, the steady-state size distribution is narrower for the higher energy. Fig. 10 shows the size distribution and the change in number fraction with time for the area in the upper left corner of

the tank, UC, at different impeller speeds. The same phenomena as in the LC case are clearly visible again in the UC case. The amount of flocs in the smallest size classes decreases more rapidly in the lower energy 199 rpm case. Also the variance in the steady-state size class amount is larger at 227 rpm. The main difference between the two energy input cases is the velocity of the flow between area LC and area UC. We assume that the dominating collision mechanism in this region of the tank is differential settling for the size range studied. The main collision mechanisms for very small particles are orthokinetic flocculation and Brownian motion. A lower convective velocity yields more time for sedimentation induced collisions. For both energy inputs we note that the 0.12 mm size class becomes the most abundant already after 8 min. The amount of the smallest size class is also surpassed by the 0.18 mm size class after about 24 min. The placement of the UC measuring area matches the one used by Ducoste (2002) using a photographic technique developed by Kramer and Clark (1996). He has found that the

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Fig. 10. Size distributions and change in fractions for the area denoted UC. Left graphs show the 199 rpm case and the right graph shows the 227 rpm case.

steady-state mean size is 120.6
m in a 5 L tank. In the top graphs in Fig. 7, we see that the steady-state maximum of the size distribution is about 120
m. The Ducoste study assumes that the entire tank volume can be described by that single size distribution and the results are used in the development of a PBM. However, as results show in the present study, both the shape and the maximum of the steady-state size distribution are different in different areas of the tank. Fig. 11 shows the size distribution and the change in number fraction with time for the area above the impeller, OI, at different impeller speeds. Again, in the OI area, we see that the amount of flocs in the smallest size class decrease more rapidly with the higher energy input at 227 rpm. However, it seems that the largest size class is more abundant at 199 rpm, thus following the trend of the LC and UC areas. 6.3.2. Mechanistic influences on different size classes In order to fully understand the growth and death mechanisms of flocs, it is necessary to follow the changes that occur

in each size class. The graphs in the following section denote changes in the fractions that occur in each size class between two areas of interest. A value in the graphs above 1 denotes growth for that particular size class at that particular time. It is important to keep in mind that the mass balances between the compared areas are not fulfilled. The graphs in Fig. 12 show how the size classes change from the UI area to the LC area during the presumed orthokinetic flocculation that occurs in the impeller stream and out towards the corners of the flocculation tank. The largest changes expressed as a percentage happen in the larger size classes with increases of up to 300% at 199 rpm (calculated as (final−initial)/initial). However, the 50% decrease in the smallest size class, in the same case, corresponds to a much greater amount of flocs. It is also interesting to note that it appears that the larger size classes reach a maximum after about 25 min in both cases. Yukselen and Gregory (2003) have shown that the ability to form flocs is lost with time. The same maximum is not as noticeable in Fig. 7 which shows the mean size

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Fig. 11. Size distributions and change in fractions for the area denoted OI. Left graphs show the 199 rpm case and the right graph shows the 227 rpm case.

of flocs. The higher energy input depicted in the right graph yields smaller changes in all the size classes. Since flocculation is induced by eddies of the same size as the flocs (Casson and Lawler, 1990) it would be interesting to examine the effects from a length scale point of view. Using the LE PIV approach in order to estimate the turbulent energy dissipation described by Kilander and Rasmuson (2005) we can calculate the Kolmogorov length scales, Eq. (6), in the impeller stream and determine if the changes are indeed turbulence controlled.  k =

3 ε

1/4 ,

(6)

After an initial growth period of 6 min, we see that the smallest size class is consumed in both the 199 and the 227 rpm cases. The Kolmogorov length scales in the impeller streams at both 199 and 227 rpm are in the order of the smallest investigated size class, Fig. 13.

However, the Kolmogorov length scales in the impeller stream are 20% smaller at 227 rpm than at 199 rpm. The region of very small length scales in the impeller area in the lower energy case is an artefact due to reflections from the impeller. The effect is larger at the lower impeller speed since the residence time of the impeller blade in the measuring plane is longer. Also, the area that is in the right order of magnitude of the length scales for inducing floc growth in the smallest size classes is larger at 227 than at 199 rpm. Thus, we would expect that the decrease in the smallest size class is greater at 199 rpm. The change at 199 rpm is a 50% decrease. At 227 rpm, the change is much smaller and we see that the curve points upwards after about 25 min, thus the difference between death and birth of the flocs of that size decreases in the higher energy input case. The same applies to the 0.12 mm size class indicating that the growth in smaller size classes is more effective in the higher energy case. The most noticeable difference between the graphs in Fig. 12, however, is the dynamics of the largest size classes.

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Fig. 12. Left graph. Changes in size classes between the area under the impeller (UI) and the lower left corner (LC) at 199 rpm (i.e., [LC]/[UI]). Right graph. Changes in size classes between the area under the impeller (UI) and the lower left corner (LC) at 227 rpm (i.e., [LC]/[UI]). A value > 1 denotes increase of that particular size in the area LC.

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Fig. 13. Kolmogorov length scales in the impeller stream for, in the left graph 199 rpm, and in the right graph, 227 rpm. Estimated using a PIV LE approach (Kilander and Rasmuson, 2005).

In both cases we have a large increase in growth after 6 to 10 min depending on the size class. The increase after that time is much larger in the lower energy case. Three plausible explanations for this are: (a) The higher energy flow at 227 rpm causes rupture in large flocs to a greater extent than in the lower energy case, both in the impeller stream and in the contracting flow into the corner jet (Kilander, 2003). (b) Studies have shown that cluster–cluster aggregation is induced by large scale turbulence and is favoured by intermediate turbulence regions like boundaries between the impeller stream and the bulk (Hansen and Ottino, 1996). Thus, the lower energy case would have larger areas of those regions between

UI and LC. (c) Cluster–cluster aggregation is favoured by the irregular or fractal shape of the flocs. The higher energy flocculation yields a higher value for the fractal dimension due to erosion yielding a more compact floc. Further, it is well known that a lower G-value gives larger flocs, however, at a smaller rate when maintaining constant geometry (e.g. Hopkins and Ducoste, 2003). Fig. 14 shows that the major changes in the size classes between the lower left corner and the upper left corner occur in the first 12 min, at both 199 and 227 rpm cases. From the previous discussion regarding Fig. 12, we can conclude that there will be more small particles available for differential settling

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Fig. 14. Left graph. Changes in size classes between the lower left corner (LC) and the upper left corner (UC) at 199 rpm (i.e., [UC]/[LC]). Right graph. Changes in size classes between the lower left corner (LC) and the upper left corner (UC) at 227 rpm (i.e., [UC]/[LC]). A value > 1 denotes increase of that particular size in the area UC.

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Fig. 15. Left graph. Changes in size classes between the upper left corner (UC) and the area over the impeller (OI) at 199 rpm (i.e., [OI]/[UC]). Right graph. Changes in size classes between the upper left corner (UC) and the area over the impeller (OI) at 227 rpm (i.e., [OI]/[UC]). A value > 1 denotes increase of that particular size in the area OI.

growth mechanisms in the high energy case than in the lower energy case. This is clearly visible when comparing the left and right graphs in Fig. 14. Looking at Fig. 7 and comparing the distances between the LC and UC lines in the 199 rpm and the 227 rpm graphs also points to this conclusion, since the distance between the lines is shorter at 199 rpm; meaning that there is less growth here. Fig. 15 shows changes in the size classes between the upper corner, UC, and the area above the impeller denoted OI. As expected we can see that it is mainly the large size classes

that have been reduced between UC and OI. It is interesting that the smallest size class has increased since it is reduced in all other areas of the tank. The apparent breakage of the flocs in the large size classes and the increase in the smallest size class is probably due to the above mentioned exchange with the water surface. The reduction in the largest size classes and the increase in the smallest size class are most apparent in the lower energy case. Large flocs are also most abundant in the upper corner at 199 rpm. This also points to the importance of breakage of flocs on the surface.

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Fig. 16. Left graph. Changes in size classes between the area over the impeller (OI) and the area under the impeller (UI) at 199 rpm (i.e., [UI]/[OI]). Right graph. Changes in size classes between the area over the impeller (OI) and the area under the impeller (UI) at 227 rpm (i.e., [UI]/[OI]). A value > 1 denotes increase of that particular size in the area UI.

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Fig. 17. Total number of flocs in the areas UI, LC, UC, OI and Bulk. Left graph shows cases at 199 rpm and the right graph shows cases at 227 rpm.

6.3.3. Breakage in the impeller zone It is a common perception that most of the breakage occurs in the impeller region. Fig. 16 depicts the changes in the size classes from area OI to area UI. No clear trend of breakage in the larger size classes can be derived from the graphs. It is, however, likely that many of the large flocs are broken up in the impeller region. It is expected that the breakage in the impeller region becomes more important as the size of the impeller increases since the forces and the time the flocs stay in the strain field increase. However we do see that the smallest size class is consumed and that the two size classes 0.12 and 0.18 mm are formed. This indicates an imbalance in the growth

in the impeller region for the smallest size classes studied. Also, there is a possibility that there is cluster–cluster growth in the impeller region as well. As expected, this is more pronounced at lower energy since we have more erosion at higher energy. There is a tendency for breakage in the larger size flocs after about 30 min at low energy, but the same is not as clear at high energy. We would expect that the flocs formed late in the flocculation run in the high energy case are stronger because the flocs are built of smaller aggregates due to rupture and erosion. Smaller building blocks mean more contact points between primary particles, thus increasing the shear strength of the floc consisting of cohesive and frictional forces. Blaser (2000) has

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Fig. 18. The left graph shows the total number of flocs in the bulk area. The right graph shows the change in fraction when the size distribution of bulk at 199 rpm is compared to the case at 227 rpm (i.e. (199 rpm bulk)/(227 rpm bulk)).

estimated floc strength using an ellipsoid model to 0.1 N/m2 for ferric hydroxide sweep flocs. However, the erosion of the flocs in a stirred tank would probably increase this strength. One important conclusion in the Blaser study is that breakage is dependent on time exposed to a high strain rate field, also indicating different breakage behaviour if the size of the impeller increases. 6.3.4. Spatial number concentration gradients Even though the tank is mixed, it is a long way from ideal mixing. The flocs tend to accumulate in certain areas of the tank. Fig. 17 depicts the number of particles that were present during the measurements in different areas of the tank. The comparison is possible since the measuring volume and the measuring time were the same in all experiments. Fig. 7 shows that the steady-state variance is greater at lower energy input, however the steady-state number of particles variance is greater at higher energy input, as shown in Fig. 17. There are a couple of likely explanations for the variance seen in Fig. 17. First, the heterogeneous type flow in combination with strong interaction between the water surface and the flocs results in floc breakage and the even seeding of small flocs across the area of the water surface. Second, the large circulation loop in the tank is more effective in carrying particles between areas UC and OI at higher energy input. The left graph in Fig. 18 shows that there are more flocs present in the bulk area at 199 rpm. The type of flocs that are present in the bulk area also differs between the two cases. The right graph in Fig. 18 shows a comparison of the size classes present in the bulk between the 199 rpm and the 227 rpm cases. As can be seen, the fraction of the large flocs is higher at 227 rpm (the value for the change is below 1 in the large size classes).

7. Conclusions Non-intrusive experiments were performed in order to calculate the spatial and temporal evolution of local size distribution. Data from the non-intrusive measurements conducted in situ were collected and analysed. These data are crucial for validation of, e.g. population balance models that simulate spatially varied particle size distributions in heterogeneous type flows. The analysis of the collected data was performed using the image analysis method connected components labelling. Repeated experiments showed that the experimental procedure yielded a stable flocculation system with reproducible flocculation dynamics. Results show that there were large spatial differences in size distributions and in the mean floc size in the tank. The shape of the size distribution and the mean size along the walls of the tank showed very good agreement with previous measurements conducted in the same area of the tank (Ducoste, 2002). Also as shown previously by, e.g. Hopkins and Ducoste (2003), the steady-state mean size variance for different parts of the tank decreased as energy input increased. Steady-state for flocs of large size was reached faster with increasing stirrer speed in all parts of the tank. Two important growth mechanisms were isolated. The first is orthokinetic flocculation in the impeller stream and the second is differential settling growth in the corner jet. Results of this study show that effects of the interaction between flocs and the water surface had substantial influence on local size distributions. It was determined that the water surface was more important for breakage of flocs than the high shearing zone around the impeller for this size of flocculation system. There were no clear trends of breakage in the impeller region. It is to be expected that an increase in tank size will

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result in a decrease in the influence of water surface breakage. Also, with a larger impeller it is to be expected that breakage in the impeller region will become more important since the forces and the time for the floc in the strain field increase. This will be investigated in further studies. The amounts of the smallest size classes decreased more rapidly at lower energy input in the differential settling area between the lower and the upper corner. A lower convective velocity yields more time for settling induced collisions. However, a more profound discussion of mechanisms would need a more complete characterization of the tank. Results show clear number concentration gradients in the system. The difference between the minimum number concentration in the impeller region and the maximum number concentration at the top corner of the tank was 32% at high energy input and 46% at low energy input. The variance in the number concentration increased as the energy input increased. The gradients in the number concentration are most likely due to spatial dependent break-up mechanisms, e.g. a high energy impeller stream and water surface effects, and the difference in the ability for flocs to follow the flow as their size increases. It is clear from this study that any development regarding PBM should incorporate spatial dependence. Notation BI C D D¯ n dj fn (dj ) G g H I N Np Ni ri , rj T V

binary image matrix impeller off bottom clearance, m impeller diameter, m number averaged particle diameter, m particle size class, m number frequency of particles with size, dj average characteristic velocity gradient, s−1 gravity constant, m s−2 height of the water level, m image matrix stirring rate, s−1 impeller power number number of images radius of flocs of size class i and j , m thresholding intensity volume of the tank, m3

Greek letters  ε ε¯ k l 
l
F

collision frequency (m3 s−1 ) local energy dissipation per unit mass (m2 s−3 ) mean energy dissipation per unit mass (m2 s−3 ) Kolmogorov length scale (m) dynamic viscosity of the fluid (Pa s) kinematic viscosity of the fluid (m2 s−1 ) density of the fluid (kg m−3 ) density of the flocs (kg m−3 )

Abbreviations A310 CCD

hydro foil impeller, Ligthnin charged coupled device

FFT LC LE OI PBM PDA PIV UC UI

fast Fourier transform lower corner, area interrogated for floc size large eddy over impeller, area interrogated for floc size population balance model photometric dispersion analyser particle image velocimetry upper corner, area interrogated for floc size under impeller, area interrogated for floc size

Acknowledgements Funding from Swedish Research Council is gratefully acknowledged. The authors would like to thank Fredrik Persson for substantial contribution to the development of experimental methodology during his Master Thesis work. References Blaser, S., 2000. Break-up of flocs in contraction and swirling flows. Colloids and Surfaces. A: Physicochemical and Engineering Aspects 166, 215–223. Bouyer, D., Line, A., Cockx, A., Do-Quang, Z., 2001. Experimental analysis of floc size distribution and hydrodynamics in a jar-test. Chemical Engineering Research and Design 79 (A8), 1017–1024. Bouyer, D., Line, A., Do-Quang, Z., 2004. Experimental analysis of floc size distribution under different hydrodynamics in a mixing tank. A.I.Ch.E. Journal 50 (9), 2064–2081. Casson, L.W., Lawler, D.F., 1990. Flocculation in turbulent flow: measurement and modeling of particle size distributions. Journal of American Water Works Association 82 (8), 54–68. Clark, M.M., 1996. Transport Modeling for Environmental Engineers and Scientists. Wiley, New York. Ducoste, J.J., 1996. The effect of tank size and impeller type on turbulent flocculation. Ph.D. Thesis, University of Illinois, Urbana-Champaign. Ducoste, J.J., 2002. A two-scale PBM for modelling turbulent flocculation in water treatment processes. Chemical Engineering Science 57 (12), 2157–2168. Ducoste, J.J., Clark, M.M., 1998. The influence of tank size and impeller geometry on turbulent flocculation: 1. Experimental. Environmental Engineering Science 15 (3), 215–224. Dyer, K.R., Manning, A.J., 1999. Observation of the settling velocity and effective density of flocs, and their fractal dimensions. Journal of Sea Research 41, 87–95. Hansen, S., Ottino, J.M., 1996. Aggregation and cluster size evolution in nonhomogeneous flows. Journal of Colloid and Interface Science 179, 89–103. Hopkins, D.C., Ducoste, J.J., 2003. Characterising flocculation under heterogeneous turbulence. Journal of Colloid and Interface Science 264 (1), 184–194. Kadambi, J.R., Martin, W.T., Amirthaganesh, S., Wernet, M.P., 1998. Particle sizing using particle imaging velocimetry for two-phase flows. Powder Technology 100, 251–259. Kemoun, A., Lusseyran, F., Skali-Lami, S., Mahouast, M., Mallet, J., Lartiges, B.S., Lemelle, L., Bottere, J.Y., 1997. Hydrodynamic field dependence of colloidal coagulation in agitated reactors. Récents Progrès en Génie des Procédés 11 (52), 33–40. Kilander, J., 2003. Hydrodynamics in a stirred square tank investigated using PIV and LDA measurements. Licentiate Thesis. Chalmers University of Technology, Göteborg. Kilander, J., Rasmuson, A., 2005. Energy dissipation and macro instabilities in a stirred square tank investigated using a LE PIV approach and LDA measurements. Chemical Engineering Science 60, 6844–6856. Koh, P.T.L., Andrews, J.R.G., Uhlherr, P.H.T., 1984. Flocculation in stirred tanks. Chemical Engineering Science 39 (6), 975–985.

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