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J. Hydrol. Hydromech., 59, 2011, 3, 184195 DOI: 10.2478/v10098-011-0015-7 PETRA BUBAKOVA, MARTIN PIVOKONSKY, LENKA PIVOKONSKA Institute of Hydrodynamics, Academy of Sciences of the Czech Republic, v.v.i., Pod Patankou 5, 166 12 Prague 6, Czech Republic; Mailto: email@example.com The paper introduces the test of aggregation as a simple, inexpensive method of evaluating suspension quality during drinking water treatment, suitable for use in both laboratory and operation conditions. The procedure and derivation of the aggregation test is described. The method is used for a demonstration of the influence of mean velocity gradient and mixing time on floc properties formed during the aggregation in a Couette reactor. It was proved that with increasing velocity gradient, the size of the aggregates present in the suspension decreases, and the suspension is substantially more homogeneous than with use of lower gradients. Further, it was confirmed that the size of aggregates reaches the steady state after a specific mixing time, which becomes shorter with increasing value of velocity gradient. KEY WORDS: Aggregation, Drinking Water Treatment, Floc Properties, Flocculation, Test of Aggregation. Petra Bubáková, Martin Pivokonský, Lenka Pivokonská: METODA HODNOCENÍ KVALITY SUSPENZE SNADNO POUZITELNÁ V PRAXI: VLIV MÍCHÁNÍ NA VLASTNOSTI VLOCEK. J. Hydrol. Hydromech., 59, 2011, 3; 22 lit. 11 obr. 8 tab. Píspvek pedstavuje test agregace jako jednoduchou a levnou metodu stanovení kvality suspenze pi úprav vody vhodnou pro pouzití v laboratorních i provozních podmínkách. Je popsán metodický postup i odvození testu agregace. Metoda je pouzita pro hodnocení vlivu stedního gradientu rychlosti a doby míchání na vlastnosti vytváených agregát (vlocek) pi agregaci v Couettov reaktoru. Bylo prokázáno, ze se vzrstajícím gradientem se snizuje velikost agregát pítomných v suspenzi a suspenze je znacn více homogenní nez pi pouzití nízkých gradient rychlosti. Dále bylo potvrzeno, ze velikost agregát dosahuje po urcité dob míchání stabilní hodnoty. Cas pro dosazení tohoto ustáleného stavu se zkracuje s rostoucí hodnotou pouzitého gradientu. KLÍCOVÁ SLOVA: agregace, flokulace, test agregace, úprava pitné vody, vlastnosti agregát. 1. Introduction In drinking water treatment, a process of coagulation/aggregation/flocculation is widely used. Its purpose is to prepare a floc suspension suitable for the following separation step(s). The floc properties are influenced by chemical (dosage of coagulant, pH and alkalinity) (Annadurai et al., 2004; Polasek and Mutl, 2005) and physical (mixing conditions, i.e. mean velocity gradient and its distribution and the retention time) factors (Bouyer et al., 2005; Mutl et al., 2006). In waterworks operation, the chemical factors, mainly the optimal dosage of coagulant, are commonly determined by jar tests. But the mixing conditions are usually not optimized. Nevertheless, 184 these very physical conditions influence the properties of floc suspension (floc size, shape and density) and thus its separability. It is needed to point out that not every floc suspension is optimally separable by all available separation technologies. For instance, large, dense and strong flocs are ideal for double-stage separation by sedimentation and subsequent depth filtration. But if the direct depth filtration (single stage separation) is used for this very suspension, mentioned flocs form on the surface of the filtration media their own undesirable filtration layer, which leads to change of the depth sand filtration to surface filtration (Hereit et al., 1980). It follows from the given example that we need to know the suspension quality to choose the best separation technology, or on the contrary, to opti- mize mixing conditions to get a suspension suitable for existing technology. The main properties characterizing the flocs are size and density. Since flocs have an irregular shape and they are porous an idealization is needed. The usual way is expressing the floc size by an equivalent diameter. But this method does not consider the floc permeability. That's why a fractal approach has been recently used. A fractal dimension that relates the floc mass (M) with the size (R) is expressed by the relation M R DF , where DF is the mass fractal dimension, which can vary between 1 and 3 in 3-dimensional space (Gorczyca and Ganczarczyk, 1999; Gregory, 2009; Li et al., 2006). This tells us about the floc density; the higher the fractal dimension, the denser the floc; the lower the fractal dimension, the more open, highly branched and loosely bound floc structure (Chakraborti et al.; 2007, Li et al., 2006). There are a few studies which deal with the effect of mixing conditions (velocity gradient (or shear) and time of its action) on the resulting suspension quality in drinking water treatment (Bouyer et al., 2005; Hopkins and Ducoste, 2003; Li et al., 2006; Mutl et al., 2006). But they examine the floc properties in the terms of the basic research without relation to the following separation technologies. There are plenty of methods for floc size determination. Gregory has summarized them in his review (2009). These methods are based on measuring of transmitted light-turbidity (Cheng et al., 2008) or scattered light (Li et al., 2006), they use microscopy, image analysis (Chakraborti et al., 2007; Kilander et al., 2006), or they estimate the floc properties from sedimentation analysis (Droppo et al., 2006; Fargues and Turchiuli, 2003; Tambo and Watanabe, 1979). They are able to provide very good image of size, shape and density of flocs present in the sample. But a problem can arise when transferring the floc suspension into the measurement device. The quality of suspension can change due to different shear conditions or when a dilution is needed. Moreover, the methods are often complicated to perform and the used devices are rather expensive. And there is one disadvantage which these methods have in common; they are not suitable for the use in waterworks operation. However, there is a method called test of aggregation developed by Hereit et al. (1980) which is ideal for waterworks usage. It is simple, cheap and does not require any special instruments. It is based on settling properties of the flocs, and it sorts the flocs according to their suitability for following separation technologies. The method will be described in the next section in detail. The aim of our paper is to show that test of aggregation can provide reliable results comparable with other authors' results, i.e. prove that with increasing velocity gradient (shear), the floc size decreases and the fractal dimension increases, which means that with higher G , the flocs are smaller but more compact (or denser) and stronger (Bouyer et al., 2005; Hopkins and Ducoste, 2003; Li et al., 2006; Mutl et al., 2006). The method was used in the laboratory conditions. The Couette reactor was chosen as a mixing device for the uniformity of velocity gradient distribution (whose evaluation is not the subject of this paper) (Pivokonsky et al., 2003). The use of this method in pilot plant tests and in waterworks operation is reported in Pivokonsky et al. 2008, 2009. 2. Methods 2.1 Test of aggregation evaluation of suspension quality Hereit et al. (1980) developed a method, the test of aggregation, which sorts the flocs (aggregates) into four groups on the basis of their properties changing during their formation and the requirements of individual separation procedures (Tab. 1). The groups are: macro-aggregates (MA), microaggregates (MI), primary aggregates (PR) and nonaggregated particles (NA). A criterion for the categorization is the sedimentation velocity of the formed flocs. As it is evident, the method does not provide information about the exact size, shape and density of individual flocs, but rather give the general knowledge of suspension quality as a whole and help to adjust the operation conditions to reach the highest separation efficiency. 2.1.1 Procedure After dosing the destabilization reagent and mixing under defined conditions (i.e. at waterworks before the inlet of formed suspension to the first or single separation stage), a sample is taken (in the laboratory conditions, it is possible to perform the aggregation test directly in the mixing vessel). The sampling vessel can be a usual 2 l beaker or a jar used in jar tests. The suspension is allowed to settle directly in the sampling vessel, and a concentration of the basic metal constituent of the destabilization 185 reagent (usually aluminum or iron) is measured in the depth of 40 mm under the water surface at defined time intervals (at time of zero, five and sixty minutes of sedimentation and after centrifugation see Tab. 1). The volume of 5 ml taken by pipette from the mentioned depth is sufficient for the aluminum/iron analysis. The proportional amount of each group of aggregates can be calculated from the expressions given in Tab. 1. 2.1.2 Derivation of the aggregation model and test of aggregation The method of aggregation test is based on the simple model of aggregation, which assumes several simplified presumptions: a) The aggregating system contains only one type of particles. b) The aggregating particles are distributed in the entire volume uniformly. c) The conditions allowing the movement of the particles are equal for all particles. d) The growth of aggregates is regular and is done step by step; two neighboring particles are joining to doublets and two neighboring doublets to quadruplets, which are the new units for further aggregation. e) The basic spherical particles are arranged in the quadruplet in such a way that their centers lie in the tops of the tetrahedron, and the particles touch each other (Fig. 1). f) The quadruplet is considered as one development population (P = population number). touching always three spheres (by tetrahedron circumscribed to these four aggregates). The resulting volume is thus an intersection of these two bodies (Fig. 2): Fig. 2. a) Schematic illustration of a sphere and tetrahedron circumscribed to four spherical particles of population P-1; b) Top view: Volume of particle of population P is given by the intersection of a sphere and tetrahedron. 53 6 + 126 3 3 DP-1 = k DP-1 , 216 where k = 3.72. VP = (1) b) To the newly formed aggregate of population P and volume VP given by the Eq. (1), an equivalent diameter DP is assigned, which is calculated as the diameter of a sphere of volume VP. Together the previous equation holds true, thus: VP = 3 3 D = k DP-1. 6 P (2) It follows from the previous equation that the diameter of particle of population P is defined as Kmultiple of the aggregate diameter of the previous population P1: DP = K DP-1 , where K = 3 6k = 1.92 . c) Because the real shape of an aggregate is not a sphere, it is needed to adjust the equivalent diameter with a shape factor, which can be expressed as: Fig. 1. a) Schematic illustration of particle arrangement in tetrahedron; b) Top view. K2 sP = . 4 (4) For the calculation, following aggregate properties were defined: a) The volume of aggregate VP for population P can be calculated as the volume of the sphere circumscribed to the four aggregates of previous population P1, which is limited by four planes d) The porosity of the first population aggregate 1 is defined as the complement of the ratio of the volume of the four aggregates of the population 0 (four spheres with diameter D0) to the volume of the population P1 (volume of spherical tetrahedron) 187 3 D0 4 V0 2 1 = 1- = 1- 6 = 1- = 0.4371 . 3 V1 3k k D0 (5) vP = ( DPsP )2 g ( P - f ) 18 f (8) The average porosity of an aggregate with population P is then expressed by the relation P = P-1 1- 1 + 1 = 1- 1- 1 )P . (6) The basic characteristics of different type of particles present in natural water (Tab. 2) were used for the calculation of respective sedimentation velocities vP and other properties. The calculated values for natural particles are given in Tab. 3. T a b l e 2. The basic characteristics (diameter and density of particle of population 0) of different type of particles present in natural water according to Hereit et al., 1980. D0 [m] 2 10-6 1 10-6 5 10-6 1.5 10-6 e) The average density of the aggregate P for the purpose of sedimentation velocity calculation is defined as: P = P-1 1- 1 + 1 f . (7) Humic particles Clay particles Fe(OH)3 particles Natural particles f) The formed aggregate sediments with a velocity vP corresponding to the sedimentation velocity of a sphere with equivalent diameter DP multiplied by the shape factor sP. 0 [kg m-3] 1200 2500 1500 1650 Table 3. Calculated characteristics of natural particles according to the model of aggregation. P  0 1 2 3 4 5 6 7 8 9 10 11 12 1) DP [m] 1.5 10-6 2.880 10-6 5.530 10-6 1.062 10-5 2.038 10-5 3.914 10-5 7.515 10-5 1.443 10-4 2.770 10-4 5.319 10-4 1.021 10-3 1.961 10-3 3.764 10-3 sP  1.00 0.92 0.85 0.78 0.72 0.66 0.61 0.56 0.52 0.48 0.44 0.41 0.38 P [kg m-3] 1650.0 1365.9 1206.0 1116.0 1065.3 1036.7 1020.7 1011.6 1006.5 1003.7 1002.0 1001.1 1000.6 P  0.000 0.437 0.683 0.822 0.900 0.943 0.968 0.982 0.990 0.994 0.997 0.998 0.999 vP [cm s-1]1) 5.414 10-5 9.543 10-5 1.682 10-4 2.965 10-4 5.227 10-4 9.214 10-4 1.624 10-3 2.863 10-3 5.047 10-3 8.897 10-3 1.568 10-2 2.765 10-2 4.873 10-2 The values of g = 9.80665 m s-2, f = 999.97 kgm-3 (8°C) and f = 1.4719 10-3 Pas (8°C) were used for the calculation of sedimentation velocity. For the purpose of verification of the aggregation model, the sedimentation velocities of aggregates of the diameters D = 0.5, 1 and 2 mm (approximately corresponding to the diameters of particles with population P = 9, 10 and 11 in Tab. 3) were experimentally measured. Assuming that ten populations are necessary to create the observed aggregate of diameter of 1 mm (measured sedimentation velocity = 1.55 10-2 cms-1), the diameter of the basic destabilized particle (P = 0) calculated according to the model is equal to 1.47 10-6 m and its density to 1670 kgm-3, which approximately corresponds to the values given in Tab. 2. The sedimentation velocities vP for equivalent diameters DP of each population are plotted on the 188 graph (Fig. 3). The particle diameters of 1 mm, 0.05 mm and 0.005 mm were selected as boundary diameters for categorization of aggregates into four mentioned groups according to the requirements of individual separation technologies. The sedimentation velocities for these three diameters were derived from the equation of the line drawn in Fig. 3. Their values are given in Tab. 4. The depth of sampling was set at 4 cm under the water level. The value was chosen to avoid both vertical aggregation and effect of surface tension of water level. The time that a particle of given diameter needs to travel these 4 cm is calculated in Tab. 4. For the purposes of aggregation test, these values were rounded off. Fig. 3. Dependence of sedimentation velocity of different types of particles on their diameter calculated according to the Eq. (8). The dashed lines represent the boundaries between the four groups of aggregates MA, MI, PR and NA. T a b l e 4. Calculated sedimentation velocities for boundary aggregate diameters and time that different types of aggregates need to settle under the chosen distance of 4 cm. d [mm] 0.005 (NA/PR) 0.05 (PR/MI) 1 (MI/MA) v [cm s-1] 1.54 10-4 1.14 10-3 1.54 10-2 time [min] (for 4 cm) 432.5 58.5 4.3 time [min] (rounded off) 440 60 5 2.2 Couette reactor optimization of velocity gradient and retention time The effect of the mean velocity gradient G and time of its action t on the suspension quality and aggregation efficiency was evaluated using a Couette reactor as a mixing device. It works on the principle of concentric cylinders, the inner one being rotating. The advantage of the Couette reactor lies in a fact that aggregation takes place in a gap between the cylinders, where a uniform distribution of the velocity gradient in a whole mixed volume can be achieved. Paddle stirrers or impellers do not meet this condition. Studies of aggregation under Couette flow have been conducted by several authors (Boadway, 1978; Mutl et al., 2006; Soos et al., 2007). Raw water (for parameters see Tab. 5) from the reservoir Flaje (Czech Rep.) was used for the research. Aluminum sulfate Al2(SO4)3.18H2O was used as a destabilization reagent. Raw water was pre-treated using lime water for adjustment of pH value. Three complete series were measured to ensure good reproducibility. Dosages of destabilization and alkalization reagent were determined by jar tests at the value of 0.076 mmol l-1 Ca(OH)2 (pH ~ 6) and 0.023 mmol l-1 Al2(SO4)3 . 18H2O. The measurements were carried out at a constant temperature of 8.0 ± 0.5ºC. The values of G = 20, 40, 60, 80, 100, 150, 200, 250, 300, 350 and 400 s-1 were evaluated. The Reynolds and Taylor numbers for defined velocity gradients are given in Tab. 6. They were calculated from the following equations (912). T a b l e 5. Quality of raw water from the reservoir Flaje (CZ). Parameter pH  alkalinity [mmol l-1] CODMn [mg l-1] Al [mg l-1] DOC [mg l-1] Min 6.11 0.12 5.22 0.04 6.68 Max 6.37 0.20 6.49 0.28 7.22 Average 6.18 0.18 5.76 0.12 7.04 T a b l e 6. Reynolds and Taylor numbers for real values of velocity gradient. 3. Results and discussion 3.1 Effect of mixing on suspension quality The theory of aggregation test presumes the development (evolution) of aggregates in time according to a scheme (Hereit et al., 1980): Non-aggregated particles Primary aggregates Micro-aggregates Macro-aggregates This scheme corresponds to a concept of multilevel structure of flocs, which describes formation of aggregates according to scheme (Gorczyca and Ganczarczyk, 1999; Francois and van Haute, 1985): Primary particles Flocculi Microflocs Floc aggregates The process of formation of individual aggregate levels ends on the level given by the velocity gradient used. Low velocity gradients allow the formation of macro-aggregates, while high gradients allow maximally the formation of microaggregates. This statement is also illustrated by the following figures (Figs. 47). In the range of low velocity gradients (20100 -1 s ), there are all types of aggregates present in the suspension and moreover there is a considerable proportion of non-aggregated particles too (at G = 20 s-1, it reaches about 9 % after 30 minutes of mixing). Suspension is then very heterogeneous. Macro-aggregates, suitable for sedimentation, comprise maximally 41 % ( G = 20 s-1, t = 30 min). On the contrary, at high gradients (150 400 s-1) a suspension consists at the beginning of mixing (t = 150 s) predominantly of primary aggregates (at G = 400 s-1 form 95 % of suspension), which turn into micro-aggregates with the mixing time (t = 900 s). Hence the suspension becomes more and more homogeneous with increasing velocity gradient used; the macro-aggregates and non-aggregated proportion decrease almost to the zero value. G [s-1] Re  1675 3349 5024 6699 8373 12560 16747 20933 25120 29307 33494 Ta  562 1123 1835 2446 3058 4586 6005 7644 9173 10701 12230 R + R2 U = 1 , 2 (9) Ta = U d d , R1 (10) Re = U d , (11) 2R R 2 rpm 2R R 1 2 1 2 , G = 2 f = R2 - R2 60 R 2 - R 2 2 2 1 1 (12) where R1 is the outer radius of the inner cylinder, R2 the inner radius of the outer cylinder, d the width of the annular space, the kinematic viscosity, the angular velocity, U the mean streaming velocity and f is frequency (van Duuren, 1968). It can be seen that the suspension is formed in the region of transitional and turbulent flow. Individual velocity gradients were applied for t = = 150, 300, 600, 900 and 1800 seconds (2.5, 5, 10, 15 and 30 min). After that tests of aggregation were carried out directly in the Couette reactor and aggregation efficiency of aluminum was evaluated. t = 150 s 100% 90% t = 300 s 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 20 40 60 MA 80 100 150 200 G [s -1] MI PR 250 300 350 NA 400 80% 70% 60% 50% 40% 30% 20% 10% 0% 20 40 60 MA 80 100 150 G [s -1] MI 200 PR 250 300 NA 350 400 Fig. 4. Proportion of aggregates for different velocity gradients Fig. 5. Proportion of aggregates for different velocity gradients at t = 150 s. at t = 300 s. t = 600 s 100% 100% t = 900 s 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 20 40 60 MA 80 100 150 G [s -1] MI 200 PR 250 300 NA 350 400 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 20 40 60 MA 80 100 150 200 G [s -1] MI PR 250 300 NA 350 400 Fig. 6. Proportion of aggregates for different velocity gradients Fig. 7. Proportion of aggregates for different velocity gradients at t = 600 s. at t = 900 s. Figs. 811 illustrate proportions of individual groups of aggregates in dependence on velocity gradient and mixing time used. These figures confirm that the size of the aggregates decreases with increasing velocity gradient (Bouyer et al., 2005; Hopkins and Ducoste, 2003; Li et al., 2006; Mutl et al., 2006). Fig. 8 shows that proportion of macroaggregates decreases with increasing G and they disappear completely when G > 250 s-1. The influence of the mixing time is not very significant especially at higher gradients ( G > 100s-1). Unlike macro-aggregates at G < 100 s-1 the proportion of micro-aggregates (Fig. 9) is not much influenced by the mixing time and its value ranges between 35 and 45 %, while at higher G the proportion of micro-aggregates increases with the mixing time until reaches the value of approximately 90 % at t = 900 s and this value does not further change any more. In the Fig. 10 there is illustrated an inverse trend, when at higher G the proportion of primary aggregates decreases with mixing time. It is undoubtedly caused by turning these primary aggregates into micro-aggregates. Again at lower G the mixing time does not influence the proportion of primary aggregates, the value of which is around 30 %. Non-aggregated particles are undesirable from technological point of view and it is important to notice that at G = 20 and 40 s-1 the non-aggregated particles does not decrease but remain at a value around 8 % (Fig. 11). On the contrary, at G 100 s-1 after 15 minutes it practically approaches zero. Fig. 8. Proportion of macro-aggregates at given mixing time for different velocity gradients. Fig. 9. Proportion of micro-aggregates at given mixing time for different velocity gradients. Fig. 10. Proportion of primary aggregates at given mixing time for different velocity gradients. Fig. 11. Proportion of non-aggregated particles at given mixing time for different velocity gradients. Generally it can be stated that at low gradients ( G = 2080 s-1) the destabilized particles gradually transform across all levels to micro- and macroaggregates, but certain proportion of nonaggregated particles remains. In the range of middle gradients ( G = 100250 s-1) a continual trend of decrease of primary aggregates, which turn to micro-aggregates and partly to macro-aggregates, can be observed. When high gradients ( G = 300 192 400 s-1) are applied, the zero values of macroaggregates and non-aggregated particles are reached yet after 150 s of mixing. The fundamental feature is then a gradual transformation of primary aggregates to micro-aggregates, which become to predominate in the system after t = 300 s. It follows from the achieved results that the intensity and time of mixing essentially influence the properties of formed suspension. It is undisputed that chemical composition and character of mole- cules present in raw water, type and dosage of destabilization reagent used and reaction pH influence the suspension properties as well (Annadurai et al., 2004; Polasek and Mutl, 2005), but their effect asserts itself more during destabilization. If a maximal possible destabilization under defined conditions is achieved, the decisive presumption for reaching high-quality drinking water is a high efficiency of aggregation, which essentially influences the efficiency of following separation steps (Hereit et al., 1980; Mutl et al., 2006). It is needed to choose the optimal magnitude of the mean velocity gradients and mixing time with respect to input quality of raw water, the destabilization reagent used and expected way of suspension separation. It is really astounding that while the destabilization conditions (reagent and pH) are commonly optimized in practice, the conditions of aggregation (mixing) are often neglected. 3.2 Statistical evaluation of aggregation test The reproducibility of the method of aggregation test was evaluated using a method of Analysis of Variance (ANOVA) the two way design with replication. The tests were performed by three different appraisers in two series of five samples under the identical conditions of G = 150 s-1 and t = 900 s. The proportions of all groups of aggregates were calculated. Each group was evaluated with ANOVA separately. The proportion of macro-aggregates is used for the illustration of the calculation. The basic data used for ANOVA are given in Tab. 7. T a b l e 7. Data for the ANOVA analysis: Proportion of macro-aggregates measured by three different people under conditions of G = 150 s-1 and t = 900 s. 1 0.12 0.12 0.11 0.12 0.10 0.11 0.13 0.12 0.12 0.11 0.11 0.10 0.12 0.12 0.11 2 0.13 0.12 0.12 0.10 0.11 0.12 0.11 0.12 0.10 0.13 0.12 0.11 0.11 0.10 0.11 The ANOVA method was performed with use of Statistica 7.1 (StatSoft, Inc.). The results are summarized in Tab. 8. The null hypotheses were tested at the significance level of = 0.05. They were accepted for all groups of aggregates (in all cases, Fcrit > F and P > .). It means that no significant deviation between different appraisers or different series was found and there is no interaction between these two factors. 4. Conclusions Based on the previous findings, it can be summarized that: - The method of the aggregation test is a simple, inexpensive method of evaluating suspension quality, which can be used both in laboratory and operation conditions. It categorizes the aggregates formed during mixing into four groups (macro-aggregates, micro-aggregates, primary aggregates and non-aggregated particles) on the basis of their diameters and sedimentation velocities. The test of aggregation does not require any special skills or understanding of complicated techniques. The basic knowledge of laboratory technician is sufficient. It provides a satisfactory reliability for evaluation of suspension quality for purposes of waterworks operation. - The applied mean velocity gradient influences the size and size distribution of formed aggregates and also its changes with time. When a higher gradient is applied ( G > 100 s-1), suspensions with homogeneous representation of aggregates, where micro-aggregates predominate, are formed (which is favourable to single-stage separation by filtration). When a lower gradient is used ( G < 100 s-1), the size distribution of aggregates in suspension is of a relatively wide range; there are both large aggregates (macroaggregates) and the smaller ones (primary aggregates and micro-aggregates) in the system and the suspension is substantially more heterogeneous. - The proportion of individual groups of aggregates is also dependent on the mixing time. After a mixing time specific for given velocity gradient, the size of aggregates reaches the steady state, after which it does not change any further. This time needed for reaching a steady-state size of aggregates becomes shorter with increasing value of velocity gradient. Appraiser 1 Appraiser 2 Appraiser 3 T a b l e 8. Two-way ANOVA with replication. ANOVA: two factor with replication Count Sum Average Variance Count Sum Average Variance Count Sum Average Variance Count Sum Average Variance SS 1.87 · 10-4 3.33 · 10-6 2.67 · 10-5 0.00212 0.002337 df 2 1 2 24 29 1 5 0.57 0.114 8 · 10-5 5 0.59 0.118 7 · 10-5 5 0.56 0.112 7 · 10-5 15 1.72 0.11467 6.95 · 10-5 MS 9.33 · 10-5 3.33 · 10-6 1.33 · 10-5 8.83 · 10-5 2 5 0.58 0.116 1.3 · 10-4 5 0.58 0.116 1.3 · 10-4 5 0.55 0.11 5 · 10-5 15 1.71 0.114 9.71 · 10-5 F 1.0566 0.0377 0.1509 P-value 0.3633 0.8476 0.8607 Total 10 1.15 0.115 9.44 · 10-5 10 1.17 0.117 9 · 10-5 10 1.11 0.111 5.44 · 10-5 Appraiser 1 Appraiser 2 Appraiser 3 Total ANOVA Source of variation Sample Column Interaction Within Total F crit. 3.4028 4.2597 3.4028 Acknowledgement. The research project has been funded by the Czech Science Foundation under the project No. P105/11/0247 and Institutional Research Plan No. AV0Z20600510. The authors acknowledge the financial assistance on this project.
Journal of Hydrology and Hydromechanics – de Gruyter
Published: Sep 1, 2011
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