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FIGURE 5.6 Temporal change in the peak of the particle size distribution for Buffalo River suspensions mixed at G = 10 sec-1.

Time (min)

FIGURE 5.7 Temporal changes in the particle size (median) for latex (LT) and Buffalo River (BR) suspensions with various shear rates.

Time (min)

FIGURE 5.7 Temporal changes in the particle size (median) for latex (LT) and Buffalo River (BR) suspensions with various shear rates.

Time (min)

FIGURE 5.8 Temporal plot of D2 for experiments with latex (LT) and Buffalo River (BR) suspensions with 10 sec-1, 40 sec-1 and 100 sec-1 mixing speeds.

Time (min)

FIGURE 5.8 Temporal plot of D2 for experiments with latex (LT) and Buffalo River (BR) suspensions with 10 sec-1, 40 sec-1 and 100 sec-1 mixing speeds.

values. The final steady-state size was found to be higher than the initial size, but lower than the peak size, and final D2 was lower than the initial value, but higher than the minimum, consistent with the above conceptual model description (Figure 5.1).

The effect of mixing speed, suggested in the results of Figure 5.7, is further demonstrated in Figure 5.9, where aggregate area is plotted as a function of size for two experiments from Experiment Set 2, using a relatively high and a relatively low mixing speed. The slopes for the lines (estimated as D2 — see Equation (5.1)) corresponding to G = 20 sec-1 and G = 80 sec-1 were 1.62 (±0.02) and 1.75 (±0.03), respectively, where the ± values are the standard errors for the regression lines. The results verify that aggregate size correlates with mixing speed (and fractal dimension), with smaller size corresponding to larger G and larger D2. For comparison, lines with D2 = 1 and

FIGURE 5.9 Effect of shear rate (G = 20 sec-1 and 80 sec-1) on aggregate size, as represented by area, and comparison with Euclidean relationship (D2 = 2).

FIGURE 5.9 Effect of shear rate (G = 20 sec-1 and 80 sec-1) on aggregate size, as represented by area, and comparison with Euclidean relationship (D2 = 2).

D2 = 2 also are drawn in Figure 5.9. With all data points falling between these two lines, it is clear that the aggregate size depends on a fractal relation.

### 5.4.1.3 Density and Porosity

Solid density and porosity for aggregates produced in Experiment Set 1 at sweep floc condition were calculated using Equations (5.4) and (5.5) and plotted as functions of aggregate size, taken as the major axis of the ellipse fitted to each aggregate (Figure 5.10). Various parameters needed in these definitions (e.g., shape factors) were evaluated using the imaging technique.18,31 Primary particle density was assumed to be 2.65 g/cm3, corresponding to clay or silt particles. For larger aggregates, large portions of the aggregate contained pores, with porosity varying between 0.92 and 0.99. Floc density varied from 1.01 to 1.10 g/cm3, considerably less than the primary particle density. Curves were fit to the data for porosity and density, along with corresponding data from Amos and Droppo.32 As shown in Figure 5.10, the smoothness of the fit for these curves indicates that aggregate properties scale with size. A similar relationship between floc size, density, and porosity has been observed in several previous studies.5,33,34 As previously noted, these properties are important for settling and general transport calculations.

### 5.4.1.4 Collision Frequency Function

Collision frequency (j) was calculated using relations summarized in Table 5.1. To illustrate the general results, j values for a latex suspension mixed with G = 20 sec-1 and treated with alum are shown in Figure 5.11. Results for other tests and other particle size combinations showed similar trends and are not shown here (see Chakraborti25 for further details). To calculate collision frequency functions, two particle sizes (i and j) are required. In these calculations, the primary particle size was taken as 10 ^m, and different sizes for the second colliding particle were assumed, varying between 10 jxm and 1 mm. Results also are shown when variable fractal

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