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4A 4B
FIGURE 4A: The graph plots normalized turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~90 mg/L; FIGURE 4B: The graph plots the residual turbidity vs. sedimentation velocity for each Alum dose ranging 10 mg/L~90 mg/L

Conclusion

Effect of length of the flocculator on residual turbidity:
The length of the flocculator has different effects on the residual turbidity depending on the initial effluent turbidity. In the next figures (label figure numbers), we are comparing the mean residual turbidity as a function of the alum dose at 2 different lengths of flocculator, 2796 cm and 8388 cm (3*2796 cm) and for different influent turbidity, 5NTU (figure ?) and 500 NTU (figure ?) .
As shown in figure ?, at 5 NTU the length has a real effect on flocculation. Low turbidity water is more difficult to flocculate than water with high turbidity because the collision potential required to make large flocs has to be higher. There are few colloidal particles in the water so the average volume occupied by a floc or a particle is bigger so that the average time between collisions is greater leading to a higher collision potential. (Mettre la formule) With a longer flocculator, the residence time is longer and the colloidal particles have more time to collide and form big flocs with a higher terminal velocity than the one at the end of the shorter flocculator. If the terminal velocity of the flocs is bigger, it means that more flocs are going to settle and it will reduce the residual velocity. As shown on figure ?, the residual turbidity is smaller for the longer flocculator.
With an effluent water of 500 NTU, the difference between the two lengths of flocculator can't really be seen in figure ?. The mean residual turbidity is even a little bit higher with the longer flocculator at high alum dose. This could be explained by the fact that we break up flocs. A high turbidity water is easier and faster to flocculate so we are making really big flocs even with the smaller flocculator and as the flocs grow bigger and bigger, they are easier to break. The hypothesis is that a sort of equilibrium is established in the flocculator. Flocs are growing but at one point they are too big and fluid shear stresses break the flocs into smaller fragments. But then these smaller fragments can flocculate again. After some time, a steady state is reached between flocculation and fragmentation and the floc size distribution stay the same. That's why the same residual turbidity is observed for the two lengths of flocculator: the steady state is reached in the two flocculators.

Effect of the alum dose on flocculation:
The next figure (figure ?) we are plotting the residual turbidity as a function of alum dose for water with a different influent turbidity in the short flocculator (2796 cm). We can observe a similar behavior between the plots. At the beginning, the residual turbidity is decreasing when we increase alum dose and then we reach a limit where the residual turbidity is almost constant when we increase alum dose. These results mean that we could optimize the cost by using the minimum alum dose that gives the minimum effluent turbidity.
We can also observe on this figure that at a given alum dose, the mean residual turbidity is different for each influent turbidity. The highest residual turbidity is found for 500 NTU then 25 NTU and 5 NTU. The lowest residual turbidity is found for an influent water of 100 NTU. This could be explained by the fact that two phenomena are happening at the same time. For the low turbidity, 5 NTU and 25 NTU, as I explained earlier, it is longer to produce large flocs and the residence time in the 2796 cm long flocculator might be too short so the residual turbidity is relatively high. For the high influent turbidity, 500 NTU, we reach a steady state in the flocculator but as we are starting with a really high turbidity, the residual turbidity is high too. Logically, the optimum result should be found for a medium influent turbidity and it is found for 100 NTU.