## 3 Results and Discussion
### C. vulgaris Sedimentation Kinetics after the use of O. cochenillifera  
After the jar test assays, the settling kinetics of the flakes was analyzed by observing the flakes settling over time in a measuring cylinder. Figures 2 and 3 represent the height of the flakes over time in these assays for each acid and alkaline coagulant dosage, respectively. In both figures, the control corresponds to the assay without coagulant. Figure 3: _Chlorella vulgaris_ sedimentation kinetics after coagulation/flocculation with alkaline _Opuntia_, _cochenillifera_ extracts. Figure 2: _Chlorella vulgaris_ sedimentation kinetics after coagulation/flocculation with acid _Opuntia_, _cochenillifera_ extracts. The starting point of the curves corresponds to the time point in which the flocs were still on the surface of the solutions. At this point, the floc height varies between samples due to the concentration of cactus nucilage in the solutions. Overall, the sedimentation kinetics differed between the assays with acid and alkaline coagulants. Lower settling times were observed when acid coagulants were used compared to the control and alkaline assays. Table 2 shows the average speed of sedimentation of the flakes over time in a measuring cylinder. The speeds were evaluated according to Figures 2 and 3. For each curve of the sedimentation kinetics of each graphic was performed the linear regression. The slopes of the regression lines are symmetrical to the value of the average falling speeds of the flakes for each concentration. Hence, it can be verified that the highest speeds are for the lowest dosages of acid extract coagulant solution. Generally, all dosages of acid extract coagulant solutions obtained higher sedimentation speeds than the alkaline extract coagulant solutions and the control. It can be observed that for the alkaline extract coagulant solutions, higher sedimentation speeds of the flakes than the one in control were observed. The sedimentation profile of suspended algae is influenced by the density, size, and shape of microalgal cells, as well as the type of coagulant. The particles settle down according to Stokes' Law; cells quickly reach their terminal velocity once the frictional force is balanced with the gravitational force. Evaluating the sedimentation kinetics realizes that the larger flakes reorganized in the graduated cylinders, leading to a shorter linear sedimentation portion and a faster sedimentation rate [39]. Hence, the kinetic tests performed with the microalgae and the _Opuntia_ (biocoagulant) with the hydrochloric acid used as eluent were much faster than with the cactus nucilage in an alkaline medium, although the highest harvest efficiency occurred in an alkaline medium. The flocculation process determines the structure, density, and settling velocity of flocs, in which flocs acid extract coagulant-microalgae cells were with more compact structures and uniform than flocs alkaline extract coagulant-microalgae cells. In other words, larger particles are more dispersed in the solution; therefore, the sedimentation kinetics takes longer. Hence, the acid extract coagulant-microalgae cells had fast sedimentation but did not result in the highest removal efficiency. The structures of flocs perform the sedimentation kinetic, but not the highest harvesting microalgae cells. Even though the acid coagulant provided higher sedimentation velocities compared to the alkaline coagulant, the harvesting efficiency after 30 min of sedimentation was lower in this case, as mentioned in Section 3.2. The sedimentation profile of suspended algae is influenced by the density, size, and shape of microalgal cells, as well as the type of coagulant. The particles settle down according to Stokes' Law; cells quickly reach their terminal velocity once the frictional force is balanced with the gravitational force. Evaluating the sedimentation kinetics realizes that the larger flakes reorganized in the graduated cylinders, leading to a shorter linear sedimentation portion and a faster sedimentation rate [39].