## 3 Results
### Flow Patterns and Dead Agitation Zones  
In the microalgae cultivation, dead zones occur when the agitation speed is not sufficient, therefore, the liquid speed is low, which causes accumulation and cell death in these areas. In addition, the formation of toxic compounds occurs, as well as the development of anaerobic zones that produce the propagation of bacteria, conditions that lead to the loss of microalgae cultivation. Due to the above, the percentage of dead zones must be minimized [14; 16]. Figure 4 shows the increase in angular velocity and the paths followed by the tracer particles, which cover more and more areas of the system as rpm increases, causing a decrease in dead zones. Figure 4a shows that turbulence occurs at the agitator outlet, followed by a dead zone. The traced routes tend to stick to the walls of the system, leaving the area of the second curve free, where the dead zone with the largest area occurs. Figure 4b represents the flow patterns at 40 rpm, where the traced routes reach the agitator's fluid suction zone more easily, which generates turbulence in the discharge, reducing the area of the dead zone. After the second corner, vortices are generated; however, the dead zone is not removed, but it does decrease. Figure 4c shows that, at a higher angular velocity, there is a greater distribution of the fluid and fewer dead zones. Linear, vortex, and annular flow  
Figure 3: Probability distribution of velocities near the wall of the Raceway bioreactor; () Experimental pdf, () Theoretical pdf. patterns are observed, the latter being characteristic of turbulence. Despite this, the dead zones are not eliminated, especially after the stirrer, because the stirrer presents suction, even in the discharge zone [8; 15]. Agitation dead zones at the Raceway represent 13.48%, 7.93%, and 4.61% at 35, 40, and 45 rpm, respectively. These obtained values are like those of [PERSON] et al. [15], where there was a reduction of %\(dz\), from 15.38% to 12.75% and 8.52%, at stirring speeds of 20, 25, and 30 rpm, respectively. Although the value of %\(dz\) at 35 and 40 rpm (Table 3) differs very little from the value reported by [PERSON] et al. [15], it can be justified by the increase in fluid velocity and the centripetal and centrifugal forces that are exerted on the second curve of the bioreactor. While the centripetal force tries to keep the flow currents at the center of the curve, the centrifugal force is greater and causes the flow currents to open more to the curve, promoting the flow to follow paths close to the wall of the bioreactor curve. At 45 rpm, the %\(dz\) shows a considerable decrease, having only 4.61% dead zones. These %\(dz\) values are comparable with those reported by [PERSON] et al. [16], which reports a reduction of dead zones from 18% to a minimum of 3% by varying the aspect ratio of a Raceway bioreactor, maintaining flow velocity between 0.15-0.33 m/s in a CFD simulation. Figure 4: Flow patterns at different agitation speeds, it is observed that, by increasing the agitation speed, the presence of dead zones decreases. Flow pattern at (**a**) 35 rpm, (**b**) 40 rpm (**c**) 45 rpm. In addition to the above, the hydrodynamic parameters in an abiotic medium were calculated to provide an approximation to the behavior of the fluid with the microorganisms in the Raceway bioreactor. Table 3 shows the linear speed values (\(v\)) at different stirring speeds (\(\omega\)). The typical stirrer speed (\(v_{tip}\)) in m/s was determined with Equation (10). \[v_{tip}=r\omega\left(\frac{2\pi}{60}\right) \tag{10}\]  
where \(r\) is the radius of the agitator, from the axis, and \(\omega\) is the angular velocity in rpm. The \(v_{tip}\) is used to determine the cell-stirrer collision energy (\(E_{ca}\)) with Equation (11). \[E_{ca}=\frac{1}{2}\left(\rho_{c}\frac{\pi}{6}d_{c}^{3}\right)\cdot v_{tip}^{2} \tag{11}\]  
where \(\rho_{c}\) and \(d_{c}\) are the density and diameter of the cell, respectively [27].