# Experimental Observations of Heat-Assisted Boycott Effect in Trapezoidal Enclosures
## 3 Results
### Effect of Heat on Average Concentration  
Figure 12 illustrates the impact of heat injection on the average concentration within the cell for cases with initial concentrations of 1500 and 3000 ppm. Additionally, it provides a linear fit for the first 6 min of the sedimentation process, showing the average sedimentation rate \(M\) in %/min, where \(M\) is negative due to the decreasing concentration over time. In the case of 1500 ppm (a), it can be observed that the suspended average concentration (\(C_{a}\)) is lower in the absence of heat injection, with a sedimentation rate of 9.86 %/min. However, imposing an initial power of 4.5 W resulted in a higher suspended concentration in the cell compared to when 9 W was applied, with sedimentation rates of 5.54 %/min and 7.49 %/min, respectively. This suggests that there is a power range  
Figure 11: Sedimentation process discretized with an initial power of 9 W. In the top row (**a**–**c**), the process evolution is observed at \(t_{1}=5\), \(t_{2}=10\), and \(t_{3}=35\) min, respectively, for an initial concentration of 1500 ppm. In the bottom row (**d**–**f**), the evolution is observed for an initial concentration of 3000 ppm at the same times: \(t_{1}\), \(t_{2}\), and \(t_{3}\). Figure 10: Sedimentation process discretized with an initial power of 4.5 W. In the top row (**a**–**c**), the process evolution is observed at \(t_{1}=5\), \(t_{2}=10\), and \(t_{3}=35\) min, respectively, for an initial concentration of 1500 ppm. In the bottom row (**d**–**f**), the evolution is observed for an initial concentration of 3000 ppm at the same times: \(t_{1}\), \(t_{2}\), and \(t_{3}\). where the particle resuspension rate is lower than the sedimentation rate, and another higher power range that generates a greater sedimentation rate compared to the particle resuspension rate. Nonetheless, it is evident that in the absence of heat injection, the resulting concentration field is inferior to that observed in both cases with heat injection. Consequently, there is no discernible advantage to be gained from the injection of heat. In the case of an initial concentration of 3000 ppm (b), it can be observed that the concentration over time is lower for the case where 9 W is imposed, with an average sedimentation rate of 8.52 %/min. In contrast, for the case of 4.5 W, there is no significant difference in terms of average concentration compared to the case without heat injection, where the sedimentation rates are 5.71 %/min and 5.96 %/min, respectively. This is consistent with the earlier observation that the concentration distribution differs between processes with and without heat injection. Figure 13 illustrates the proportion of concentration below 300 ppm and 600 ppm (\(C_{L}\)), representing 20% of the initial concentrations of 1500 ppm (a) and 3000 ppm (b), respectively. In this work, clear water is defined as the portion with concentrations below 20% of the initial concentration. Additionally, a linear fit is applied to the first 12 min of the process, where the slope \(M\) represents the average clear water generation rate in %/min, based on the cutoff values of 300 and 600 ppm mentioned above. This analysis aims to evaluate, to some extent, the effect of heat injection on the generation of clear water. Furthermore, the generation of clear water is also plotted using the PNK model, adjusted to the trapezoidal cell used in the experiments, similar to the approach by [44]:  
\[\frac{DH}{dt}=\frac{V_{0}\cdot X}{X-\frac{H}{\tan\theta}} \tag{1}\]  
where \(H\) is the height of the clear water layer, \(V_{0}\) is the experimentally obtained vertical sedimentation velocity, and \(X\) is the base length of the trapezoid. In the graph on the left in Figure 13a, it can be observed that the process without heat injection achieves a higher generation rate of water with a concentration below 300 ppm, at 3.69 %/min, compared to the processes with a heat injection of 4.5 and 9 W, which generate clear water at rates of 0.42 %/min and 1.45 %/min, respectively.