## 3 Results and Discussion
The highest %DR achieved by using SDS was approximately 8.03% at concentrations of 1000 ppm and angular velocity of 3000 rpm. From Figures 2 and 3, we can conclude that both PIB and SDS were able to reduce drag; however, DR of PIB is more pronounced than that of SDS. This outcome could be the result of the viscoelastic nature of the polymer, which is limited with the surfactant. Figure 2: Effects of (**a**) Polyisobutylene (PIB) concentrations; and (**b**) \(Re\) on drag reduction percentage (%DR) of diesel fuel with polymer additives. Figure 4a shows the effects of five different complexes prepared from PIB and SDS at various concentrations, while Figure 4b depicts the effect of the Re on %DR as a function of the different complex concentrations. This study investigates the DR performance of the complexes with respect to various rotational speeds of the disk. The result indicates that all the complexes investigated showed increases in DR with corresponding increase in the rpm. Such increase in rpm is the same with the increase in torque. From the Figure 4a,b, the complex mixture of PIB 150 + Di-Octyl 1000 showed the best result and was followed by the complex mixture of PIB 100 + Di-Octyl 1000. At the commencement of the experiment, all the concentrations tested followed a regular pattern. This quality was illustrated by the increase in the DR, which could be attributed to the polymer concentration. Polymers are more effective than the surfactants and complexes in certain occasions [38]. As Re increased to approximately 332,450, DR of all investigated complexes registered a corresponding increase. However, at a Re above 392,896, the surfactants started to gain momentum for the formation of micelles and reached the CMC (critical micelles concentration) point. At this point, the surfactants contributed to the DR efficiency of the polymer, thereby contributing to the entire process. Hence, the surfactant CMC responded to the change of environmental condition that affected the entire complex mixture [39]. However, when the situation realigns and re-enacts the DR attribute, DR reached its peak at approximately \(Re=453\),341. Similar observations were reported in [38], where DR complexes were observed to be influenced by the surfactant re-micellization. Figure 3: Effects of (**a**) sodium dicotyl sulfosuccinate (SDS) concentrations; and (**b**) \(Re\) on %DR of diesel fuel with surfactant additive. Figure 5a shows a comparative study of various best additives that were investigated while considering their torque with respect to \(Re\). Overall, all materials showed torque increase with the corresponding \(Re\) increase. From the data obtained in the present study, the best performance in this respect was obtained for the complex mixture of PIB 150 + SDS 1000 ppm. Next was PIB at 150 ppm and the least DR was only obtained for the SDS at 1000 ppm despite the high concentration of SDS at approximately 1000 ppm. PIB of only 150 ppm was observed to show a better performance than SDS. This observation further confirms initial observations and conclusions that the DR efficiency of polymers is greater than that of the surfactants [38]. Figure 4: Effects of (**a**) complex mixture concentrations (five PIB concentration + 1000 ppm SDS) and (**b**) \(Re\) on %DR of diesel fuel with complex additives. Figure 5: _Cont._  
In addition, the complex mixture formed from the combination of any two or more additives performs better than the individual parties. A similar observation was made in [24; 29; 30]. This performance was expected because of the successful interaction between the surfactant micelles and polymers chains that formed a viscoelastic polymer-surfactant complex. This complex can interfere with the turbulence structures in the main flow (eddies) and can suppress an extensive spectrum of these eddies because of the modified properties gained by forming such a complex. Thus, this result confirms that the contributory action and synergistic act of these additives have a major role to play in the complex mixture.