## 3 Results and Discussion  
### Taylor Cone Formation of Single Electrified Al/N-Decane Nanofluid Fuel Droplets  
A spray was first produced by pumping the nanofluid fuel into the nozzle in a uniform transverse electric field. During spraying, some of the single large electrified droplets possibly took secondary breakup. Before the breakup, these electrified droplets deformed to resist its breakup behavior, but eventually, it was obliged to produce a Taylor cone and take possibly secondary breakup. Figure 2 illustrates the Taylor cone formation of representative single electrified Al/n-decane nanofluid fuel droplets at different Al nanoparticle concentrations. At each concentration, the single large droplets reproductively deformed and even break up. As the single large droplets separated from the adjacent fine droplets, the moments were considered as \(t=0.00\) ms. The droplets then moved solely in the electric field. During falling, the large droplets continuously electrified to reach the maximum Charge-to-Mass ratio and simultaneously transformed. At any nanoparticle concentration, the transformations were similar. The tip surfaces at the left of the droplets gradually shaped to spherical surfaces, and the droplets became the ellipsoids. Finally, the surfaces on the right were gradually squeezed to the cones. As the cones at the right side, called the Taylor cones, met the requirement of coulomb fragmentation, the droplets would produce cone-jetting. The transformations made the centroids of the droplets change, which were marked by the red stars.  
Figure 2: Formation of Taylor cones.  
During the Taylor cone formation, it can be inferred that the induced charges on the surface transferred and rearranged to make the droplet surface deform and produce the Taylor cone. The charges were mainly concentrated on the tip of Taylor cones at the right side. In the cases of present work, these induced charges on the right were negative, which were opposite to the polarity of the right electrode.  
The deformations of single droplets primarily attribute to the contribution of electric field force, surface tension, and aerodynamic force acting on the droplet surface. The evolution of the surface tension of single droplets at different Al nanoparticle concentrations is shown in Figure 3. Herein, the surface tension was obtained by calculating the products of the surface tension coefficient and the perimeter of droplets. At different concentrations, the surface tension of droplets, two order polynomial formula to time, gradually decreased to the minimum and then increased slightly. It suggests that the breakup of droplets did not occur when their surface tension reached a minimum, whereas it occurred when the Taylor cones were destabilized. It is astonishingly found that the single electrified droplets at the concentrations of 1.0 mg/mL and 3.0 mg/mL did not be disintegrated, indicating that the breakup probability at low concentration (<4.0 mg/mL) is further smaller than that at high concentrations (>4.0 mg/mL).  
The formation time and the angles of Taylor cones at different concentrations are listed in Table 1. It demonstrates that the average formation time of these Taylor cones ranged from 4.17 ms to 13.00 ms, and the average cone angles ranged from 35.1\({}^{\circ}\) to 88.4\({}^{\circ}\). The formation time and the angle of Taylor cones depended on the Al nanoparticle concentration, but not monotonously.  
Figure 3: Surface tension during Taylor cone formation.