## 3 Results and Discussion
### Mechanism of the Secondary Breakup of Single Electrified Al/N-Decane Nanofluid Fuel Droplets  
In electrostatic field, the secondary breakup mechanism of single electrified nanofluid fuel droplet focuses on: (1) charge transportation at the droplet surface, (2) deformation and breakup of the droplet, (3) nanoparticle concentration effect on charge transportation, droplet deformation and breakup. Figure 7a demonstrates a pattern of inductive charging. The left electrode connects with the negative pole of the high-voltage source, whereas the right electrode connects with the ground. The direction of the electric field directs towards the left side. The single droplets sprayed from the nozzle are electrified in the uniform strong electric field. Since the permittivity of the droplet fluid is finite and low, an electric field could have existed inside the droplet owing to the presence of the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Concentration (mg/mL)** & \(C^{\prime}\)/E **(m/N\({}^{1/2}\))** & **Concentration (mg/mL)** & \(C^{\prime}\)/E **(m/N\({}^{1/2}\))** \\ \hline
2.0 & 0.206 \(\pm\) 0.006 & 7.0 & 0.203 \(\pm\) 0.006 \\
4.0 & 0.193 \(\pm\) 0.005 & 8.0 & 0.208 \(\pm\) 0.006 \\
5.0 & 0.203 \(\pm\) 0.006 & 9.0 & 0.203 \(\pm\) 0.006 \\
6.0 & 0.180 \(\pm\) 0.005 & 10.0 & 0.189 \(\pm\) 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The \(C^{\prime}\)/E value at the point of disintegration. Figure 6: The average diameters of secondary breakup sub droplets at different Al nanoparticle concentrations. external strong electric field. It causes polarization of the droplet medium due to the realignment of the molecules in the droplet with the electric field, resulting in the presence of induced charges on the droplet boundary [25]. Therefore, for electrically charged droplets of dielectric liquids, in the external electric field, there will exist both \"free\" and \"induced\" charge at the droplet surface. Supposing the single large electrified droplet is ellipsoidal, the free charges and induced charges uniformly distribute at its surface, as shown in Figure 7b. In the uniform electric field, these charges transfer towards the two opposite polarity electrodes, resulting in a negative gradient of charge density from the center to the two sides of a single droplet. On the left boundary, the positive ends of the molecules are aligned, and similarly the negative ends of the molecules on the right boundary. The induced charges significantly increase the total surface charges on one side of the droplet and simultaneously reduces it on the opposite side [26]. At the apexes of two sides, the charge density reaches maximum. The charge density gradient would oblige the droplet to suffer the non-uniform electrical force. However, the surface tension would adjust to resist the non-uniform electrical force, leading to the deformation of the droplet (See Figure 7c). Finally, the deformation of the droplet gradually forms the Taylor cone. It can be testified by observing the experimental results shown in Figure 2.  
Overall, the droplet is unstable, and the location of the point of maximum surface charge density is a function of the free charges, the induced charges, and the direction of the external electric field [27]. The induced polarization charges and free charges at the droplet surface can contribute towards the fission of the droplet. If the local electric field force exerted on the Taylor cone was over the surface tension, the liquid within the droplet would be extruded from the tip of the Taylor cone and break into the Rayleigh limit and take secondary breakup (See Figure 7d). The breakup of the droplet relates to the dielectric (conductivity) ratios between the droplet and continuum fluids, e.g., \(\varepsilon_{\text{d}}\)/\(\varepsilon_{\text{g}}\) (\(\sigma_{\text{d}}\)/\(\varepsilon_{\text{g}}\)), and liquid viscosity [28].