## 3 Results and Discussion
### Charge-to-Mass Ratio of Single Electrified Al/N-Decane Nanofluid Fuel Droplets  
The dripping single droplets primarily suffered from the gravity force, the electric field force, and the drag force. The drag force is negligible, compared to the electric field force, thus in the horizontal direction following correlation can be obtained according to [PERSON]'s Second Law:  
\[qE=ma \tag{1}\]  
where \(E\) is the electric field intensity; \(q\) and \(m\) represent the charge and mass of an individual droplet, respectively; \(a\) is the acceleration in the horizontal direction.  
While  
\[E=\frac{U}{L} \tag{2}\]  
where \(U\) and \(L\) represent the voltage and electrode spacing, respectively. Thus, the Charge-to-Mass ratio can be expressed as  
\[\frac{q}{m}=\frac{aL}{U} \tag{3}\]  
In this work, the X-direction displacement (s\({}_{\rm x}\)) of droplet centroids (see Figure 2) is defined as the X-direction distance of droplet centroids between any moment (\(t\)) and initial zero time. The displacement data were extracted and plotted in Figure 4. It demonstrates that the X-direction displacement was quadratic polynomial related to time, i.e., \(s_{\rm x}=At^{2}+Bt+C\). The fitting results are listed in Table 2. The correlation coefficients are almost close to 1.0. Therefore, the acceleration (\(a_{x}\)) can be obtained by finding the second derivative of the displacement (s\({}_{\rm x}\)), i.e., \(a_{x}=d^{2}(s_{x})/dt^{2}\), which is equal to 2A. During dripping, the accelerations are possibly positive or negative, which depends on the polarity of the large droplet residual charge as separated from the adjacent fine droplets. In these cases, the accelerations at Al nanoparticle concentrations of 1.0 mg/mL and 3.0 mg/mL were negative constant during dripping, suggesting that the droplets at 1.0 mg/mL and 3.0 mg/mL took uniformly retarded motion. While at other concentrations, the single droplets were taking uniformly accelerated motion in the electrostatic field.  
The Charge-to-Mass of multiple large droplets were calculated for each nanoparticle concentration. According to the Equation (3), if the charge polarity was not considered, the average Charge-to-Mass ratio and the error of single droplets can be solved by \(\overline{q/m}=\frac{1}{n}\sum\limits_{1}^{n}\left(q_{i}/m_{i}\right)\) and \(u(\overline{q/m})=\frac{1}{\sqrt{n}}\sqrt{\frac{\sum\limits_{i}\left(q_{i}/m_{ i}-\overline{q/m}\right)^{2}}{\left(n-1\right)}}\), where \(n\) is the droplet number (\(4\leq n\leq 7\) in this work). The calculated results are listed in Table 2. The order of magnitude of the Charge-to-Mass ratio reached \(10^{-7}\)-\(10^{-5}\) C/kg. At any concentration, these single droplets have been completely electrified with saturated charge value till breakup. Despite the volumetric charges of single droplets were saturated, the surface charges transferred freely at the surface of single droplets in the electrostatic field. The transportation of the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Concentration** & **Time** & **Average Time and** & **Taylor Cone Angle** & **Average Taylor Cone** \\
**(mg/mL)** & **(ms)** & **Error (ms)** & **(\({}^{\circ}\))** & **Angle and Error (\({}^{\circ}\))** \\ \hline
1.0 & 7.10 & 7.05 \(\pm\) 0.07 & 75.8 & 77.0 \(\pm\) 1.6 \\
2.0 & 4.00 & 4.17 \(\pm\) 0.23 & 60.8 & 63.5 \(\pm\) 0.6 \\
3.0 & 5.50 & 5.60 \(\pm\) 0.  
charges made the distribution of surface charge nonuniform, resulting in the local deformation of single droplets and producing the Taylor cones.