## 3 Experimental Process and Results
The major and minor axis diameters were calculated for each image and then averaged. To verify the accuracy of the calculations, fuel droplets of different sizes were quantitatively generated using a micropipette. Then, the droplet sizes were calculated from the images. The results calculated from the images were compared with the readings from the micropipette, as quantitatively demonstrated in Table 2. By comparison, it was found that the error in droplet size calculated from the images was no greater than 5%, indicating that this method can be regarded as accurate. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Serial Number** & **Micropipette Measurement** & **Calculated from Image** & **Uncertainty (95\%)** \\ \hline
1 & 1.500 \(\mu\)L & 1.437 \(\mu\)L & \(\pm\)0.082 \(\mu\)L \\
2 & 1.000 \(\mu\)L & 0.976 \(\mu\)L & \(\pm\)0.042 \(\mu\)L \\
3 & 0.500 \(\mu\)L & 0.491 \(\mu\)L & \(\pm\)0.008 \(\mu\)L \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of calculation results. Figure 8: Droplet image and scale factor. The droplet undergoes a preheating process before ignition. [PERSON] et al. [25] conducted a study focusing on droplets with a diameter of 1.68 mm. They discovered that the time required for the internal temperature field of a droplet to reach a uniform maximum temperature increases exponentially with rising ambient temperature. At ambient temperatures above 650 K, the average heating rate of the droplets is relatively high, resulting in a significantly shorter time to reach the maximum internal temperature compared to the ignition delay times observed in this study. Therefore, it is considered that the droplet has reached a fully heated state prior to the ignition occurring within the vapor layer. The minimum ignition equivalent diameter \(d_{0}\) of anhydrous ethanol, n-heptane, and n-dodecane across different temperatures is systematically presented in Appendix A. Due to the large number of experimental measurements, to more intuitively illustrate the ignition boundary of the droplet, some duplicate and highly dispersed data were removed from the table. Finally, the equivalent diameter \(d_{0}\) of droplets versus ignition temperature \(T_{\infty}\) was plotted in a scatter plot, as shown in Figure 9.  
The scatter plots of the three fuels clearly demonstrate a negative correlation between the equivalent diameter \(d_{0}\) and ignition temperature \(T_{\infty}\) of the droplets. Specifically, larger droplet diameters correspond to lower ignition temperatures, while smaller droplets require higher temperatures to achieve ignition. [PERSON] [10] concluded that this phenomenon originates from the pre-vaporized diffusion combustion mechanism, where fuel vapor from the droplet surface mixes with ambient air to establish a combustible mixture. In the brief moment just before ignition, the droplet is in a state of evaporation, the concentration of fuel vapor decreases with increasing distance from the droplet surface, and the temperature distribution increases with distance from the droplet surface, approaching the ambient temperature. [PERSON] performed numerical integration based on the energy and  
Figure 9: Scatter plots of the three fuels. diffusion equations derived by previous scholars [10], and summarized the characteristic curves of fuel concentration \(Y_{f}\), oxygen concentration \(Y_{ox}\), and temperature \(T_{f}\) variations with radial distance within the gas-phase region surrounding the fuel droplet in the evaporation regime. As is evident from Figure 10, if the ambient temperature at a certain interface reaches the ignition point under the local fuel vapor concentration, droplet ignition occurs. As the droplet size further decreases, the droplet may completely evaporate before ignition occurs [26]. This results in the fuel vapor concentration no longer increasing, thereby preventing ignition. Due to differences in the volatilities of the three fuels, their evaporation rates vary under identical surface area and temperature conditions.