## 4 Conclusions  
This work uses Micro-PIV to investigate the internal flow fields in the \(\text{PODE}_{2}/\text{PODE}_{4}\) binary droplets with different content ratios during combustion, as well as those of pure \(\text{PODE}_{2}\) and \(\text{PODE}_{4}\) droplets for comparison. The flow field structure, flow velocity, and the influence of the internal flow on the mass transfer process and content gradient formation in the binary droplets are analyzed. The main conclusions are summarized below:  
1. The buoyancy-driven upward vapor flow around the droplet is found to initiate two opposite radial flows in the droplet that form two vortex cores near the surface, while the gravitational effect and Marangoni effect resulting from the content and temperature gradients in the binary droplets can induce disturbance to the two flows.
2. The binary droplets have comparable spatially averaged flow velocities at the stable evaporation stage to those of pure droplets, which are around 3 mm/s. The velocity curves of the binary droplets are more fluctuant and tend to slightly increase and reach peak values at around 250 ms, and then decrease until droplet atomization.
3. The flow velocities in the droplet interior are generally higher than those near the droplet surface, forming a parabolic velocity profile along the horizontal radial direction. The peak velocity first increases to 5-9 mm/s as the radial flow and vortex structure start to form and then decreases to around 3 mm/s until droplet atomization.
4. The radial flow with a spatially averaged velocity of 3 mm/s can only run around one lap at the most during the stable evaporation, which implies that the convection-induced mass transfer is relatively weak, and consequently, the content gradient along the radial direction of the binary droplet is still mainly controlled by mass diffusion.  
B.H.; data curation, formal analysis, investigation, and writing--original draft, H.Z.; investigation, methodology, software, Z.L.; methodology, X.Y.; methodology, W.L.; methodology, Y.L.; conceptualization, resources, supervision, writing--review and editing. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (52206164), Science Center for Gas Turbine Project (P2022-B-II-017-001), Oceanic Interdisciplinary Program of Shanghai Jiao Tong University (SL2022 ZD104), and China Postdoctoral Science Foundation (2021M702098). Not applicable.  
**Informed Consent Statement**: Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Binary Droplet** & \(D_{0}\) **(mm)** & \(D_{1}\) **(mm)** & \(D_{\text{aver}}\) **(mm)** & \(t_{1}\) **(ms)** & \(L\) **(mm)** & \(n\) \\ \hline
10P2/90P4 & 1.270 & 0.680 & 0.975 & 852 & 2.506 & 1.020 \\
30P2/70P4 & 1.360 & 0.910 & 1.135 & 465 & 2.917 & 0.478 \\
50P2/50P4 & 1.280 & 1.100 & 1.190 & 280 & 3.058 & 0.275 \\
70P2/30P4 & 1.540 & 1.230 & 1.385 & 443 & 3.669 & 0.373 \\
90P2/10P4 & 1.430 & 1.070 & 1.250 & 495 & 3.212 & 0.462 \\ \hline \hline \end{tabular}
\end{table}
Table 2: A list of droplet diameter parameters (\(D_{0}\), \(D_{1}\), and \(D_{\text{aver}}\)), measured duration time \(t_{1}\), averaged maximum perimeter of the radial flow \(L\), and radial flow laps \(n\) of the five investigated binary droplets at the stable evaporation stage.  
**Data Availability Statement:** Data will be made available on request.  
**Acknowledgments:** The authors appreciate [PERSON] and [PERSON] for the constructive discussion.  
**Conflicts of Interest:** The authors declare no conflict of interest.