## 3 Results and Discussion
### Flow Velocity Evolution and Distribution of the Investigated Droplets  
#### 3.2.1 Spatially Averaged Flow Velocity Evolution of the Investigated Droplets  
The blue curves in Figure 4 show the spatially averaged flow velocity evolution of the five investigated binary droplets. It can be seen that there is a short vibration and increase in the averaged flow velocity after ignition. This is mainly because the electric spark in the ignition process can cause a vibration in the droplet and increase the flow velocity. This disturbance in the flow field quickly disappears after around 60 ms, and the droplets enter into the stable evaporation stage when the flow field keeps stable. After a certain period of time, the velocity quickly increases, and the curve becomes unstable. This means that the droplet has entered into the atomization stage when bubbles are formed and grow in the droplet because of the content gradient and temperature gradient [23]. The droplet atomization process can lead to strong vibration of the droplet, and thus, the averaged flow velocity in the droplet at this stage is relatively large and fluctuant. Therefore, these velocity curves can reveal the atomization delay time of these binary droplets. It can be seen that the 50P2/50P4 droplet has the shortest atomization delay time, which is in accordance with our previous study on the combustion of \(\mathrm{PODE_{n}}\) binary droplets [7]. The red points in Figure 4 represent the correlation values of these velocities. According to the DaVis 8.4 software, the velocity can be regarded as accurate if the correlation value is higher than 0.7. Therefore, it can be seen that the velocities at the atomization stage are not accurate because the correlation values are all lower than 0.6. This is mainly because under the strong vibration and large averaged flow velocity conditions, the same particle in the adjacent frames cannot be accurately identified, so the calculation is not reliable. Therefore, only the velocity results in the stable evaporation stage are useful and will be discussed here. Figure 5 shows the comparison of spatially averaged flow velocity evolution at the stable evaporation stage among the investigated pure and binary droplets. It can be seen that the binary droplets generally have comparable averaged flow velocities with the pure droplets. For pure droplets, \(\mathrm{PODE_{2}}\) and \(\mathrm{PODE_{4}}\) droplets generally have comparable flow velocities of around 3 mm/s. Their velocities are relatively stable and stay almost unchanged during the whole droplet evaporation stage. Since the internal flows in the pure droplets are only controlled by the upward vapor flow, it can be seen that the flow velocities caused by the upward vapor flow in the suspended droplets are at mm/s scale. For binary droplets, the content ratios of \(\mathrm{PODE_{2}}\) and \(\mathrm{PODE_{4}}\) seem to only have little effect on the flow velocity. This is mainly because the content-gradient-induced flow velocities under the  
Figure 4: Evolution of the spatially averaged velocities (blue curves) and the corresponding correlation values of the flow velocities (red points) in the five investigated binary droplets. gravitational and Marangoni effect are only at the scale of \(\mu\)m/s [14; 15], much smaller than the vapor-flow-induced flow velocities. Therefore, the different content gradients caused by different content ratios of the binary droplets cause little difference to the flow velocity. However, strong fluctuation can be found on the velocity curves of the binary droplets, and their averaged flow velocities first increase a little after ignition and then gradually decrease until atomization. As mentioned above, the flow field in the pure droplet is only controlled by the upward vapor flow, while the flow field in the binary droplet is disturbed by the gravitational effect and Marangoni effect caused by content gradient and temperature gradient.