Figure 3 Relative deviation plots of the experimental breakup time. (a) System No.1, N=330 ~480 rpm; (b) System No.1-3, N=330 rpm; (c) System No.1,4-5, N=480 rpm.
The size distribution of the daughter drop (DDSD) is the product of different drop breakup processes. Recently, several studies were carried out to investigate the influence factors on the DDSD.28,35,41,44 However, whether the volume fraction of the fragment corresponds to different drop breakup time is still a problem to be settled. In this work, the influence of the daughter droplet size on the breakup time is analyzed through binary breakup events. By dividing the volume fraction of the smaller fragment (fv ) into several intervals, the arithmetic average breakup time of the binary breakup is determined and is presented in Figure 4. Figure 4a-c show the results under different rotating speeds. It can be seen that the breakup time is slightly higher for the higher fv , and the phenomenon is relatively obvious for the lower rotating speed. For the process of drop deformation, the energy is transferred from the surrounding turbulent eddies to the drop surface. An increase in fvusually characterizes the greater surface area changes before and after drop deformation, corresponding to the greater energy requirement from surroundings. With the rough assumption that the energy transfer rate at the drop surface is constant and not affected by other conditions, the larger energy demand thus means longer transfer time, which eventually leads to the increase of breakup time. However, the above discussion is based on a very subjective hypothesis. Practically, due to the complexity of the drop breakup process and energy transfer in the turbulent field, the breakup time and DDSD are more likely to be determined by the trajectory of drop deformation. As the trajectory is complex and is influenced by multiple factors, the relationship between the DDSD and the breakup time is often inconspicuous, especially for the stronger external flow field and the smaller interfacial tension, as is shown in Figure 4c-g. Reasonably, the influence of the daughter droplet volume fraction on the breakup time is no longer considered in the following discussion.
Figure 5 shows the influence of the fragment number on the drop breakup for systems No.1-5. It is indicated that the breakup time is almost impervious to the fragment number. For multiple breakages, the drop generally breaks up into two main larger drops and several concomitant satellite droplets. The formation of the satellite droplet exists in the final phase from deformation to breakage, as is shown in Figure 2b-c. The time for the satellite to be generated can be neglected compared with the deforming process. The dominant influencing factor of the breakup time is the drop deforming trajectory. In this case, the breakup time is arguably independent of the number of fragments. Meanwhile, it should be pointed out that the drop may also break up into several fragments of similar size, leading to a discrepant breakup time compared to the binary breakup. However, the occurrence probability of this breakup mode is very small in this study and is not enough to have a significant impact on the average breakup time. Therefore, it is still reasonable to consider that the influence of the fragment number on the breakup time can be ignored in this work.
Based on the discussion above, the average breakup time was measured for mother droplet with a certain size ignoring the effect of the number or size distribution of the daughter droplets. Figure 6a shows the average breakup time at different rotating speed. It indicates that the rotating speed has an inapparent influence on the average breakup time. This means that the energy transfer rate at the drop surface is little changed with different rotating speeds in this study. Figure 6b shows the influence of the interfacial tension on the average breakup time. The results reveal that the lower interfacial tension will result in a longer breakup time. Solsvik and Jakobsen observed similar behavior in comparing the breakup time of different experiment systems34. They attributed the higher breakup time for drops with lower interfacial tension to the relatively higher viscous grade, which can result in a larger degree deformation before drop breakup34. This explanation can make sense as similar breakup behavior was observed for the drops with higher viscosity and lower interfacial tension. However, our experimental results showed that the breakup time is more sensitive to the change of interfacial tension than the change of viscosity, the latter can be seen in Figure 6c. This indicates that the difference in the breakup time shown in Figure 6b is more likely to be affected by the inherent nature of the interfacial tension. That is, for the higher interfacial tension, the drop has a stronger interfacial reforming capability. Therefore, once the drop deformation starts, the local surface of the drop (especially the terminals of the deformed drop) will be reshaped more quickly, making a shorter time for the deforming process. The influence of the dispersed phase viscosity on the breakup time is shown in Figure 6c. The dispersed phase viscosity can significantly hinder the drop deformation rate and also block the local drop surface reshaping. The former will directly prolong the breakup time of the drop, while the latter will induce a more significant deformation before drop breakup and thus increase the deforming time. It should benoted that during the deformation, the drop with high viscosity tends to stretch into a thin filament in the middle of the deformed drop, and may generate several small satellite droplets. What’s more, all three images in Figure 6 show that the average breakup time monotonically increases with the increasing of the drop diameter. As the drop getting larger, the drop surface needs to undergo the deformation with a longer trajectory before the breakage. Considering that the transfer rate of energy at the drop surface will not change significantly with the increase of drop size, resulting in that the breakup time increases for the larger drop.