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.