Figure 2 Broken sequences of drops and corresponding breakup
times, N=390rpm, n-dodecane. (a) binary breakup; (b) ternary
breakup; (c) quaternary breakup.
The breakup of a drop is a complicated process in the turbulent flow. At
present, the quantitative description of the breakup time is not well
addressed in literature as the breakup definition is conflicting in
various studies37. In this work, we adopted a
quantitative method, that is, recording the time since the spherical
droplet before deformation to the moment when the last daughter droplet
is formed. The duration of the whole process is the breakup
time54. Generally, the drop undergoes the deformation,
stretch or revolve until generating fragments, as is shown in Figure 2.
It is indicated that fragments experience the reshaping process after
the breakage. The drop breakup time characterizes how fast the drop
breaks up under the external disruptive stress. Considering that the
reshaping process is controlled by the interfacial tension of the drop,
the drop will spontaneously reform into a sphere even if the external
forces are withdrawn. Therefore, the duration of the reshaping process
is not included in the statistics of breakup time. The breakup time in
this study is thus equivalent to the time of deformation and breakup, as
shown in Figure 2. In the subsequent analysis, the influences of the
fragment number, size distribution of the fragment, rotating speed,
interfacial tension and dispersed phase viscosity on the breakup time
were discussed.
As is indicated in Figure 2, before breaking up, the drop deformed with
a different magnitude due to the turbulent velocity fluctuation. The
deformation process is affected by various factors, such as deformation
position, instantaneous fluctuation velocity, and direction, droplet
trajectory, etc. This leads to certain randomness in the process of a
drop breaking up. Corresponding, the breakup time will not be constant
for a drop with a certain diameter. Experimental data indicated that the
measured breakup time has a large variance.30,34 Such
phenomena were also observed in this study. For detail, the
distributions of the breakage time were analyzed using the index of the
relative deviation (dr ), i.e., , as shown in
Figure 3. Figure 3 exhibits the influence of the rotating speed,
interfacial tension and the dispersed phase viscosity on the
distribution of the relative deviation. The distributions show the
similar distribution for different experimental conditions. Moreover,
the distribution is approximately symmetric overdr = 0, which indicate symmetric frequency
distribution of the breakup time around the arithmetic average valuetb,ave . Accordingly, the arithmetic average valuetb,ave can be reasonably adopted for the
subsequent analysis of the breakup time. As will be discussed in the
following sections, tb,ave is affected by droplet
size, rotating speed of the mixer, as well as physical properties of the
liquids.