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the interfacial tension of the drop, the drop will spontaneously reform into a sphere even if the external forces are withdrawn.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.