Figure 9 The proportion of the different numbers of fragments.
In this section, the probability distribution of the number of fragments, the maximum stable drop diameter, and the percentage of binary breakage was discussed. Figure 9 shows the proportion of binary, ternary, quaternary, and quaternary+ breakage. Similar to our previous studies41,58, the binary breakup is dominant over the whole breakup events. Figure 9 also indicated that the occurrence probability of the multiple breakages is increasing for the drops with lower interfacial tension, which can be seen from the Systems No.2-3 in Figure 9. This is mainly due to the larger size of the drops relative to the maximum stable drop, which will be analyzed in detail in the following text.
The impeller Weber number (We =ρcN2D3 /σ ) is widely used to model the Sauter mean diameter (d 32) and the maximum stable drop diameter (d max).59–63 A common conclusion with the vast majority of systems is thatd 32 and d max depend on the -0.6 power of We in stirred vessels.60,64,65 In such a scenario, we plotted the d 32 andd max using the We -0.6 as the abscissa, as is shown in Figure 10a. It can be seen that except for the most viscous system (System No.5, N = 480 rpm), thed 32 and d max display the linear dependence on the We -0.6. The least-squares fitted lines are thus plotted in Figure 10a. Considering the influence of the dispersed phase viscosity on thed 32 and d max, the mechanistic model proposed by Calabrese et al.66 and Wang and Calabrese67 can be adopted. The expression for the d 32 is shown in Equation 14. Moreover, Sprow68 proposed that the the maximum diameter is proportional to the average drop size, the conclusion is also valid in this study. Thus, the correlation for the d maxwas expressed as Equation 15. The fitting parameters for Equations 14, 15 were showed in Table 3.
And:
Where D is the diameter of the impeller.