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.