Figure 12 Comparison between the experimental breakup rate and
predicted results using the breakup rate model of Han Zhou et al.
(2019) 45, c10 = 11,β = 2. (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.
In our previous research45, an empirical correlation
of the drop breakup rate was constructed based on the dimensionless
analysis. The correlation is expressed as:
And:
Where σ drop is the drop restoring stress,
representing the ability resisting the drop deformation.σ v,c, and σ v,d represent
the viscous stress of the continuous phase and the dispersed phase
respectively. τ t is the disruptive stress, which
can be calculated using Equation 5 in Section 3.2.
Equation 17 was adopted to predict the breakup rate in this study. The
calculated results were plotted in Figure 12. It can be seen that a good
agreement between the predicted value and the experimental breakup rate
is obtained, which further proved the accuracy and expansibility of
Equation 17. Moreover, it should also be pointed out that Equation 17
presents the monotone property of the breakup rate with increasing the
drop diameter. Considering that the drop breakup time is getting larger
with the increase of drop size, while the breakup probability of the
drop has an upper limit of 100%. Thus, the monotone property of
Equation 17 can only be strictly valid when the breakup probability of
the drop is relatively low. Based on the experimental breakup rate in
Figure 12 and the correlation of the breakup time in Equation 12, the
breakup possibility (P b) in this study can be
calculated using Equation 20. The results are then plotted in Figure 13.
It can be seen that the values of P b are all
lower than 10%, which further proved the applicability of the breakup
model used in this study.