Figure 7 Experimental breakup time versus the predicted breakup
time based on Equation 12.
Based on the analysis above, it can be reasonably assumed that the drop
breakup time tb follows a linear relationship
with the oscillation period. Moreover, the breakup time is slightly
higher for drops with larger viscosity as shown in Figure 6c. For the
high viscous drops, the influence of the viscosity on breakup time can
be determined by introducing the Ohnesorge number, Oh =μd /(ρdσd )1/2.
As a result, the empirical correlation 12 is proposed to predict the
breakup time. The parameters in the correlation is determined based on
least-squares fitting. The calculated results of the correlation were
compared with the experimental data as shown in Figure 7 and a good
agreement can be observed.
Solsvik and Jakobsen34 studied the drop breakup time
by single drop experiments in a stirred liquid-liquid tank. They
established polynomial/power functions for the breakup time of four
kinds of drops (n-dodecane, toluene, petroleum, and 1-octanol), as
presented in Equation 13. The drop diameter in their study varies from
0.5mm to 4mm. In this study, Equation 13 was adopted to calculate the
breakup times of the four kinds of oils and 8 points with equal
intervals (0.5mm) were selected, as shown in Figure 8. These data points
represent the average droplet breakup time in the experiments of Solsvik
and Jakobsen34. Meanwhile, Equation 12 is used to
calculate the breakup times for the droplets of the four kinds of oils
and plotted in Figure 8. The results show that the model constructed in
this study is in good agreement with the experimental data of Solsvik
and Jakobsen34, which further verifies the accuracy
and applicability of Equation 12.