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.