Figure 6 Experimental breakup time. (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.

Modeling analysis of the breakup time

As mentioned above, the experimental studies on drop breakup time have been carried out by researchers with different systems. However, the quantitative description of the influences of operating parameters and physical properties on the breakup time is still limited. Coulaloglou and Tavlarides17 estimated the breakup time using Equation 7:
Vankova et al.55 modified Equation 7 by introducing a dependency on the densities of two phases:
Where , is the Reynolds number in the drop.
Eastwood et al.16 investigated the influence of the drop viscosity on the deforming time and indicated that the breakup time is in silimar scale with the capillary time:
Maaß and Kraume30 proposed a new model for the breakage time in the turbulent regime:
Where is the classic rate of the elongation and is the capillary forces with the critical thread diameter of the elongated drop , . The limitation associated with Equation 10 is the lack of generality when applied to other equipment or systems.34
Based on the experimental results in the above section, the value of the breakup time depends on the drop size, interfacial tension, and the dispersed phase viscosity. That is to say, the intrinsic characteristics of the drop determine the value of breakup time. For a spherical drop, the natural frequency of then th-order shape oscillation represents its temporal properties. The fundamental mode of oscillation, corresponding to n =2, is the most important mode16,56,57. Thus, the oscillation period Tcan be estimated according to the second-order surface oscillating frequency of drop, as is shown in Equation 11.