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.