To begin the experiment, the stirred tank was firstly filled with the
deionized water, then the motor was started to turn on the impeller. The
rotating speed of the impeller was controlled by adjusting the frequency
of the motor. After steady state was achieved, the organic phase was
injected into the stirred tank from the bottom. Then videos with a
timer-period of 1.334s were recorded. The system was cleaned and
restarted every 30 seconds until enough videos were obtained. In this
study, we recorded 50 videos for each experimental condition. It should
be noted that the volume fraction of the dispersed phase is no more than
2% for each operating condition, thus the coalescence between drops can
be omitted and only the drop breakup behavior is considered. The breakup
event was manually tracked in the video, and the duration of the breakup
process, i.e. the breakup time, and the number of fragments were
recorded. The breakup rate was also measured using Equation 1, which is
consistent with the method adpoted by our previous
study45.
Where Γ(d ) is the breakup rate of the drop with a diameter ofd . tc is the
time
duration of the video. n (d )∆d denotes the number
density of the droplets with diameter in the range of ∆d aboutd , whilenb (d )∆drepresents the number density of the broken drops.
Calculation of the disruptive
stress
The rotating speed of impeller was larger than 330 rpm in this study,
corresponding to the impeller Reynolds number Re larger than
10000. Zhang et al.46 indicated that the velocity
fluctuation levels show Reynolds independent behavior for Reynolds
numbers equal to or higher than 6000. Thus, the local dissipation rate
of the turbulent eddies can be modeled using Equation 2.
Where k is the turbulent kinetic energy, which is roughly
estimated using in a cylindrical vessel with four equispaced
baffles.47,48 Λ donates the distance over which the
vortex velocity varies significantly, and is approximately 0.14D .47,48 Therefore, the turbulent eddy dissipation rate
in the turbine impeller discharge flow is estimated as:
Where N is the rotating speed of the impeller and D is the
diameter of the impeller. Equation 3 was also adopted by Tsouris and
Tavlarides22 and Han et al.49. In
this study, the experimental equipment is a cubic stirred tank without
baffles, the power consumption is about 75% of that of the cylindrical
vessel with four equispaced baffles under the same rotating
speed.50 Corresponding, the turbulence eddy
dissipation should also be reduced by 25%, resulting:
In this study, the largest length scale of the turbulent eddies is of
the order of the impeller radius22, i.e. . The minimum
size of eddies in the inertia subrange can be calculated according to
the Kolmogorov microscale , i.e., . In this study, the upper limit of
the is approximately 3e-5 m which is much smaller than the diameter of
the broken drops. Thus, the breakage is thought to be caused by the
turbulent eddies lying in the inertial subrange. In this case, the
velocity difference between any two points with a distance of can be
calculated using Equation 5.51,52 Thus, the disruptive
stress acting on a drop of diameter d is obtained using Equation
6.53
Where β =2.0 according to Luo et al.23