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