Abstract
The process of breakup of a liquid drop in a shear field is irreversible and discontinuous, and the deformed shape of and the flow behavior in the drop at the step of breakup are too complex to analyse.
As the first approach in this paper, the macroscopic balance of mechanical energy, taking into account the changes of surface and kinetic energies and energy dissipation, is applied to the deformation process and conservation of mechanical energy in the dispersed phase during the breakup process is assumed. From this analysis, it is found that under a shear stress changed stepwise the minimum loaded time, θ2, required for breaking up a drop into two droplets is inversely proportional to the excess shear rate ΔG (=G -GB).
However, the state of drop at the natural breakup under shear stress continuously loaded cannot be shown as a singular state in the first approach. Thus, as the second approach, the catastrophe theory is applied to the breakup process.
In the cusp-type catastrophe, if the excess shear rate ΔG and the loaded time θ · ΔGas two external variables, and the state of drop as the internal variable are chosen, the process of de-formation and breakup can be well interpreted. The dependencies of the loaded time and the number of droplets at the natural breakup process on the excess shear rate, predicted by the theory, have been proved by the experimental data.
