Electric field mediated droplet spheroidizing in an extensional flow

A 3D mathematical model coupling the phase-field model and the electric current model is applied to describing the DC electric control of droplet deformation in an extensional flow field. Based on this model, electric field mediated droplet spheroidizing in an extensional flow is explored, and the underlying electro-hydrodynamics is clarified. Regime diagrams are plotted to quantitatively recognize the operating regimes for different droplet morphologies, from which the critical electro-hydrodynamic criteria for droplet spheroidizing are summarized. In addition, the influence of electrophysical parameters of fluids on electric field mediated droplet spheroidizing is analyzed. It is indicated that the hydrodynamic forces imposed on the droplet from the pure extensional flow can be completely counterweighted by imposing a proper electric field, so as to realize spheroidizing of the droplet. Within the scope of the current investigation, the critical electric capillary number (Ca-E) for droplet spheroidizing is found to have linear relationship with the hydrodynamic capillary number (Ca), which can be expressed as Ca-E=aCa. Specifically, the linear coefficient, a, decreases with increment of RS (i.e., the product of conductivity ratio and permittivity ratio between the droplet and continuous phase) when RS>1, while it decreases with decreasing RS when RS<1. Compared with RS>1, the critical Ca-E for droplet spheroidizing is generally smaller under RS<1 for a given Ca, suggesting less electric effort is required to realize droplet spheroidizing.