Deformation and coalescence of water droplets in viscous fluid under a direct current electric field

Deformation and coalescence behaviors of water droplets in viscous fluid under a direct current electric field are investigated with experiments and numerical simulations. An electro-hydrodynamic model is developed based on fluid dynamics equations and electrostatic equations. A coupled level set and volume of fluid method is proposed to capture the dynamic interface. The numerical results are validated to be in good accordance with classic results in the literature. The effects of electric capillary number Ca and viscosity ratio λ on droplet deformation and coalescence are systematically analyzed. Two different droplet response modes are obtained, namely overdamping response and underdamping response. The conversion of response modes is discussed with the (Ca, λ) phase diagram. Moreover, the distributions of electric field and flow field before and after the droplets contact are compared and analyzed. Numerical results show the time evolution of liquid bridge is dominated by the interfacial tension and viscosity of continuous phase. The electric stress is extremely weak at the liquid bridge and has a slight influence on evolution of liquid bridge. The correlation formula between dimensionless liquid bridge radius and conical angle during the growth of liquid bridge is regressed. These results are helpful for the optimization of electro-coalescence process.