Dynamics of Falling Droplet Under Effects of Electric Fields

Physical properties and especially the size of drops are important parameters in many industrial and medical applications. High voltage electric field is one of the effective means to control the final size of drops during the fabrication process which could greatly influence the final size of the product. Therefore a detailed study of electric field effect on a liquid drop is very important. In this work deformation and fragmentation of a falling droplet under gravity and electric force have been studied numerically. The electric force is used as an effective external controlling mechanism to influence the deformation of a drop. The three-dimensional deformation of a falling droplet is studied numerically using the open-source volume of-fluid solver, Gerris with dynamic adaptive grid refinement. The numerical results are compared with previous analytical, experimental and numerical data and excellent agreements between the results are obtained. The results are presented for a broad range of Bond numbers (Bo) from low Bond number (drop with small deformation) to large Bond number (drop breakup and fragmentation). The results revealed that the electric field can be used as a powerful controlling tool in delaying and expediting the falling drop breakup process. The results also showed that falling drop deforms severely by increasing Bo number which leads to the breakup and fragmentation compared to the cases of low Bo number in which the drop deforms mildly without breakup. Moreover, analytical solutions of drop’s deformation are presented in detail and then the outcomes were compared with numerical results. The numerical results are presented for various values of density ratios and electrical conductivity and permittivity. The comparison of the results shows a great agreement between the analytical solutions and the direct numerical simulation (DNS) results