Large deformation of a conductive nanodroplet in a strong electric field

Despite their remarkable effect on printing accuracy and uniformity, charge migrations that dominate the deformation of ink droplets during electrohydrodynamic jet printing have not been widely investigated. In this work, the large deformation mechanisms of a conductive nanodroplet under a strong electric field are examined from the point of view of charge migrations. It is found that the charge migrations include the charge relaxation in the bulk of the droplet and surface charge convection at the fluid interface. A conductive nanodroplet first evolves into an ellipsoid through charge relaxation. Then, the ellipsoid is deformed by the convection of the surface charges in four modes, namely, tip streaming (mode 1), lobe formation (mode 2), finger stretching (mode 3), and dumbbell stretching (mode 4). Finally, the stretched nanodroplet is broken into secondary droplets. Modes 1, 2, and 4 are in agreement with the experimental observations. Furthermore, it is found that over 20% of the charges are distributed inside the bulk nanodroplet and the other charges are distributed at the surface, causing the four deformation modes. Analysis based on the electric Reynolds number (the ratio of electric field force to viscous force) and the Coulombic capillary number (the ratio of surface tension to Coulombic force) shows that the nanodroplet is prolate if the electric field force is dominant. When the Coulombic force plays a crucial role, the nanodroplet deforms into an ellipsoid with wide cones. By contrast, the nanodroplet will generate hemispherical ends if the deformation is dominated by the effect of surface tension.