Electric driven instability in a charged drop immersed in a viscous dielectric fluid

Linear stability analysis is performed on an electrically charged spherical viscous liquid drop with a spherical rigid core surrounded by a second Newtonian uncharged fluid of different dielectric properties. Dispersion relation and growth rate of the most unstable interfacial mode is found by taking into account, viscous, electrostatic, gravity, and surface tension effects. Several physical interesting cases, such as drop oscillations in vacuum or those involving planar 2D interfaces, are obtained as limiting cases. Numerical simulations are performed for various geometrics, flow, and electric parameters in order to determine the threshold value of the applied voltage or electric charge which lead to multi-jetting phenomena on the interface. The characteristic wave-length (spacing) and size of these radial protrusions is determined in terms of the electric forcing which is an important design parameter for the controlled needleless electrospinning phenomena.