Shape, stability and dynamics of a charged drop falling on a substrate

The stability of charged droplets emanating from a jet is paramount in electrostatic jet-based applications, such as colloid thruster, electroprinting, electrospinning, electrostatic atomization and spray deposition. Among the number of factors governing the stability, the drop-substrate interaction is imperative as the droplets ultimately settle onto a surface. In this study we numerically investigate the shape, stability and dynamics of a charged droplet falling normal to a ground conducting substrate. The boundary element method (BEM) is used to solve electrostatics and hydrodynamics of an inherently charged droplet as it approaches the surface at different conditions. The numerical results imply several previously unreported behaviors of a charged drop caused by the interplay between its dynamics, the flow fields and the electrostatics. The study emphasizes the influence of fall distance (s(0)), net charge at drop surface (Q), Bond number (Bo) and viscosity (mu) on the drop shape, its kinetics and stability limits. The observations suggest that the critical charge limit (Q(C)) of a settling drop is governed by the fall distance (s(0)), Bond number and the shape perturbations. Interestingly the Q(C) can be larger or smaller than the Rayleigh critical charge limit depending on the governing parameters. The breakup modes of a droplet above critical charge limit are identical; however, the stable droplets exhibit peculiar shape-transitions, not seen in charged droplets levitated near wall or in infinite space. The observations reported here highlight the profound effect of nozzle position from substrate in the abovementioned applications, in addition to the electrical and physical properties of the systems.