The Limit to Concentric Electrohydrodynamic Analysis of a Sedimenting Compound Drop

Researchers have extensively investigated the phenomenon of electrohydrodynamic sedimentation of single drops. But until now, very few have addressed the electrohydrodynamic settling of a compound drop when it is under dual effect of charge convection and interface deformation. The choice between analysis for concentric or eccentric regime is a crucial decision that must be made before beginning any compound drop analysis. Hence, the limit to concentric electrohydrodynamic analysis of compound drops needs to be established. In this paper, we attempt to resolve so by creating a three-dimensional analytical model of a circular compound drop subjected to electrostatic field with varied orientation of electric field. In order to establish the demarcating limit between analysis for concentric and eccentric regime, critical assessment of viscosity, permittivity and conductivity of the phases, electric field application direction, and relative size of the shell and core on the involved electrohydrodynamic settling are also carried out. According to our research, the compound drop's directional divergence from the path of gravity can be effectively controlled by adjusting the conductivity and permittivity ratio. Moreover, the shell and core drop may attempt to deviate laterally in different directions at high viscosity ratios. This finally paves the way to establish that the validity of analysis for concentric and eccentric regime of compound drop is dictated by the polynomial relation between viscosity ratio and radius ratio of the two drops.