Charge convection and interfacial deformation of a compound drop in plane Poiseuille flow under an electric field

The electrohydrodynamics of a concentric compound drop migrating and deforming in a plane Poiseuille flow under the influence of an arbitrarily orientated uniform electric field is investigated using a double asymptotic approach with the electric Reynolds number and capillary number as small perturbation parameters. The effect of viscosity, conductivity, and permittivity ratios, the orientation of the applied electric field, and radius ratio is thoroughly investigated, and the underlying physics is examined in terms of surface charge distribution and shape deformation of the shell and core of the compound drop. For an undeformable compound drop, we found that as the radius ratio increases, the magnitude of lateral velocity due to charge convection increases for both the shell and core, while the longitudinal velocity decreases. The intensity of the drop to lag behind the imposed flow increases as the electric field strength increases. For deformable compound drops, it is observed that the influence of the tilt angle of the applied electric field in altering the direction of motion gets dampened out or minimized when the size of the core increases. We also find that under the combined action of charge convection and shape deformation, the increase in electric Reynolds number enhances the lateral velocity of both the shell and the core drop while the longitudinal velocity decreases. However, it is found that the magnitude of the lateral and longitudinal velocity of the shell and core drop increases with an increase in the capillary number. Finally, by solving for the velocity field of an eccentric compound drop under plane Poiseuille flow and subjected to an applied electric field, we show that there is a critical eccentricity limit and critical time limit within which the concentric and eccentric compound drop configurations produce similar results and beyond which the increment or decrement in shell and core drop velocity is dictated by the value of eccentricity. ©2022 American Physical Societ