Electrohydrodynamic settling of drop in uniform electric field: beyond Stokes flow regime

Abstract

The electrohydrodynamics of a weakly conducting buoyant drop under the combined influence of gravity and a uniform electric field is studied computationally, focusing on the inertia-dominated regime. Numerical simulations are performed for both perfectly dielectric and leaky dielectric drops over a wide range of dimensionless parameters to explore the interplay of fluid inertia and electrical stress to govern the drop shape and charge convection. For perfectly dielectric drops, the fluid inertia alters the drop shape and the deformation behaviour of the drop follows a non-monotonic path. The drop shape at steady state exhibits the transition from oblate to prolate shape on increasing the electric field strength, in sharp contrast to the cases concerning the Stokes flow regime. Similar behaviour is also obtained for leaky dielectric drops for certain fluid properties. For leaky dielectric drops, the fluid inertia also affects the convective transport of charges at the drop surface and thereby alters the drop dynamics. Unlike the Stokes flow regime, where surface charge convection has little effect on the settling speed, the same modifies the drop settling speed quite significantly in the finite inertial regime depending on the combination of electrical conductivity ratio and permittivity ratio. For oblate drops at low capillary number, charge convection alters drop shape, while keeping the nature of deformation unaltered. However, for relatively large capillary number, the oblate drop transforms into a dimpled shape due to charge convection. For all cases, an interesting fact is noticed that under the combined action of electric and inertial forces, the resultant deformation is less than the summation of the deformations caused by individual effects, when inertial effects are strong. These results are likely to provide deep insights into the interplay of various nonlinearities towards altering electrohydrodynamic settling of drops and bubbles.