Effect of charge convection on gravitational settling of drop in uniform electric field

Abstract

Dynamics of droplets in an electrified medium is largely dictated by an intricate interplay between interfacial charge convection and Ohmic conduction within the bulk. The extent of this interaction is quantified by the electric Reynolds number, ReE, delineating their relative strengths. The reported asymptotic theories consider vanishingly low values of ReE, i.e., negligible surface charge convection as compared to the bulk Ohmic conduction, which, in turn, enables decoupling of the contributions of drop deformation and charge convection. This, however, is grossly inaccurate toward establishing an appropriate inter-connection between surface charge convection and morpho-dynamic evolution of the drop beyond such limiting conditions. Circumventing these limits, here we present a theoretical approach that is capable of bringing out the underlying physics beyond low ReE limits. We realize this by incorporating nonlinear charge-convection effects in the leading-order and first-order problem. The present analytical model not only predicts the drop speed accurately but also shows noticeable improvement over the predictive capabilities of the existing asymptotic models. Our results demonstrate that convection of charges can lead to a substantial increase or decrease in gravitational settling speed, depending on the relative electrical properties of the droplet and the carrier. In sharp contrast to previously reported findings, we show that sufficiently strong charge convection can overwhelm the effect of deformation and hence can reverse the trends in the settling speed reported earlier. Comparison with results from full-scale numerical simulations justifies the accuracy of our analytical approach up to a fair level of high asymmetric deformation.