  Dynamics of a liquid drop falling through a quiescent medium of another
liquid is investigated in external uniform electric field. The
electrohydrodynamics of a drop is governed by inherent deformability of the
drop (defined by capillary number), the electric field strength (defined by
Masson number) and the surface charge convection (quantified by electric
Reynolds number). Surface charge convection generates nonlinearilty in a
electrohydrodynamics problem by coupling the electric field and flow field. In
Stokes limit, most existing theoretical models either considered weak charge
convection or weak electric field to solve the problem. In the present work,
gravitational settling of the drop is investigated analytically and numerically
in Stokes limit considering significant electric field strength and surface
charge convection. Drop deformation accurate upto higher order is calculated
analytically in small deformation regime. Our theoretical results show
excellent agreement with the numerical and shows improvement over previous
theoretical models. For drops falling with moderate Reynolds number, the effect
of Masson number on transient drop dynamics is studied for (i) perfect
dielectric drop in perfect dielectric medium (ii) leaky dielectric drop in the
leaky dielectric medium. For the latter case transient deformation and velocity
obtained for significant charge convection is compared with that of absence in
charge convection which is the novelty of our study. The present study suggests
that for both the regimes, surface charge convection tends to increase or
decrease the settling speed depending upon the ratios of electrical properties.
Notably, in the inertial regime, deformation and velocity are seen to be
altered prominently in the existence of significant charge convection.
