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Uniform electric field induced lateral migration of a sedimenting drop

We investigate the motion of a sedimenting spherical drop in the presence of an applied uniform electric field in an otherwise arbitrary direction in the limit of low surface charge convection. We analytically solve the electric potential in and around the leaky dielectric drop, and solve for the Stokesian velocity and pressure fields. We obtain the drop velocity through perturbations in powers of the electric Reynolds number which signifies the importance of the charge relaxation time scale as compared to the convective time scale. We show that in the presence of electric field either in the sedimenting direction or orthogonal to it, there is a change in the drop velocity only in the direction of sedimentation due to an asymmetric charge distribution in the same direction. However, in the presence of an electric field applied in both the directions, and depending on the permittivities and conductivities of the two fluids, we obtain a non-intuitive lateral migration of drop in addition to the buoyancy driven sedimentation. These dynamical features can be effectively used for manipulating drops in a controlled electro-fluidic environment.