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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.

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Two dimensional steady Newtonian flow past oblate and prolate spheroid particles confined in cylindrical tubes of different diameters has been numerically investigated. The flow and drag phenomena of confined spheroid particles are governed by the equations of continuity and conservation of momentum. These equations along with appropriate boundary conditions have been solved using commercial software based on computational fluid dynamics. Extensive new results were obtained on individual and total drag coefficients of spheroid particles, along with streamline contours, distributions of pressure coefficients, and vorticity magnitudes on the surface of spheroid particles as functions of the Reynolds number (Re), the aspect ratio (e), and the wall factor (λ) over the following range of conditions: 1 ≤ Re ≤ 200, 0.25 ≤ e ≤ 2.5, and 2 ≤ λ ≤ 30. For all values of the aspect ratio, as values of the Reynolds numbers and/or the wall factor increase, the length of recirculation wake increases. For fixed values of the aspect ratio and the Reynolds number, the increase in the value of the wall factor decrease both individual and the total drag coefficients. On the whole, regardless of the value of the aspect ratio, the wall effect was found to gradually diminish with the increasing Reynolds number and/or the wall factor. Finally, on the basis of the present numerical results a simple correlation has been proposed for the total drag coefficient of confined spheroid particles which can be used in new applications