A small-deformation perturbation analysis is developed to describe the effect of a uniform electric field on drop deformation and orientation in linear flows and emulsion shear rheology. All media are treated as leaky dielectrics, and fluid motion is described by the Stokes equations. The one-particle contribution to the effective stress of a dilute emulsion is obtained from the drop stresslet. Analytical solutions are derived as regular perturbations in the limits of small capillary number and large viscosity ratio. The results show that both shape distortion and charge convection modify emulsion rheology. Drop deformation due to application of an electric field in a direction perpendicular to the shear flow gives rise to normal stresses and may lead to shear thickening or shear thinning, depending on the electric properties of the fluids. Charge convection due to the imposed shear affects both the shear viscosity and normal stresses.
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