Drop deformation and emulsion rheology under the combined influence of uniform electric field and linear flow

Abstract

Electrohydrodynamics of a leaky dielectric suspended drop subjected to the combined influence of a uniform electric field and linear velocity field is analysed analytically and numerically. In the limit of small charge convection and small shape deformation, an analytical solution is obtained for the deformed drop shape when the imposed linear flow is of uniaxial extensional type with the extensional component aligned in the direction of the electric field. This perturbation approach is then applied towards obtaining the effect of a uniform electric field on the effective extensional rheology of a dilute emulsion. Key results indicate that the magnitude and sense of drop deformation not only depends on the material properties of the drop and medium but is also governed by the strength of the applied electric field relative to the applied flow field. The interfacial charge convection is found to increase or decrease the drop deformation depending on the direction of electrohydrodynamic flow and relative strength of electric field. The electrohydrodynamic flow and drop deformation modulates the effective extensional viscosity of the emulsion. Importantly, the presence of the electric field leads to strain-rate-dependent effective extensional viscosity of the emulsion. The emulsion is found to exhibit strain-rate thinning/thickening behaviour depending on the drop to medium charge relaxation time scale. The analytically obtained drop shape and deformation are in excellent agreement with numerical simulations for the small deformation ranges.