Effect of viscoelasticity on drop deformation in a uniform electric field

We study the effect of an external electric field on the deformation of a viscoelastic drop suspended in another viscoelastic medium. Leaky dielectric drops suspended in another leaky dielectric medium, when subjected to a uniform electric field, undergo deformation. We use the Oldroyd-B constitutive relation to model viscoelasticity and equations for leaky dielectric materials to solve for the electric field. We perform numerical simulations of the Navier-Stokes equations using a volume-of-fluid method to simulate the two-phase electrohydrodynamic flow. By performing an asymptotic analysis, we solve for the deformation of a droplet in the limit of small capillary number (ratio of viscous to capillary forces) and Deborah number (ratio of relaxation time constant and flow time scale). A viscoelastic drop suspended in Newtonian medium results in a smaller deformation compared to a Newtonian drop suspended in a Newtonian medium. The effect of viscoelasticity is more prominent when a Newtonian drop suspended in a viscoelastic medium is subjected to an external electric field. We also study effect of permittivity and conductivity ratios on the extent of deformation. Results from the volume of fluid based numerical simulations are in good agreement with the asymptotic analysis results.