Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field

Abstract

A detailed nonlinear analysis of the deformation and breakup of a perfect dielectric (PD) drop, suspended in another perfect dielectric fluid, in the presence of a quadrupole electric field is presented using analytical (asymptotic) and numerical (boundary integral) methods. The quadrupole field is the simplest kind of an axisymmetric non-uniform electric field. A drop, when placed at the center of such a field, does not translate, thus allowing systematic investigation of the effect of non-uniformity of the electric field. The deformation of a drop under a quadrupole field for PD-PD systems exhibits several novel features as compared to that of a drop under a uniform electric field. The first order analysis predicts oblate deformation for a PD-PD system when the dielectric constant of the suspending medium is larger than that of the drop (Q = εi/εe < 1). This is in sharp contrast to uniform electric fields where oblate shapes are observed only in leaky dielectric systems. Prolate shapes are observed for Q > 1, and the deformation is larger than that for uniform fields for similar electric capillary numbers. The steady state shapes are defined by higher harmonics as compared to the uniform field. At large capillary numbers, prolate deformations (Q > 1) show breakup whereas oblate deformations (Q < 1) do not. Positive and negative dielectrophoresis is observed when the drop is placed off center, and its translation and simultaneous deformation under quadrupole fields is also investigated. The electro-hydrostatics is unaffected by the viscosity ratio. However, the breakup of the drop and the dielectrophoretic motion and deformation strongly depend upon the viscosity ratio.