(552d) Deformation of a Liquid Drop in a Quadrupole Electric Field

The two way interaction of electric field and fluid motion is a classical problem due to its importance in explaining natural phenomenon (such as thunderstorms and blue-haze found over rain forests) and many technological applications. In most of the applications electric field is seldom uniform. Moreover, in a non-uniform electric field, uncharged drops may deform and show dielectrophoretic motion which is important in many applications such as multiphase separation, biophysics and micro-fluidic systems. We study the deformation, motion and breakup of a liquid drop freely suspended in another immiscible liquid in a non-uniform axisymmetric electric field. In particular, we report the electrohydrodynamic behavior of the interface in a quadrupole electric field using analytical (asymptotic) and numerical (Boundary Element) method. The quadrupole electric field is simplest non-uniform axisymmetric electric field and when a drop is placed at the center of the field does not translate allowing systematic investigation of drop deformation and breakup.  The drop behaviour is reported in a phase diagram for different electric and fluid properties. Drop in a quadrupole field shows variety of shapes depending of conductivity ratio and permittivity ratio of the fluid pair. The steady shapes are described by higher harmonics as compared to drop under uniform electric field. 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 break-up of the drop and the dielectrophoretic motion and deformation strongly depend upon the viscosity ratio.