Shape of a drop in an electric field

Abstract

The shape of an axisymmetric dielectric drop in a uniform electric field is computed numerically. The problem is formulated as a nonlinear integro-differential system of equations. They are discretized and the resulting algebraic system is solved by Newton’s method. The results show that when the dielectric constant ε is larger than a critical value εc, the drop develops two obtuse-angled conical points at its ends for a certain field strength. For ε<εc, the drop elongates and retains its original nearly prolate spheroidal shape without developing conical points as the field is increased. The numerical results are in good agreement with the moment and two-point approximations. The energy, volume, and area of the drop are computed, and the two-dimensional case is also treated.