The deformation of a fluid drop in an electric field: a slender-body analysis

The deformation of a fluid droplet in an electric field is computed by a slender body analysis. The drop shape is assumed slender and axisymmetric, but is otherwise arbitrary. Both the shape and aspect ratio l/b of the drop are obtained, in the limit of a strong imposed field, to O(lnl/b)-1. The shape is found to be nearly spheroidal with sharper ends, as observed experimentally and as predicted by full numerical solutions.