Drops with conical ends in electric and magnetic fields

Slender-body theory is used to determine the approximate static shape of a conically ended dielectric drop in an electric field. The shape and the ele ctric-held distribution follow from solution of a second-order nonlinear or dinary differential equation that can be integrated numerically or analytic ally. An analytic formula is given for the dependence of the equilibrium co ne angle on the ratio, epsilon/<(epsilon)over bar>, of the dielectric const ants of the drop and the surrounding fluid. A rescaling of the equations sh ows that the dimensionless shape depends only an a single combination of ep silon/<(epsilon)over bar> and the ratio of electric stresses and interfacia l tension. In combination with numerical solution of the equations, the res caling also establishes that, to within logarithmic factors, there is a cri tical field E-min for cone formation proportional to (epsilon/<(epsilon)ove r bar> - 1)(-5/12), at which the aspect ratio of the drop is proportional t o (epsilon/<(epsilon)over bar> - 1)(1/2). Drop shapes are computed for E in finity > E-min. For E-infinity much greater than E-min the aspect ratio of the drop is proportional to E-infinity(6/7). Analogous results apply to a f errofluid in a magnetic field.