## Abstract

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 electric-field distribution follow from solution of a second-order nonlinear ordinary differential equation that can be integrated numerically or analytically. An analytic formula is given for the dependence of the equilibrium cone angle on the ratio, 6/e, of the dielectric constants of the drop and the surrounding fluid. A rescaling of the equations shows that the dimensionless shape depends only on a single combination of e/e and the ratio of electric stresses and interfacial tension. In combination with numerical solution of the equations, the rescaling also establishes that, to within logarithmic factors, there is a critical field Em-m for cone formation proportional to (e/e- 1)~5/12, at which the aspect ratio of the drop is proportional to (e/ë- 1)1/2. Drop shapes are computed for EOO > E_{min}. For EOO 3≥ E_{min} the aspect ratio of the drop is proportional to E> . Analogous results apply to a ferrofluid in a magnetic field.

Original language | English (US) |
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Pages (from-to) | 329-347 |

Number of pages | 19 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 455 |

Issue number | 1981 |

DOIs | |

State | Published - 1999 |

## All Science Journal Classification (ASJC) codes

- General Mathematics
- General Engineering
- General Physics and Astronomy

## Keywords

- Conical ends
- Dielectric liquids
- Drop deformation
- Electric fields
- Taylor cones