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Singular Shape of a Fluid Drop in an Electric or Magnetic Field

Hao Li·Thomas C. Halsey·Alexander Lobkovsky
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Abstract

Beyond a threshold, electric or magnetic fields cause a dielectric or ferromagnetic fluid drop respectively to develop conical tips. We analyze the appearance of the conical tips and the associated shape transition of the drop using a local force balance as well as a global energy argument. We find that a conical interface is possible only when the dielectric constant (or permeability) of the fluid exceeds a critical value $ε_c=17.59$. For a fluid with $ε>ε_c$, a conical interface is possible at two angles, one stable and one unstable. We calculate the critical field required to sustain a drop with stable conical tips. Such a drop is energetically favored at sufficiently high field. Our results also apply to the formation of conical dimples when a pool of fluid is placed in a normal field.

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Hao Li, Thomas C. Halsey, Alexander Lobkovsky. 1994-01-26. Singular Shape of a Fluid Drop in an Electric or Magnetic Field. https://doi.org/10.1209/0295-5075%2F27%2F8%2F004

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