Deformation of a fluid drop subjected to a uniform electric field

Abstract

We theoretically investigate the deformation of a perfect dielectric drop suspended in a second dielectric liquid subject to a uniform electric field. Axisymmetric equilibrium shapes are found by solving simultaneously the Young–Laplace equation at the interface and Laplace equation for the electric field. Analytical solutions are constructed for the governing nonlinear boundary-value problem using domain perturbation method together with a special type of Hermite–Padé approximation. The results show the existence of a critical electric capillary number beyond which no axisymmetric figure is possible.

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Correspondence to Youness Filali.

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Filali, Y., Er-Riani, M. & El Jarroudi, M. Deformation of a fluid drop subjected to a uniform electric field. Z. Angew. Math. Phys. 72, 12 (2021). https://doi.org/10.1007/s00033-020-01439-w

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Keywords

  • Drop deformation
  • Drop breakup
  • Electrohydrodynamic effect
  • Electric capillary number

Mathematics Subject Classification

  • 41A21
  • 76E25
  • 35J05