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Electrohydrodynamics of viscous drops in strong electric fields: numerical simulations

Published online by Cambridge University Press:  14 September 2017

Debasish Das  and
David Saintillan Open the ORCID record for David Saintillan [Opens in a new window]
Debasish Das
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
David Saintillan*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
*
†Email address for correspondence: [email protected]
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Abstract

Weakly conducting dielectric liquid drops suspended in another dielectric liquid and subject to an applied uniform electric field exhibit a wide range of dynamical behaviours contingent on field strength and material properties. These phenomena are best described by the Melcher–Taylor leaky dielectric model, which hypothesizes charge accumulation on the drop–fluid interface and prescribes a balance between charge relaxation, the jump in ohmic currents from the bulk and charge convection by the interfacial fluid flow. Most previous numerical simulations based on this model have either neglected interfacial charge convection or restricted themselves to axisymmetric drops. In this work, we develop a three-dimensional boundary element method for the complete leaky dielectric model to systematically study the deformation and dynamics of liquid drops in electric fields. The inclusion of charge convection in our simulations permits us to investigate drops in the Quincke regime, in which experiments have demonstrated a symmetry-breaking bifurcation leading to steady electrorotation. Our simulation results show excellent agreement with existing experimental data and small-deformation theories.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Drops and Bubbles: Drops Drops and Bubbles: Electrohydrodynamic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 829 , 25 October 2017 , pp. 127 - 152
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© 2017 Cambridge University Press 

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Footnotes

‡

Present address: Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.

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Das and Saintillan supplementary material movie 1

Movie showing the deformation and flow field in the simulations of figure 4

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