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Electrohydrodynamic instability of dielectric liquid between concentric circular cylinders subjected to unipolar charge injection

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Abstract

In this paper, we demonstrate instability of dielectric liquid subjected to unipolar charge injection from a pair of cylindrical electrodes at high Scmidt and high Peclet numbers. The transport of charge density in the annulus is governed by the Nernst-Planck equation and the electric potential by the Poisson equation. The fluid flow is governed by the Navier-Stokes equation together with the continuity equation. The base solutions composed of the one-dimensional conduction state are obtained numerically and the temporal growth of their perturbations is determined from the normal-mode instability analysis by using numerical simulations. The critical values of the parameter for the onset of 2D convective motion are obtained and compared well with the results of full-2D calculation. At high injection, the system tends to be more unstable for the inner injection case and more stable for the outer injection case, as the radius of the inner cylinder is decreased; this trend is however reversed at low injection. It turns out that the critical angular wave number obtained from the flatplate case well predicts the one for an annulus for a wide range of the inner cylinder’s radius.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Dong-A University, Saha-gu, Busan, 604-714, Korea

    Dolfred Vijay Fernandes, Heon-Deok Lee & Yong Kweon Suh

  2. Department of Mechanical and System Design Engineering, Hongik University, Seoul, Korea

    Seungho Park

Authors
  1. Dolfred Vijay Fernandes
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  2. Heon-Deok Lee
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  3. Seungho Park
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  4. Yong Kweon Suh
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Corresponding author

Correspondence to Yong Kweon Suh.

Additional information

Recommended by Associate Editor Dongshin Shin

Dolfred Vijay Fernandes received his B. E. degree in Mechanical Engineering from MAHE University, Manipal, India in 2003. He received his M. Tech. degree from NIT, Calicut, India in 2006. He then received his Ph.D. degree from Dong-A University, Busan, Korea, in 2012. Dr. Fernandes is currently Assistant Professor at the Department Mechanical Engineering, Dong-A University. His research interests are in the field of computational fluid dynamics, microfluidics and electrokinetics.

Yong Kweon Suh received his B.S. degree in Mechanical Engineering from Seoul National University, Korea, in 1974. He received his Ph.D. degree from SUNY Buffalo in 1986. Dr. Suh is currently Professor at the Department of Mechanical Engineering, Dong-A University, Busan, Korea. His research interests include electrokinetic phenomena such as electrohydrodynamics, electroosmosis, electrophoresis, motion of magnetic particles, and mixing in micro and nano scales.

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Fernandes, D.V., Lee, HD., Park, S. et al. Electrohydrodynamic instability of dielectric liquid between concentric circular cylinders subjected to unipolar charge injection. J Mech Sci Technol 27, 461–467 (2013). https://doi.org/10.1007/s12206-012-1260-3

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  • DOI: https://doi.org/10.1007/s12206-012-1260-3

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