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Electrohydrodynamic linear stability analysis of dielectric liquids subjected to unipolar injection in a rectangular enclosure with rigid sidewalls

Published online by Cambridge University Press:  10 October 2014

A. T. Pérez ,
P. A. Vázquez ,
Jian Wu  and
P. Traoré
A. T. Pérez*
Affiliation:
Departamento de Electrónica y Electromagnetismo, Universidad de Sevilla, Facultad de Física, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain
P. A. Vázquez
Affiliation:
Departamento de Física Aplicada III, Universidad de Sevilla, ESI, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain
Jian Wu
Affiliation:
Institut PPRIME, Département Fluide-Thermique-Combustion, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France
P. Traoré
Affiliation:
Institut PPRIME, Département Fluide-Thermique-Combustion, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the linear stability threshold of a dielectric liquid subjected to unipolar injection in a two-dimensional rectangular enclosure with rigid boundaries. A finite element formulation transforms the set of linear partial differential equations that governs the system into a set of algebraic equations. The resulting system poses an eigenvalue problem. We calculate the linear stability threshold, as well as the velocity field and charge density distribution, as a function of the aspect ratio of the domain. The stability parameter as a function of the aspect ratio describes paths of symmetry-breaking bifurcation. The symmetry properties of the different linear modes determine whether these paths cross each other or not. The resulting structure has important consequences in the nonlinear behaviour of the system after the bifurcation points.

JFM classification

Complex Fluids: Dielectrics Instability: Instability MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 758 , 10 November 2014 , pp. 586 - 602
Copyright
© 2014 Cambridge University Press 

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