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On the limitation of imposed velocity field strategy for Coulomb-driven electroconvection flow simulations

Published online by Cambridge University Press:  26 June 2013

Philippe Traoré  and
Jian Wu
Philippe Traoré*
Affiliation:
Institut PPRIME, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France
Jian Wu
Affiliation:
Institut PPRIME, Boulevard Pierre et Marie Curie, BP 30179, 86962 Futuroscope-Chasseneuil, France
*
†Email address for correspondence: [email protected]
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Abstract

This study refers to the article of Chicón, Castellanos & Martion (J. Fluid Mech., vol. 344, 1997, pp. 43–66), who presented a numerical study of electroconvection in a layer of dielectric liquid induced by unipolar injection. An important characteristic of the numerical strategy proposed by Chicón et al. lies in the fact that the Navier–Stokes equations are never solved to obtain the velocity field, which is subsequently needed in the charge density transport equation. Instead, the velocity field is explicitly provided by an expression obtained with some assumptions about the flow structure and related to the electric field (the imposed velocity field approach; IVF). The validity of the above simplification is examined through a direct comparison of the solutions obtained by solving the Navier–Stokes equations (the Navier–Stokes computation approach; NSC). It is clearly demonstrated that, even in the strong injection regime ($C= 10$), the results look very similar for a given range of the mobility parameter $M$; however, in the weak injection regime ($C= 0. 1$), significant discrepancies are observed. The rich flow structures obtained with the NSC approach invalidate the use of the IVF approach in the weak injection regime.

JFM classification

Mathematical Foundations: Computational methods Convection: Convection MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , R3
Copyright
©2013 Cambridge University Press 

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