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Electromagnetically driven flow of electrolyte in a thin annular layer: axisymmetric solutions

Published online by Cambridge University Press:  05 September 2017

Sergey A. Suslov Open the ORCID record for Sergey A. Suslov [Opens in a new window] ,
James Pérez-Barrera  and
Sergio Cuevas
Sergey A. Suslov*
Affiliation:
Department of Mathematics, H38, Swinburne University of Technology, John Street, Hawthorn, Victoria 3122, Australia
James Pérez-Barrera
Affiliation:
Instituto de Energías Renovables, Universidad Nacional Autónoma de México, A.P. 34, Temixco, Morelos 62580, México
Sergio Cuevas
Affiliation:
Instituto de Energías Renovables, Universidad Nacional Autónoma de México, A.P. 34, Temixco, Morelos 62580, México
*
†Email address for correspondence: [email protected]
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Abstract

Experimental observations of an azimuthal electrolyte flow driven by Lorentz force in a thin annular fluid layer placed on top of a magnet show that it develops a robust vortical system near the outer cylindrical wall. It appears to be a result of instabilities developing on a background of steady axisymmetric flow. Therefore, the goal of this paper is to establish a scene for a future comprehensive stability analysis of such a flow. We discuss popular depth-averaged and quasi-two-dimensional approximate solutions that take advantage of the thin-layer assumption first, and argue that they cannot lead to the observed flow patterns. Thus, three-dimensional toroidal flows are considered. Their similarities to various other well-studied rotating flow configurations are outlined, but no close match is found. Multiple axisymmetric solutions are detected numerically for the same governing parameters, indicating the possibility of subcritical bifurcations, namely type 1, consisting of a single torus, and type 2, developing a second counter-rotating toroidal flow near the outer cylinder. It is suggested that the transition between these two axisymmetric solutions is likely to be caused by the centrifugal instability, while the shear-type instability of the type 2 solution may be responsible for the observed vortex structures. However, a dedicated stability analysis which is currently underway and will be reported in a separate publication is required to confirm these hypotheses.

JFM classification

MHD and Electrohydrodynamics: MHD and Electrohydrodynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 573 - 600
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Copyright
© 2017 Cambridge University Press 

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