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Steady and Unsteady Vortex Flow Generated
by Electromagnetic Forcing
C.G. Lara, A. Figueroa and S. Cuevas
Abstract In this paper, we present a numerical and experimental study of the laminar
flow that results from the interaction of vortices driven electromagnetically in a thin
layer of an electrolyte. The fluid motion is generated by a Lorentz force due to a uni-
formD.C. current and a non-uniformmagnetic field produced by different symmetric
arrays of small permanent magnets placed on the perimeter of a circle. Depending
on the number of magnets and the intensity of the electric current, we find that steady
or unsteady vortex flow patterns may arise. We developed a quasi-two-dimensional
numerical model that accounts for the effect of the boundary layer adhered to the
bottom wall. Once the velocity field is obtained, we perform a Lagrangian tracking
that shows a good qualitative comparison with the experimental flow visualization.
From numerical and experimental results, a map of stability that defines regions
of steady and unsteady flow, according to the electric current intensity and magnet
arrays, is built. We find that the larger the number of magnets, the less intense the
applied current required to transit from steady to unsteady flow patterns.
1 Introduction
Vortex dynamics is a topic of great importance in many natural and technological
phenomena. In particular, the study of laminar vortices may improve the comprehen-
sion of the fundamental mechanisms involved in mixing processes at low Reynolds
numbers (Ottino 1990 ). Usually, the interaction of vortices gives rise to very inter-
esting behaviors and flow patterns as occurs, for instance, when a pair of corotating
vortices merge into a single structure (Meunier and Leweke 2005 ). To a large degree,
 
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