Steady and Unsteady Vortex Flow Generated by Electromagnetic Forcing

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 uniform D.C. current and a non-uniform magnetic 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.