Magnetohydrodynamic flow of a binary electrolyte in a concentric annulus

We study theoretically magnetohydrodynamic (MHD) motion of a binary electrolyte in a concentric annulus subjected to a uniform, axial magnetic field. The annulus’ cylindrical surfaces serve as electrodes. When a potential difference is imposed across the cylindrical electrodes, radial electric current flows in the solution and interacts with the axial magnetic field to induce a Lorentz body force that drives azimuthal fluid flow. When the annulus is infinitely long, a purely azimuthal flow (analogous to the classical Dean flow) is possible. We determine the velocity profile, ion concentration fields, and current density as functions of the electrodes’ potential difference and study the linear stability of the azimuthal flow. Of particular interest is the effect of the ions’ concentration fields on the centrifugal Dean instability. When the current is directed outwardly, electrochemical effects destabilize the flow, and the MHD flow loses stability at a Dean number much lower than its analogous, pressure d...