Study of the spherical Couette flow with electromagnetic stirring

Abstract The flow driven by electromagnetic forcing of an electrolytic fluid in a concentric sphere system with differential rotation is studied experimentally and theoretically in the laminar regime. The electromagnetic force is generated by the interaction of a direct current injected radially through electrodes located at the equatorial zone of the spheres and a dipolar magnetic field produced by a permanent magnet inside the inner sphere. Even though the flows are fully three-dimensional, under some assumptions, they can be mathematically modeled with a general one-dimensional solution from the incompressible Navier–Stokes equations. Additionally, in order to deepen the flow dynamics, a full three-dimensional numerical simulation is also obtained. Experimentally, velocity profiles in the equatorial plane between spheres were obtained with particle image velocimetry. The analytical solution reproduces qualitatively the experimental profiles, whereas the numerical solution reproduces quantitatively the experimental measurements.