Mixing quantification in electromagnetically driven flow between concentric spheres

The mixing quantification of a scalar in the gap of a two concentric spheres is studied theoretically. The flow is electromagnetically driven and is mainly rotational. The driving Lorentz force is generated by the interaction of a dc electric current radially injected in the equatorial zone and a dipolar magnetic field. A full three-dimensional numerical model was developed and has been calibrated with experimental velocity data. A new mixing protocol for high P\'eclet number has been developed. This method is based on the diffusive sheet method (Mart\'inez-Ruiz, Meunier, Favier \& Duchemin, J. Fluid Mech., vol. 837, 2018, pp. 230-257), which has been proven to be accurate in the mixing description of three-dimensional flows, however this new method is simpler and less time consuming.