Magnetohydrodynamics of insulating spheres

The effect of electric and magnetic fields on a conducting fluid surrounding an insulating object plays a role in various industrial, biomedical and micro-fluidic applications. Computational simulations of the magnetohydrodynamic flow around an insulating sphere, with crossed magnetic and electric fields perpendicular to the main flow, are performed for Rm << 1 in the ranges 0.1 ≤ Re ≤ 100, 1 ≤ Ha ≤ 20 and 0.01 ≤ N ≤ 1000. Careful examination of this fundamental three-dimensional flow reveals a rich physical structure with surface charge on the sphere neighbouring volume charge of opposite sign. Hartmann layers, circulating current and asymmetric velocity and current profiles appear as a result of the applied magnetic and electric field. A parametric study on the magnetic field’s influence on the drag coefficient is performed computationally. The obtained results bridge a gap between various analytical solutions of limiting cases and show good correspondence to earlier work. Correlations for the drag coefficient are proposed that can be valuable for the description of insulating inclusions in various flow applications with magnetic fields.