Steady and rotating states of a polarizable spheroid subjected to a magnetic field and a shear flow

A polarizable particle in a magnetic field subjected to a shear flow exhibits a stable stationary state at high magnetic field, and possibly rotating states at low magnetic field. The dynamics of the particle is analyzed for the case where the magnetic field is not parallel to the flow plane. General results are derived for the transition between these states and the dynamics in the limit of low and high magnetic field, and the special cases of a spherical particle and a thin rod.