Dynamics of polarizable spheroid in a shear flow subjected to a parallel magnetic field

The orientation vector of a spheroid in a viscous shear flow rotates in closed Jeffrey orbits on a unit sphere. If the spheroid is polarizable and it is subjected to a magnetic field, the particle tends to align along the field. The transition between static and rotating states of a polarizable spheroid in a magnetic field subjected to shear flow is analyzed, and the phase boundaries and nature of the bifurcations are identified.