Dynamics of paramagnetic and ferromagnetic prolate spheroids in simple shear flow and uniform magnetic field

We present a theoretical analysis of rotational dynamics for paramagnetic and ferromagnetic particles of prolate ellipsoidal shapes in an unbounded Newtonian shear flow at zero-Reynolds numbers and under a uniform magnetic field. In the absence of a magnetic field, both particles will perform periodic rotations known as Jeffery’s Orbit. The application of a magnetic field affects the rotational dynamics of paramagnetic and ferromagnetic particles differently due to their magnetic properties. To describe the relative strength between the magnetic and hydrodynamic torques, we introduce two dimensionless parameters and determine their critical values above which particle rotations are impeded. In a weak magnetic field, both particles perform periodic rotations but with different symmetry properties. We discuss the relationship between the symmetry of their rotation and the direction of the magnetic field. In a strong magnetic field, the paramagnetic and ferromagnetic particles are impeded at different steady angles and their stability is analyzed. The differences of particle dynamics result in different lateral migration behaviors in wall-bounded shear flows, which are demonstrated by numerical simulations.