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

The dynamics of a polarizable spheroid in a shear flow subjected to a magnetic field is determined by a balance between the hydrodynamic torque and the magnetic torque due to the induced magnetic moment. The magnetic moment of the particle is an odd function of H·ao� which saturates to constant for |H·ao�|â�«1, where H is the magnetic field and ao� is the orientation vector of the particle. Three different models are used, the realistic Langevin model and the simpler linear and signum approximations. These models contain two dimensionless parameters, I�=(I¼0I�|H|2/I�) and I�s=(I¼0ms|H|/I�), where I� is the characteristic hydrodynamic torque, I¼0 is the magnetic permeability of free space, I� is the polarizability for low magnetic field, and ms is the saturation moment. The dynamics of the spheroid is analyzed for the case where the magnetic field is aligned along the flow plane. For the linear model, an analytical solution for the evolution of the particle orientation is obtained; there is a continuous transition between a rotating state and a static state when the parameter I� exceeds a critical value which depends on the orientation of the magnetic field and the aspect ratio of the particle. The phase portrait for the signum model exhibits a rich variety in dynamical behavior, including continuous and discontinuous transitions between the rotating and static states, and the possibility of multiple steady states. The transition between stationary and rotating states, and the orientation and magnetic torque in both states, are numerically determined for the Langevin model. © 2021 American Physical Society.