Dynamics of spherical particles in the presence of shear and oscillating magnetic field

Magnetically actuated particles find a number of applications in microscale systems, like mixing, pumping, rheological measurements etc. At higher concentrations their collective behavior can give rise to jamming. Hence, they are used for magnetorheological applications – based on the instantaneous change in the fluid viscosity due to field. However, these require more understanding of the particle’s response to different temporal and spatial fields. In the current study the single particle dynamics of a magnetic spheroid with ferro and paramgnetic properties are analysed in the presence of an oscillating magnetic field. A hard ferromagnetic particle is modeled as a permanent dipole along the long- axis of the spheroid. The dynamics of such a spheroid depends on the dimensionless number ω † , the ratio of field frequency to the viscous relaxation rate. For ω † ≪ 1, the particle is almost always oriented along the field direction, other than the time
range close to the maximum value of the field. The fluid torque is proportional to √ω † , independent of the initial condition. At higher values of ω † , the particle makes small amplitude oscillations about it its initial condition. The torque is independent of ω † but depends on the initial condition.
The hysteresis in soft ferromagnetic materials is modeled using the Stoner-Wohlfarth model. The moment is in the plane of the field and the particle orientation. The particle dynamics in this case is also dependent on the dimensionless number, h, the ratio of the Zeeman and the anisotropy energies. At small h, the particle dynamics is similar to that of a permanent dipole. The moment oscillates about one pole of the orientation and is called the oscillating moment. For larger h, the moment switches from one pole of the orientation to the other. This is called the switching moment and the particle makes small amplitude oscillations about the field’s positive direction. For intermediate values of h, the particle exhibits both types of behavior based on the initial condition (ϕi ) and ω †.
For paramagnetic spheroids, the Langevin, linear and signum models demonstrate that the particle eventually aligns with the field direction. Thus, they do not give rise to sustained torque fluctuations.