Ph.D Thesis Defence: Isha Misra

Dynamics of magnetic spheroids in time periodic magnetic fields.

Magnetic nano and micro particles are used for a lot of novel  applications, like mixing in inherently laminar microscale systems, bi= o-rheological measurements, drug delivery, and proctored surgeries. Several studies have elucidated the movement of magnetic  particles of different shapes and magnetic natures in the presence of  different types of magnetic fields, analytically and experimentally. In the current study, a fundamental approach to understand  the motion of spheroids in the presence of time periodic fields is  adopted by accounting for the different magnetic natures of the  particles. The non-hysteretic superparamagnetic particles can be  modelled by the signum, linear, or the Langevin moment models. The  moment of the hysteretic soft ferromagnetic particles is modelled by the  Stoner-Wohlfarth (SW) model. The hard ferromagnetic materials’ moment is  modelled as a permanent dipole. The hydrodynamic torque acting on the  particle counters the magnetic torque applied by the field. The study considers different aspects of the motion of magnetic spheroids in time-dependent magnetic fields and under shear flow.

 In the presence of a rotating field, magnetic particles corotate with  the field at small field frequency. When the field frequency exceeds the  breakdown frequency, the particle slips relative to the field. The  trajectory is termed parallel if it is in the same plase as the field;  else, it is precessed motion. In the current work we understand this  from a dynamical systems perspective in terms of non-dimensional  numbers. For the simpler non-hysteretic models, the dynamics is  completely defined by the ratio of the field frequency and the  particle viscous relaxation rate. The more practical models, the  Langevin and the SW models require one more material parameter. For the  non-hysteretic Langevin model, this is the ratio of the magnetic  saturation and the product of the magnetic susceptibility and the field  strength , and for the hysteretic SW model, the second parameter is h,  the ratio of the Zeeman and anisotropy energies. The dynamics of the  two-parameter models can be mapped onto the one-parameter models, which  broadly depict the behaviours of parallel corotation and slip and  precessed corotation and slip. The SW model captures experimental  results of initial condition dependent stable states of precessed  corotation and parallel slip at higher field frequencies.

 In the next part of the study, the dynamics of a magnetic spheroid in an  oscillating magnetic field is examined. For superparamagnetic materials,  the particles align along the field, in the long time limit. For hard  ferromagnetic spheroids (permanent dipole), the spheroid oscillates with  the field, and the trajectories are initial condition dependent.  The effect of simple shear on a permanent dipolar spheroid in the  presence of an oscillating magnetic field is studied. The relevant  non-dimensional numbers are the ratio of field frequency and strain  rate and the ratio of magnetic and hydrodynamic torques. The  rotation  number is defined as the ratio of the particle angular velocity and the  field frequency. Different types of particle behaviour are mapped on to the parameter space consisting of the scaled magnetic field magnitude and frequency. For high magnetic field amplitude, the rotation number is 1. At low amplitude, there is complex dynamics depending on the ratio of the field frequency and the strain rate.