Gyromagnetic effects in dynamics of magnetic microparticles

We derive equations of motion for paramagnetic and ferromagnetic particles fully accounting for gyromagnetic effects. Considering the Einstein-de Haas effect for an ellipsoidal paramagnetic particle we find that starting from a quiescent non-magnetized state, after the field is switched on a rotation along the short axis is established. This is confirmed by the stability analysis of the fixed points of the corresponding ordinary differential equations. In the case of a ferromagnetic particle we integrate the equations of motion in the dissipationless case by finding the integrals of motion. We also reformulate the equations in a Hamiltonian framework in this case and find a period of small nutation oscillations.Comment: 24 pages, 15 figure

On the optimal shape of magnetic swimmers

Magnetic actuation of elasto-magnetic devices has long been proposed as a simple way to propel fluid and achieve locomotion in environments dominated by viscous forces. Under the action of an oscillating magnetic field, a permanent magnet, when attached to an elastic tail, is able to generate bending waves and sufficient thrust for propulsion. We study the hydrodynamical effects of the magnetic head geometry using a geometrically exact formulation for the elastic tail elastohydrodynamics. We show that the spherical head geometry fails to take full advantage of the propulsive potential from the flexible tail. Nevertheless, while elongated prolate spheroids demonstrate a superior swimming performance, this is still regulated by the nature of the imposed magnetic field. Interestingly, the highest swimming speed is observed when the magnitude of the magnetic field is weak due to delays between the orientation of the magnetic moment and the oscillating magnetic field. This allows the stored elastic energy from the deformed tail to relax during the phase lag between the imposed magnetic field and the swimmer's magnetic moment, favouring in this way the net propulsion. In particular, this result suggests the existence of optimal magnetic actuations that are non-smooth, and even discontinuous in time, in order to fully explore the propulsive potential associated with the relaxation dynamics of periodically deformed elastic filaments. Copyright 2013 Pleiades Publishing, Ltd