## Dynamics of externally actuated magnetic propellers

Technology based on magnetic micro-/nanopropellers that can be actuated remotely by a low strength rotating magnetic field and steered at high precision through various fluidics environments is considered attractive towards potential biomedical applications. Despite the substantial progress in microfabrication, the complete understanding of the magnetic properties and dynamics of such propellers is still lacking. In this talk I will review our recent theoretical research in the field. In particular, an approximate theory for the dynamics of slender magnetic (and polarizable) helical propellers will be discussed. Tumbling-to-wobbling transition and the dependence of nanomotor orientation and propulsion on actuation frequency, magnetization (or susceptibility) and geometry will be presented. For polarizable propellers, the effective polarizability is not readily available and it can be determined using either approximate slender body theory or rigorous numerical computations. I will compare both approaches and show that the propeller’s geometry, in particular filament cross-section elongation and orientation, plays a central role in determining its magnetic anisotropy and polarizability. I will then show that the original approximate theory can be readily generalized for an arbitrary-shaped object actuated by the rotating magnetic field. We have found that in a certain range of driving frequency, there is multiplicity of the steady dynamical states. This multiplicity results, in some cases, in propulsion in opposite directions, depending on propeller’s orientation with respect to the field. The developed theory can be used to determine optimal shape and/or magnetization of the propeller. Predictions of the theory corresponding to (a) helical propellers of an arbitrary length ; (b) achiral clusters and random aggregates of magnetic nanoparticles will be reviewed.