Role of shape and symmetry in externally driven micromotors

Motion in fluids at the micrometric scale is dominated by viscosity. One efficient propulsion method relies on a weak uniform rotating magnetic field that drives a chiral object. From bacterial flagella to artificial magnetic nanohelices, rotation of a corkscrew is considered as a universally efficient propulsion gait. Although approximate theories concerning dynamics of slender magnetic helices are available, actuation of geometrically achiral particles or random aggregates was not well understood. I will present a general theory of magnetized object of arbitrary shape in a rotating magnetic field. It appears that its propulsion velocity can be written in a compact form as Rayleigh quotient in terms of geometry-dependent chirality matrix Ch, where both the diagonal elements (owing to inherent handedness) and off-diagonal entries (that do not necessitate handedness) contribute in a similar way. The theory anticipates multiplicity of stable rotational states predicting that, e.g., two identical magnetic objects may propel with different speeds or even in opposite directions. However, for a class of simple planar objects, there is particular magnetization whereas the pair of symmetric rotational states degenerates into a unique propulsion gait closely resembling that of an ideal helix. In other words, geometrically achiral object can acquire effective chirality due to its interaction with the external magnetic field. The developed theory was further applied to optimize the geometry/magnetization and to obtain purely geometric constraint on propulsion speed of arbitrary shaped magnetic object. Finally, I will discuss general symmetries (such as parity and charge conjugation) and establish correspondence between propulsive states of geometrically achiral planar objects depending on orientation of the dipolar moment.

K. I. Morozov et al., Phys. Rev. Fluids 2, 044202 (2017)
Y. Mirzae et al., Science Robotics 3, eaas8713 (2018)
J. Sachs et al., Phys. Rev. E, to appear (2018)