Role of symmetry in driven propulsion at low Reynolds number

Abstract

We theoretically and experimentally investigate low-Reynolds-number propulsion of geometrically achiral planar objects that possess a dipole moment and that are driven by a rotating magnetic field. Symmetry considerations (involving parity, P , and charge conjugation, C) establish correspondence between propulsive states depending on orientation of the dipolar moment. Although basic symmetry arguments do not forbid individual symmetric objects to efficiently propel due to spontaneous symmetry breaking, they suggest that the average ensemble velocity vanishes. Some additional arguments show, however, that highly symmetrical ( P -even) objects exhibit no net propulsion while individual less symmetrical ( C P -even) propellers do propel. Particular magnetization orientation, rendering the shape C P -odd, yields unidirectional motion typically associated with chiral structures, such as helices. If instead of a structure with a permanent dipole we consider a polarizable object, some of the arguments have to be modified. For instance, we demonstrate a truly achiral ( P -and C P -even) planar shape with an induced electric dipole that can propel by electro-rotation. We thereby show that chirality is not essential for propulsion due to rotation-translation coupling at low Reynolds number.

Trends in Micro‐/Nanorobotics: Materials Development, Actuation, Localization, and System Integration for Biomedical Applications

“…Remote driving of the m‐bots by DC and AC electric fields is emerging as a new wireless controllable and fuel‐free actuation method that uses electrophoretic motion, electro‐osmotic flow, and electrorotation. [ 226–236 ] When a uniform DC electric field is applied, the charged objects migrate toward the electrode having opposite charge due to the Coulomb interactions. [ 227 ] When an AC electric field is applied, m‐bots can be also actuated in a controlled manner.…”

“…[ 227,228 ] Electrorotation of magnetic and nonmagnetic nanowires with precisely controlled rotational speed can be also achieved by four phase‐shifted AC voltages with a sequential phase shift of 90°. [ 226,236 ] Wang et al. [ 229 ] developed poly(pyrrole)‐cadmium (PPy‐Cd) and CdSe–Au–CdSe semiconductor nanowires and actuated them under an external AC electric field by the electro‐osmotic flow mechanism to obtain the directional locomotion of nanowires because of the electro‐osmotic flow.…”

µ-PIV Measurements of Flows Generated by Photolithography-Fabricated Achiral Microswimmers

“…The swimming mechanism of the achiral microswimmer was studied by Sachs et al [39] and Cheang et al [18], and a brief analysis was provided in supplementary materials. In order to observe microswimmers in motion, we mounted an electromagnetic coil system onto a fluorescence microscope in which the PIV experiment was performed.…”

Propulsion and energetics of a minimal magnetic microswimmer

“…In spite of all these achievements, experimental prototypes actuated by external magnetic fields demonstrated simplicity in design, as they require a finite number of well identified, independent, degrees of freedoms to propel in a fluid medium. Some examples include elementary stiff dumbbells 30,31 , triplets 32 , chiral 16,17 or other planar achiral structures [33][34][35][36] . Developing minimal microswimers is appealing for different reasons, even if their speed performance may be inferior to other prototypes which make use of flexible or helical parts.…”