The wobbling-to-swimming transition of rotated helices

Abstract

A growing body of work aims at designing and testing micron-scale synthetic swimmers. One method, inspired by the locomotion of flagellated bacteria, consists of applying a rotating magnetic field to a rigid, helically-shaped, propeller attached to a magnetic head. When the resulting device, termed an artificial bacteria flagellum, is aligned perpendicularly to the applied field, the helix rotates and the swimmer moves forward. Experimental investigation of artificial bacteria flagella shows that at low frequency of the applied field, the axis of the helix does not align perpendicularly to the field but wobbles around the helix, with an angle increasing as the inverse of the field frequency. By numerical computations and asymptotic analysis, we provide a theoretical explanation for this wobbling behavior. We numerically demonstrate the wobbling-to-swimming transition as a function of the helix geometry and the dimensionless Mason number which quantifies the ratio of viscous to magnetic torques. We then employ an asymptotic expansion for near-straight helices to derive an analytical estimate for the wobbling angle allowing to rationalize our computations and past experimental results. These results can help guide future design of artificial helical swimmers.

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Cited by in corpus (7)

• Dynamics and polarization of superparamagnetic chiral nanomotors in a rotating magnetic field
• Selectively Controlled Magnetic Microrobots with Opposing Helices
• Optimization and small-amplitude analysis of Purcell's three-link microswimmer model
• Dynamics of groups of magnetically driven artificial microswimmers
• Torsional oscillations of a sphere in a Stokes flow
• Propulsion by stiff elastic filaments in viscous fluids
• Relative Equilibria of Magnetic Micro-Swimmers