Light-propelled self-sustained swimming of a liquid crystal elastomer torus at low Reynolds number

Abstract

The well-known Purcell's toroidal swimmer can translate in low Reynolds number fluid, by periodically changing its own shape in a nonreciprocal way to overcome the scallop theorem originating from the time independence of the Stokes equation. Based on a liquid crystal elastomer (LCE) torus motor with zero-elastic-energy mode, this paper proposes a mechanism for light-powered self-sustained swimming of a torus at low Reynolds number. By adopting the well-established dynamic LCE model and viscous hydrodynamics for the motion of a thin torus in Stokes flow, the self-sustained swimming of the LCE torus under steady and homogeneous illumination is theoretically investigated. The light-driven moment propelling the self-sustained swimming is derived, and the translation velocity and rotation angular velocity of the LCE torus swimmer in Stokes fluid are analytically formulated by force balance and moment equilibrium. The results show that the translation velocity and rotation angular velocity of the self-sustained swimming only depend on several simple dimensionless parameters, including light intensity, penetration depth, elastic modulus, curvature and payload. Especially, there exists a critical payload for reverse swimming in the opposite direction. The results provide a theoretical basis for the LCE-based self-propelled motor with zero-elastic-energy mode, and the self-propulsion mechanism may also inspire the design of self-sustained swimmers based on other stimuli-responsive toruses.