Floppy swimming: Viscous locomotion of actuated elastica

TL;DR

This paper presents a theoretical analysis of elastic filament-based swimming in viscous fluids, deriving velocities, optimal parameters, and discussing multi-filament strategies, offering insights into bio-inspired locomotion mechanisms.

Contribution

It introduces a theoretical framework for elastic swimming, deriving analytical velocities, optimal conditions, and strategies for straight trajectories, advancing understanding of elastic propulsion in viscous environments.

Findings

Derived analytical elastic swimming velocities at small actuation amplitudes.

Identified optimal actuation frequencies and body shapes for efficient swimming.

Discussed strategies for straight swimming trajectories using multiple filaments.

Abstract

Actuating periodically an elastic filament in a viscous liquid generally breaks the constraints of Purcell's scallop theorem, resulting in the generation of a net propulsive force. This observation suggests a method to design simple swimming devices - which we call "elastic swimmers" - where the actuation mechanism is embedded in a solid body and the resulting swimmer is free to move. In this paper, we study theoretically the kinematics of elastic swimming. After discussing the basic physical picture of the phenomenon and the expected scaling relationships, we derive analytically the elastic swimming velocities in the limit of small actuation amplitude. The emphasis is on the coupling between the two unknowns of the problems - namely the shape of the elastic filament and the swimming kinematics - which have to be solved simultaneously. We then compute the performance of the resulting swimming device, and its dependance on geometry. The optimal actuation frequency and body shapes are derived and a discussion of filament shapes and internal torques is presented. Swimming using multiple elastic filaments is discussed, and simple strategies are presented which result in straight swimming trajectories. Finally, we compare the performance of elastic swimming with that of swimming microorganisms.