Floppy swimming: Viscous locomotion of actuated elastica

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.

23 pages, 6 figures

References in corpus (4)

• Experimental Investigations of Elastic Tail Propulsion at Low Reynolds Number
• Numerical Study of a Microscopic Artificial Swimmer
• Propulsion with a Rotating Elastic Nanorod
• Non-equilibrium hydrodynamics of a rotating filament

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• The mechanism of propulsion of a model microswimmer in a viscoelastic fluid next to a solid boundary
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• Nonlinear dynamics and bifurcations of a planar undulating magnetic microswimmer
• Well-posedness and applications of classical elastohydrodynamics for a swimming filament
• Dynamics of Purcell-type microswimmers with active-elastic joints
• Viscotaxis of Beating Flagella at Surfaces
• Fluid transport by active elastic membranes
• Modal analysis and optimization of swimming active filaments