Elastic swimmer on a free surface

We present here a novel experimental setup with self-propelled swimmers on a free surface. The swimmers, modeled as flexible thin filaments, are composed of a cylindrical body of diameter 0.5 mm made of a flexible polymer (polyvynil syloxane), with a small embedded magnet constituting the head. They float through capillary forces at the free surface of a water tank. A time-varying but spatially uniform magnetic field is generated using a Helmholtz pair of coils powered by an AC voltage. The field actuates the head of the swimmer by producing an oscillating magnetic torque as the permanent magnet attempts to align with the alternating field. The rotational oscillations of the magnet generate a backward-propagating wave along the flexible tail, causing it to swim forward. Fig. 1 shows a 5 cm long swimmer with its head oscillating at 13 Hz.

An analysis of the fluid-structure interaction problem of these passive anguilliform swimmers in the inertial regime,¹ using beam theory and Lighthill's theory for slender fish swimming,² highlights two crucial points: on the one hand, the propagative nature of the elastic wave that mimics the anguilliform kinematics (and allows for a higher efficiency than what the most efficient standing bending wave could achieve) is strongly dependent on the energy dissipation along the body of the swimmer due to fluid damping (see also Ref. 3). On the other hand, the performance of the swimmer is limited by the global drag, since the final cruising swimming speed U is determined by a balance between the forward thrust generated by the body undulations and the drag experienced by the filament. The precise quantification of drag for an undulating body is not a straightforward problem, and depending on the particular geometry and kinematics different sources such as form drag or skin friction may play more or less dominant roles (see also Ref. 4). The visualisations shown in Fig. 1 motivated the choice of a form drag model in the analysis of the experiments with the present setup described in Ref. 1.

We gratefully acknowledge support by EADS Foundation through project Fluids and elasticity in biomimetic propulsion.