Lauga Eric
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Apr;75(4 Pt 1):041916. doi: 10.1103/PhysRevE.75.041916. Epub 2007 Apr 26.
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 dependence 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 micro-organisms.
周期性地驱动粘性液体中的弹性细丝通常会打破珀塞尔扇贝定理的限制，从而产生净推进力。这一观察结果提示了一种设计简单游泳装置的方法——我们称之为“弹性游泳者”，其中驱动机制嵌入在固体中，由此产生的游泳者可以自由移动。在本文中，我们从理论上研究了弹性游泳的运动学。在讨论了该现象的基本物理图景和预期的标度关系之后，我们在小驱动幅度的极限情况下解析地推导了弹性游泳速度。重点在于该问题的两个未知量之间的耦合——即弹性细丝的形状和游泳运动学——这两个未知量必须同时求解。然后，我们计算了由此产生的游泳装置的性能及其对几何形状的依赖性。推导了最优驱动频率和身体形状，并对细丝形状和内部扭矩进行了讨论。讨论了使用多根弹性细丝的游泳，并提出了能产生直线游泳轨迹的简单策略。最后，我们将弹性游泳的性能与游泳微生物的性能进行了比较。
