Department of Mechanical Engineering, Institute of Applied Mathematics, University of British Columbia, Vancouver, BC V6T 1Z4, Canada.
Department of Mechanical Engineering, Santa Clara University, Santa Clara, CA 95053, USA.
Soft Matter. 2017 Mar 22;13(12):2339-2347. doi: 10.1039/c6sm02880b.
At low Reynolds numbers the locomotive capability of a body can be dramatically hindered by the absence of inertia. In this work, we show how propulsive performance in this regime can be significantly enhanced by employing spatially varying flexibility. As a prototypical example, we consider the propulsive thrust generated by a filament periodically driven at one end. The rigid case leads to zero propulsion, as so constrained by Purcell's scallop theorem, while for uniform filaments there exists a bending stiffness maximizing the propulsive force at a given frequency; here we demonstrate explicitly how considerable further improvement can be achieved by simply varying the stiffness along the filament. The optimal flexibility distribution is strongly configuration-dependent: while increasing the flexibility towards the tail-end enhances the propulsion of a clamped filament, for a hinged filament decreasing the flexibility towards the tail-end is instead favorable. The results reveal new design principles for maximizing propulsion at low Reynolds numbers, potentially useful for developing synthetic micro-swimmers requiring large propulsive force for various biomedical applications.
在低雷诺数下，由于缺乏惯性，物体的运动能力可能会受到显著阻碍。在这项工作中，我们展示了如何通过采用空间变化的柔韧性来显著提高这种情况下的推进性能。作为一个典型的例子，我们考虑了由一端周期性驱动的纤维产生的推进推力。刚性情况导致零推进，因为普塞尔的扇贝定理就是这样约束的，而对于均匀纤维，存在一个弯曲刚度，在给定频率下使推进力最大化；在这里，我们明确地展示了如何通过简单地沿纤维改变刚度来实现相当大的进一步改进。最佳柔韧性分布强烈依赖于配置：虽然增加末端的柔韧性可以增强夹紧纤维的推进，但对于铰链纤维，相反，减小末端的柔韧性是有利的。结果揭示了在低雷诺数下最大化推进的新设计原则，这对于开发需要用于各种生物医学应用的大推进力的合成微型游泳者可能是有用的。
