J. Stefan Institute, Jamova, Ljubljana, Slovenia.
Phys Rev Lett. 2012 Sep 21;109(12):128105. doi: 10.1103/PhysRevLett.109.128105. Epub 2012 Sep 19.
We study the efficiency of self-propelled swimmers at low Reynolds numbers, assuming that the local energetic cost of maintaining a propulsive surface slip velocity is proportional to the square of that velocity. We determine numerically the optimal shape of a swimmer such that the total power is minimal while maintaining the volume and the swimming speed. The resulting shape depends strongly on the allowed maximum curvature. When sufficient curvature is allowed the optimal swimmer exhibits two protrusions along the symmetry axis. The results show that prolate swimmers such as Paramecium have an efficiency that is ∼20% higher than that of a spherical body, whereas some microorganisms have shapes that allow even higher efficiency.
我们研究了低雷诺数下自主游动游泳者的效率，假设维持推进表面滑移速度的局部能量成本与该速度的平方成正比。我们通过数值确定了游泳者的最佳形状，使得在保持体积和游泳速度的同时，总功率最小。所得形状强烈依赖于允许的最大曲率。当允许足够的曲率时，最佳游泳者在对称轴上表现出两个突起。结果表明，像草履虫这样的长形游泳者的效率比球体高约 20%，而有些微生物的形状则允许更高的效率。
