Optimal swimming of a sheet.
Optimal swimming of a sheet.
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床单的最佳游泳。
DOI：
10.1103/physreve.89.060701
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
E. Lauga
中科院分区：
文献类型：
--
作者：
T. Montenegro;E. Lauga
在微观尺度上的推进通常是通过沿着被称为鞭毛的毛发状细胞器传播行波来实现的。泰勒的二维游泳片模型经常被用来提供深入了解鞭毛推进问题。我们推导出数值的大振幅波形的二维游泳片，产生最佳的流体动力学效率：游泳速度的平方的工作速率的片材对流体的比率。使用边界元法，我们表明，最佳波形是一个前后对称的正则化尖点，比最佳正弦波的效率高25%。这种最佳的二维形状是光滑的，与莱特希尔的最佳三维鞭毛的扭结形式有质的不同，不是由小振幅理论预测的，也不同于主动弹性细丝的光滑圆弧状形状。
Propulsion at microscopic scales is often achieved through propagating traveling waves along hairlike organelles called flagella. Taylor's two-dimensional swimming sheet model is frequently used to provide insight into problems of flagellar propulsion. We derive numerically the large-amplitude wave form of the two-dimensional swimming sheet that yields optimum hydrodynamic efficiency: the ratio of the squared swimming speed to the rate-of-working of the sheet against the fluid. Using the boundary element method, we show that the optimal wave form is a front-back symmetric regularized cusp that is 25% more efficient than the optimal sine wave. This optimal two-dimensional shape is smooth, qualitatively different from the kinked form of Lighthill's optimal three-dimensional flagellum, not predicted by small-amplitude theory, and different from the smooth circular-arc-like shape of active elastic filaments.