Coq Naïs, Roure Olivia du, Fermigier Marc, Bartolo Denis
PMMH ESPCI ParisTech, CNRS UMR 7636, Université Pierre et Marie Curie, Université Denis Diderot, 10 rue Vauquelin 75231 Paris cedex 05, France.
J Phys Condens Matter. 2009 May 20;21(20):204109. doi: 10.1088/0953-8984/21/20/204109. Epub 2009 Apr 21.
We investigate the propulsive force resulting from the rotation of a flexible filament in the low Reynolds number regime. Using a simple linear model, we establish the nonlinear torque-force relations for two torque-driven actuation modes. When the rotation of the filament is induced by two perpendicular transverse oscillating torques, the propulsive force increases monotonically with the torque amplitude. Conversely, when a constant axial torque is applied, the torque-force characteristics displays an unstable branch, related to a discontinuous transition in the shape of the filament. We characterize this shape transition using two geometrical parameters, quantifying the wrapping around and the collapse on the axis of the filament. The proposed theoretical description correctly accounts for our experimental observations and reveals a strong dependence of the filament dynamics on the anchoring conditions.
我们研究了在低雷诺数 regime 下柔性细丝旋转所产生的推进力。使用一个简单的线性模型，我们建立了两种扭矩驱动致动模式下的非线性扭矩 - 力关系。当细丝的旋转由两个垂直的横向振荡扭矩引起时，推进力随扭矩幅度单调增加。相反，当施加恒定的轴向扭矩时，扭矩 - 力特性显示出一个不稳定分支，这与细丝形状的不连续转变有关。我们使用两个几何参数来表征这种形状转变，这两个参数量化了细丝围绕轴的缠绕以及在轴上的坍缩。所提出的理论描述正确地解释了我们的实验观察结果，并揭示了细丝动力学对锚固条件的强烈依赖性。
