Department of Physics and Center for Nonlinear Dynamics, University of Texas at Austin, Austin, TX 78712, USA.
Proc Natl Acad Sci U S A. 2013 Jan 29;110(5):E338-47. doi: 10.1073/pnas.1219831110. Epub 2013 Jan 14.
The swimming of a bacterium or a biomimetic nanobot driven by a rotating helical flagellum is often interpreted using the resistive force theory developed by Gray and Hancock and by Lighthill, but this theory has not been tested for a range of physically relevant parameters. We test resistive force theory in experiments on macroscopic swimmers in a fluid that is highly viscous so the Reynolds number is small compared to unity, just as for swimming microorganisms. The measurements are made for the range of helical wavelengths λ, radii R, and lengths L relevant to bacterial flagella. The experiments determine thrust, torque, and drag, thus providing a complete description of swimming driven by a rotating helix at low Reynolds number. Complementary numerical simulations are conducted using the resistive force theories, the slender body theories of Lighthill and Johnson, and the regularized Stokeslet method. The experimental results differ qualitatively and quantitatively from the predictions of resistive force theory. The difference is especially large for and/or , parameter ranges common for bacteria. In contrast, the predictions of Stokeslet and slender body analyses agree with the laboratory measurements within the experimental uncertainty (a few percent) for all λ, R, and L. We present code implementing the slender body, regularized Stokeslet, and resistive force theories; thus readers can readily compute force, torque, and drag for any bacterium or nanobot driven by a rotating helical flagellum.
细菌或仿生纳米机器人在旋转螺旋鞭毛的驱动下的游动通常可以用 Gray 和 Hancock 以及 Lighthill 提出的阻力理论来解释，但该理论尚未针对一系列物理相关参数进行测试。我们在高粘度流体中对宏观游泳者进行了阻力理论测试，与微生物游泳相比，其雷诺数小，因此非常接近单位。测量范围涵盖了与细菌鞭毛相关的螺旋波长 λ、半径 R 和长度 L。实验确定了推力、扭矩和阻力，从而为低雷诺数下旋转螺旋驱动的游泳提供了完整的描述。使用阻力理论、Lighthill 和 Johnson 的细长体理论以及正则化 Stokeslet 方法进行了补充数值模拟。实验结果与阻力理论的预测在定性和定量上都存在差异。对于和/或参数范围常见的细菌，差异尤其大。相比之下，Stokeslet 和细长体分析的预测与实验室测量结果在实验不确定性（百分之几）内一致，适用于所有 λ、R 和 L。我们提供了实现细长体、正则化 Stokeslet 和阻力理论的代码；因此，读者可以轻松计算任何由旋转螺旋鞭毛驱动的细菌或纳米机器人的力、扭矩和阻力。
