Dunkel Jörn, Zaid Irwin M
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 1):021903. doi: 10.1103/PhysRevE.80.021903. Epub 2009 Aug 5.
Small organisms (e.g., bacteria) and artificial microswimmers move due to a combination of active swimming and passive Brownian motion. Considering a simplified linear three-sphere swimmer, we study how the swimmer size regulates the interplay between self-driven and diffusive behavior at low Reynolds number. Starting from the Kirkwood-Smoluchowski equation and its corresponding Langevin equation, we derive formulas for the orientation correlation time, the mean velocity and the mean-square displacement in three space dimensions. The validity of the analytical results is illustrated through numerical simulations. Tuning the swimmer parameters to values that are typical of bacteria, we find three characteristic regimes: (i) Brownian motion at small times, (ii) quasiballistic behavior at intermediate time scales, and (iii) quasidiffusive behavior at large times due to noise-induced rotation. Our analytical results can be useful for a better quantitative understanding of optimal foraging strategies in bacterial systems, and they can help to construct more efficient artificial microswimmers in fluctuating fluids.
小生物体（如细菌）和人造微型游动器的运动是主动游动和被动布朗运动共同作用的结果。考虑一个简化的线性三球体游动器，我们研究在低雷诺数下，游动器大小如何调节自驱动行为和扩散行为之间的相互作用。从柯克伍德-斯莫卢霍夫斯基方程及其相应的朗之万方程出发，我们推导了三维空间中取向相关时间、平均速度和均方位移的公式。通过数值模拟说明了分析结果的有效性。将游动器参数调整为细菌的典型值，我们发现了三种特征模式：（i）短时间内的布朗运动，（ii）中间时间尺度上的准弹道行为，以及（iii）长时间内由于噪声诱导旋转导致的准扩散行为。我们的分析结果有助于更好地定量理解细菌系统中的最优觅食策略，也有助于在波动流体中构建更高效的人造微型游动器。
