论文标题
涡流中的Microswimmers：动力学和陷阱
Microswimmers in vortices: Dynamics and trapping
论文作者
论文摘要
生物学和人工微晶状体通常在涡旋性质的外部流中自我propel；相关的例子包括小型海洋涡流中的藻类，子宫蠕动流中的精子和微流体设备中的细菌。最近的一个实验表明，模型涡流中的游泳细菌一直从涡流一直驱逐到定义明确的耗竭区（Sokolov and Aranson（2016）“通过涡流流量快速驱逐微晶状体。”自然通讯7，11114）。在本文中，我们提出了一个理论模型，以研究基本涡流中伸长的微晶状体的动力学，即两维旋转中的活性颗粒。确定性模型首先揭示了涡流和其他地方无限轨道附近的有界轨道的存在。我们进一步发现了保守数量的运动，该运动允许我们根据轨道的类型（边界与无限）绘制相位空间。接下来，我们将翻译和旋转噪声引入系统。使用Fokker - Planck形式主义，我们通过检查逃生的概率和逃离确定性界限轨道区域的平均逃脱时间来量化涡旋中心附近的捕获质量。我们最终展示了如何使用这些发现来制定耗竭区半径的预测，该预测与Sokolov和Aranson（2016）的实验相比有利。
Biological and artificial microswimmers often self-propel in external flows of vortical nature; relevant examples include algae in small-scale ocean eddies, spermatozoa in uterine peristaltic flows and bacteria in microfluidic devices. A recent experiment has shown that swimming bacteria in model vortices are expelled from the vortex all the way to a well-defined depletion zone (Sokolov and Aranson (2016) "Rapid expulsion of microswimmers by a vortical flow." Nature Comm. 7, 11114). In this paper, we propose a theoretical model to investigate the dynamics of elongated microswimmers in elementary vortices, namely active particles in two- and three-dimensional rotlets. A deterministic model first reveals the existence of bounded orbits near the centre of the vortex and unbounded orbits elsewhere. We further discover a conserved quantity of motion that allows us to map the phase space according to the type of the orbit (bounded vs unbounded). We next introduce translational and rotational noise into the system. Using a Fokker--Planck formalism, we quantify the quality of trapping near the centre of the vortex by examining the probability of escape and the mean time of escape from the region of deterministically bounded orbits. We finally show how to use these findings to formulate a prediction for the radius of the depletion zone, which compares favourably with the experiments of Sokolov and Aranson (2016).
