Title: Motility and rotation of multi-timescale microswimmers in linear background flows Show Chinese title

Title: 多时间尺度微游动器在线性背景流中的运动和旋转

Abstract: Microswimming cells and robots exhibit diverse behaviours due to both their swimming and their environment. One of the core environmental features impacting inertialess swimming is background flows. While the influence of select flows, particularly shear flows, have been extensively investigated, these are special cases. Here, we examine inertialess swimmers in more general flows, specifically general linear planar flows that may also possess rapid oscillations. Relatively weak symmetry constraints are imposed on the swimmer to ensure planarity and to reduce complexity. A further constraint reflecting common observation is imposed, namely that the swimmer is inefficient, which we suitably define. This introduces two separate timescales: a fast timescale associated with swimmer actuation, and a second timescale associated with net swimmer movement, with inefficiency dictating that this latter timescale is much slower, allowing for a multiple timescale simplification of the governing equations. With the exception of mathematically precise edge cases, we find that the behaviour of the swimmer is dictated by two parameter groupings, both of which measure balances between the angular velocity and rate of strain of the background flow. While the measures of flow angular velocity and strain rates that primarily govern the rotational dynamics are modulated by swimmer properties, the primary features of the translational motion are determined solely by a ratio of flow angular velocity to strain rate. Hence, a simple classification of the swimmer dynamics emerges. For example, this illustrates the limited extent to which, and how, microswimmers may control their orientations and trajectories in flows. Show Chinese abstract

Abstract: 由于它们的游泳方式和环境，微小游动细胞和机器人表现出多样的行为。 影响无惯性游泳的核心环境特征是背景流。 虽然选择性流体（特别是剪切流）的影响已被广泛研究，但这些是特殊情况。 在这里，我们研究更一般的流体中的无惯性游泳者，特别是可能还具有快速振荡的一般线性平面流。 对游泳者施加了相对较弱的对称性约束，以确保平面性和减少复杂性。 进一步施加了一个反映常见观察结果的约束，即游泳者效率低下，我们对此进行了适当的定义。 这引入了两个独立的时间尺度：一个与游泳者驱动相关的快时间尺度，以及一个与净游泳者运动相关的第二时间尺度，低效率表明后者的时间尺度要慢得多，从而允许对控制方程进行多时间尺度简化。 除了数学上精确的边缘情况外，我们发现游泳者的行为由两个参数分组决定，这两个分组都衡量了背景流的角速度和应变率之间的平衡。 虽然主要支配旋转动力学的流体角速度和应变率的度量受到游泳者特性的影响，但平移运动的主要特征仅由流体角速度与应变率的比值决定。 因此，出现了游泳者动力学的简单分类。 例如，这说明了微小游泳者在流体中能够控制其方向和轨迹的有限程度以及方式。