Hydrodynamic instabilities in a two-dimensional sheet of microswimmers embedded in a three-dimensional fluid
Hydrodynamic instabilities in a two-dimensional sheet of microswimmers embedded in a three-dimensional fluid
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DOI：
10.1017/jfm.2023.985
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发表时间：
2024-02
影响因子：
3.7
通讯作者：
V. Škultéty;Dóra Bárdfalvy;Joakim Stenhammar;C. Nardini;Alexander Morozov
中科院分区：
文献类型：
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作者：
V. Škultéty;Dóra Bárdfalvy;Joakim Stenhammar;C. Nardini;Alexander Morozov
摘要 浸入不可压缩流体中的微型游泳者集合的特征是由于个体生物体产生的流体动力场的长程性质而具有强相互作用。因此，诸如细菌之类的后驱动“推动器”游泳者的悬浮液表现出一种集体运动状态，通常被称为“细菌湍流”，其特征是大规模的混沌流。推动器悬架中集体运动的开始是在偶极游泳者的平均场动力学理论框架内进行经典理解的。在二维和三维空间中，该理论预测导致细菌湍流的不稳定性是由于游泳者相互重新定向造成的，并且在悬浮液可用的最大长度尺度上发生。在这里，我们针对偶极微游泳器悬架仅限于嵌入三维不可压缩流体中的二维平面的情况构建了类似的动力学理论。此设置定性地模仿了靠近二维界面游泳的效果。我们表明，尽管三维散装流体不可压缩，但平面内流场是有效可压缩的，并且微型游泳器平均充当源（推）或汇（拉）。我们分析了均匀和各向同性状态的稳定性，并发现了两种与本体三维情况有本质不同的不稳定性：首先，我们表明，导致本体系统中细菌湍流的定向推动器不稳定性的类似情况发生在系统可用的最小长度尺度上。其次，作为有效面内压缩性的一般结果，拉拔器悬架中会出现与密度变化相关的不稳定性。鉴于这些相对于标准体积设置的定性差异，我们得出结论，限制在确定微型游泳器悬浮液的集体行为方面可以发挥至关重要的作用。
Abstract A collection of microswimmers immersed in an incompressible fluid is characterised by strong interactions due to the long-range nature of the hydrodynamic fields generated by individual organisms. As a result, suspensions of rear-actuated ‘pusher’ swimmers such as bacteria exhibit a collective motion state often referred to as ‘bacterial turbulence’, characterised by large-scale chaotic flows. The onset of collective motion in pusher suspensions is classically understood within the framework of mean-field kinetic theories for dipolar swimmers. In bulk two and three dimensions, the theory predicts that the instability leading to bacterial turbulence is due to mutual swimmer reorientation and sets in at the largest length scale available to the suspension. Here, we construct a similar kinetic theory for the case of a dipolar microswimmer suspension restricted to a two-dimensional plane embedded in a three-dimensional incompressible fluid. This setting qualitatively mimics the effect of swimming close to a two-dimensional interface. We show that the in-plane flow fields are effectively compressible in spite of the incompressibility of the three-dimensional bulk fluid, and that microswimmers on average act as sources (pushers) or sinks (pullers). We analyse the stability of the homogeneous and isotropic state, and find two types of instability that are qualitatively different from the bulk, three-dimensional case: first, we show that the analogue of the orientational pusher instability leading to bacterial turbulence in bulk systems instead occurs at the smallest length scale available to the system. Second, an instability associated with density variations arises in puller suspensions as a generic consequence of the effective in-plane compressibility. Given these qualitative differences with respect to the standard bulk setting, we conclude that confinement can have a crucial role in determining the collective behaviour of microswimmer suspensions.