The fluid dynamics of microswimmers has received attention from the fields of microbiology, microrobotics, and active matter. Microorganisms have evolved organelles termed cilia for propulsion through liquids. Each cilium periodically performs effective and recovery strokes, creating a metachronal wave as a whole and developing a propulsive force. One well-established mathematical model of ciliary swimming is the squirmer model, which focuses on surface squirming velocities. This model is also useful when studying active colloids and droplets. The squirmer model has been recently used to investigate the behaviors of microswimmers in complex environments, their collective dynamics, and the characteristics of active fluids. Efforts have also been made to broaden the range of applications beyond the assortment permitted by the squirmer model, which was established to specifically represent ciliary flow and incorporate biological features. The stress swimmer model imposes stresses above the cell body surface that enforce the no-slip condition. The ciliated swimmer model precisely reproduces the behaviors of each cilium that engages in mutual hydrodynamic interactions. Mathematical models have improved our understanding of various microbial phenomena, including cell–cell and cell–wall interactions and energetics. Here, I review recent advances in the hydrodynamics of ciliary swimming and then discuss future challenges.

中文翻译：

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蠕动体和纤毛微生物的流体动力学

微型游泳器的流体动力学受到微生物学、微型机器人和活性物质领域的关注。微生物已经进化出称为纤毛的细胞器，用于在液体中推进。每个纤毛周期性地进行有效和恢复性的行程，整体上产生异时波并产生推进力。蠕动模型是一种完善的纤毛游动数学模型，该模型侧重于表面蠕动速度。该模型在研究活性胶体和液滴时也很有用。蠕动模型最近被用来研究微型游泳者在复杂环境中的行为、它们的集体动力学以及活性流体的特征。人们还努力扩大应用范围，超出蠕动模型允许的范围，该模型的建立是为了专门代表纤毛流动并结合生物学特征。应力游泳者模型在细胞体表面上方施加应力，以强制执行防滑条件。纤毛游泳者模型精确地再现了参与相互流体动力学相互作用的每个纤毛的行为。数学模型提高了我们对各种微生物现象的理解，包括细胞与细胞、细胞与壁的相互作用和能量学。在这里，我回顾了纤毛游动的流体动力学的最新进展，然后讨论了未来的挑战。