AI 中文总结
本文理论研究周期性边界附近蠕动体的运动，揭示拉力型游动体被捕获于波纹谷、推力型呈振荡运动，取向倾斜可分离两类游动体，为微游动体输运研究提供新认识。
AI 中文摘要
游动微生物常处于复杂受限环境中，长程流体动力相互作用与短程排斥作用的耦合会产生有趣的动力学行为。本文从理论上研究了以蠕动体（squirmer）为模型的微游动体在周期性边界存在时的运动轨迹。周期性边界会改变其游动速度，导致其行为与在平面壁附近游动存在质的差异。采用基于双球坐标和洛伦兹互易定理的微扰方法，在小表面振幅极限下表征蠕动体与周期性表面的相互作用，并系统探究其对边界波纹波长、蠕动体类型、取向及游动体-表面距离的依赖性。最重要的是，结果表明，拉力型（puller）游动体会被捕获在表面波纹的谷中，这与它们在平面壁附近的滑动运动形成对比；推力型（pusher）游动体的近表面动力学表现出振荡，反映了表面结构的周期性。游动体相对于表面波纹的取向倾斜会产生与波长相关的漂移，可将推力型与拉力型游动体分离。这些发现凸显了流体动力相互作用在塑造结构化边界附近微游动体输运中的作用，对生物膜形成等微生物现象及技术应用具有潜在意义。
英文摘要
Swimming microorganisms often operate in complex confinement, where an interplay of long-ranged hydrodynamic interactions and a short-ranged repulsive interaction can give rise to interesting dynamical behaviors. Here, we theoretically investigate the trajectories of microswimmers - modeled as squirmers - in the presence of periodic boundaries. The latter modify their swimming velocity, leading to behaviors that differ qualitatively from swimming near planar walls. Using a perturbative approach based on bispherical coordinates and the Lorentz reciprocal theorem, we characterize the interaction between a squirmer and a periodic surface in the limit of small surface amplitude and systematically explore its dependence on the boundary corrugation wavelength, squirmer type, orientation, and swimmer-surface distance. Most importantly, our results reveal that pullers become trapped in the valley of the surface corrugations, in contrast to their sliding motion near planar walls. Furthermore, the near-surface dynamics of pushers display oscillations, reflecting the periodicity of the surface structure. A tilt of the swimmer orientation with respect to the surface corrugations results in a wave-length dependent drift that sorts pushers from pullers. These findings highlight the impact of hydrodynamic interactions in shaping microswimmer transport near structured boundaries with potential implications for microbiological phenomena, such as biofilm formation, and technological applications.
