Théry Albane, Wang Yuxuan, Dvoriashyna Mariia, Eloy Christophe, Elias Florence, Lauga Eric
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK.
Université de Paris, CNRS UMR 7057, Laboratoire Matière et Systèmes Complexes MSC, F-75006 Paris, France.
Soft Matter. 2021 May 12;17(18):4857-4873. doi: 10.1039/d0sm02207a.
Motivated by recent experiments demonstrating that motile algae get trapped in draining foams, we study the trajectories of microorganisms confined in model foam channels (section of a Plateau border). We track single Chlamydomonas reinhardtii cells confined in a thin three-circle microfluidic chamber and show that their spatial distribution exhibits strong corner accumulation. Using empirical scattering laws observed in previous experiments (scattering with a constant scattering angle), we next develop a two-dimension geometrical model and compute the phase space of trapped and periodic trajectories of swimmers inside a three-circles billiard. We find that the majority of cell trajectories end up in a corner, providing a geometrical mechanism for corner accumulation. Incorporating the distribution of scattering angles observed in our experiments and including hydrodynamic interactions between the cells and the surfaces into the geometrical model enables us to reproduce the experimental probability density function of micro-swimmers in microfluidic chambers. Both our experiments and models demonstrate therefore that motility leads generically to trapping in complex geometries.
受近期实验（该实验表明游动藻类会被困在排水泡沫中）的启发，我们研究了限制在模型泡沫通道（普拉托边界的一部分）中的微生物的轨迹。我们追踪了限制在一个薄的三圆微流体腔室中的单个莱茵衣藻细胞，并表明它们的空间分布呈现出强烈的角落聚集现象。利用在先前实验中观察到的经验散射定律（以恒定散射角散射），我们接下来建立了一个二维几何模型，并计算了三圆台球内被困和周期性轨迹的相空间。我们发现大多数细胞轨迹最终会到达一个角落，这为角落聚集提供了一种几何机制。将我们实验中观察到的散射角分布纳入，并将细胞与表面之间的流体动力相互作用纳入几何模型，这使我们能够重现微流体腔室中微游泳者的实验概率密度函数。因此，我们的实验和模型都表明，运动性通常会导致在复杂几何形状中被困。
