Albane Théry: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK. at830@cam.ac.uk e.lauga@damtp.cam.ac.uk. ORCID
Yuxuan Wang: Université de Paris, CNRS UMR 7057, Laboratoire Matière et Systèmes Complexes MSC, F-75006 Paris, France.
Mariia Dvoriashyna: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK. at830@cam.ac.uk e.lauga@damtp.cam.ac.uk. ORCID
Christophe Eloy: Aix Marseille Univ., CNRS, Centrale Marseille, IRPHE, 13013 Marseille, France. ORCID
Florence Elias: Université de Paris, CNRS UMR 7057, Laboratoire Matière et Systèmes Complexes MSC, F-75006 Paris, France. ORCID
Eric Lauga: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK. at830@cam.ac.uk e.lauga@damtp.cam.ac.uk. ORCID
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.
References
J R Soc Interface. 2014 Feb 26;11(94):20131160
[PMID: 24573332]
