Organizing bacterial vortex lattices by periodic obstacle arrays

Henning Reinken,Markus Bär,Daiki Nishiguchi,Igor S Aranson,Andrey Sokolov,Sabine H L Klapp,Sebastian Heidenreich

doi:10.1038/s42005-020-0337-z

Abstract

Recent experiments have shown that the complex spatio-temporal vortex structures emerging in active fluids are susceptible to weak geometrical constraints. This observation poses the fundamental question of how boundary effects stabilize a highly ordered pattern from seemingly turbulent motion. Here we show, by a combination of continuum theory and experiments on a bacterial suspension, how artificial obstacles guide the flow profile and reorganize topological defects, which enables the design of bacterial vortex lattices with tunable properties. To this end, the continuum model is extended by appropriate boundary conditions. Beyond the stabilization of square and hexagonal lattices, we also provide a striking example of a chiral, antiferromagnetic lattice exhibiting a net rotational flow, which is induced by arranging the obstacles in a Kagome-like array.

Highlights

Recent experiments have shown that the complex spatio-temporal vortex structures emerging in active fluids are susceptible to weak geometrical constraints
We employ a coarse-grained continuum description[25,27,30,31,32,33,34,35], where the dynamics of the bacterial suspension is described by the effective bacterial velocity v
We show how periodic arrays of small pillars impose minimal geometrical constraints that lead to the stabilization of complex vortex lattices in an originally turbulent bacterial suspension

Summary

Introduction

Recent experiments have shown that the complex spatio-temporal vortex structures emerging in active fluids are susceptible to weak geometrical constraints This observation poses the fundamental question of how boundary effects stabilize a highly ordered pattern from seemingly turbulent motion. The observed states are characterized by neighboring vortices rotating spontaneously in the same (ferromagnetic) or opposite direction (antiferromagnetic), resembling magnetic spin lattices The stabilization of such structures and related vortex patterns in an otherwise turbulent bacterial suspension is achieved by imposing strong confinement in an ordered array of coupled flow chambers. It yields a pronounced circulation on a length scale much larger than the individual vortex size

Methods

Results

Conclusion