FREE BOUNDARY PROBLEMS FOR SWARMS OF MAGNETOTACTIC BACTERIA*

Active matter is characterized by the generation of mechanical motion, driven by internal energy sources. An exemplary instance of this is a suspension of magnetotactic bacteria, where the resulting flows can be regulated by an applied magnetic field [1]. Here we illustrate how active stress in a suspension of magnetotactic bacteria induces flow due to its action on the free boundary. The microaerobic magnetotactic bacteria find an optimal concentration within the system, for example, in a capillary with a free end. We consider how this band of bacteria, which exists in a layer with thickness  and is subject to the action of an applied magnetic field that makes angle  with the midline of the band, induces a Couette-like flow at the band end, which then exponentially decays on both sides of the band. The velocity on the boundary of the band depends on the force dipole of the bacteria, their concentration as well as the thickness of the cell  and the field orientation angle . The velocity at the boundary of the band at realistic values of the governing parameters is around 20 , which is in good agreement with experiment. The mechanism we describe represents a new approach to describing the dynamics of free boundary problems related to swarms of magnetotactic bacteria, caused by the influence of active stress on the free boundary. Simulations also indicate that the swarm compresses along the field direction, adopting a pancake-like shape.

1. M.Marmol,E.Gachon, and D.Faivre, Rev.Mod.Phys. (to be published)