  Recent experimental studies have shown that confinement can profoundly affect
self-organization in semi-dilute active suspensions, leading to striking
features such as the formation of steady and spontaneous vortices in circular
domains and the emergence of unidirectional pumping motions in periodic
racetrack geometries. Motivated by these findings, we analyze the
two-dimensional dynamics in confined suspensions of active self-propelled
swimmers using a mean-field kinetic theory where conservation equations for the
particle configurations are coupled to the forced Navier-Stokes equations for
the self-generated fluid flow. In circular domains, a systematic exploration of
the parameter space casts light on three distinct states: equilibrium with no
flow, stable vortex, and chaotic motion, and the transitions between these are
explained and predicted quantitatively using a linearized theory. In periodic
racetracks, similar transitions from equilibrium to net pumping to traveling
waves to chaos are observed in agreement with experimental observations and are
also explained theoretically. Our results underscore the subtle effects of
geometry on the morphology and dynamics of emerging patterns in active
suspensions and pave the way for the control of active collective motion in
microfluidic devices.
