  Active particles, including swimming microorganisms, autophoretic colloids
and droplets, are known to self-organize into ordered structures at fluid-solid
boundaries. The entrainment of particles in the attractive parts of their
spontaneous flows has been postulated as a possible mechanism underlying this
phenomenon. Here, combining experiments, theory and numerical simulations, we
demonstrate the validity of this flow-induced ordering mechanism in a
suspension of active emulsion droplets. We show that the mechanism can be
controlled, with a variety of resultant ordered structures, by simply altering
hydrodynamic boundary conditions. Thus, for flow in Hele-Shaw cells, metastable
lines or stable traveling bands can be obtained by varying the cell height.
Similarly, for flow bounded by a plane, dynamic crystallites are formed. At a
no-slip wall the crystallites are characterised by a continuous out-of-plane
flux of particles that circulate and re-enter at the crystallite edges, thereby
stabilising them. At an interface where the tangential stress vanishes the
crystallites are strictly two-dimensional, with no out-of-plane flux. We
rationalize these experimental results by calculating, in each case, the slow
viscous flow produced by the droplets and the dissipative, long-ranged,
many-body active forces and torques between them. The results of numerical
simulations of motion under the action of the active forces and torques are in
excellent agreement with experiments. Our work elucidates the mechanism of
flow-induced phase separation (FIPS) in active fluids, particularly active
colloidal suspensions, and demonstrates its control by boundaries, suggesting
new routes to geometric and topological phenomena in active matter.
