Collective dynamics of small clusters of particles flowing in a quasi-two-dimensional microchannel

Spatially ordered equilibrium states - crystals - and their excitations - phonons - are the mainstay of condensed matter physics. Flowing, nonequilibrium crystalline states of microparticles and droplets are desirable for microfluidic logic, assembly, and control, and have been achieved in recent work via exploitation of viscous hydrodynamic interactions in geometric confinement. For the most part, these studies considered large ensembles of particles and, accordingly, large scale collective modes arising from small displacements of individual particles. Via theoretical modeling and computational simulations, we show that for small clusters of flowing particles tightly confined in a shallow, "quasi-two-dimensional" microchannel, new types of ordered behavior emerge, varying from steady states in which particles maintain their relative positions, to exquisitely coordinated collective motion with large particle displacements. These new collective behaviors require a thin channel geometry: strong confinement in one spatial direction and weak confinement in another. We elucidate principles and techniques for the a priori construction or rapid numerical discovery of these states, which could be exploited for the orchestration of particle motion in lab-on-a-chip devices and other applications.