Pattern formation of inertial particles in oscillatory flow

Particles exposed to oscillatory flows interact with each other through complex inertial forces, which can cause them to self-assemble. We develop a particle dynamics framework to study the organization and pattern formation of spherical particles exposed to a uniform oscillating background flow. The framework is based on semi-analytical pairwise interactions that capture the time-averaged inertial dynamics of multiple particles with a density in contrast to the fluid. The collective dynamics are organized by two dimensionless parameters: a frequency that describes the ratio of inertial and viscous forces over an oscillation, and an oscillation amplitude that quantifies the ratio of inertial to gravity forces. At large amplitudes, particles form multiple layers of hexagonal domains perpendicular to the oscillation axis. At small amplitudes, these domains coalesce into a single hexagonal lattice when gravity acts along the oscillation axis. However, with gravity perpendicular to the axis, the particles organize into one or many chains depending on the frequency. We organize these behaviors on a frequency-amplitude phase plane, finding that the framework recovers several experimental observations.