Collective dynamics of inertial particles in oscillatory flow

Suspensions of particles in oscillatory flows are known to display intricate collective behaviors. In this study, we present a semi-theoretical framework designed to predict the dynamics of interacting particles within a uniform oscillatory flow. Our focus is on the time-averaged collective behavior of multiple particles resulting from pairwise particle interactions.

Starting with a pair of particles, we perform a dual multipole expansion to characterize the oscillatory disturbance flow created by each particle. Utilizing the Lorentz reciprocal theorem, we calculate time-averaged hydrodynamic interaction forces between the particles. The theory reveals collective patterns such as planar hexagonal clusters or into chains depending on the alignment of the particle line-of-centers with the applied flow as well as Stokes Number, which is regulated by particle size, frequency and fluid viscosity.