Collective dynamics and pattern formation in 2D regular arrays of spherical particles in Stokes flow between two parallel walls

We present results of our numerical and theoretical investigations of collective dynamics of linear trains and regular square arrays of spherical particles suspended in a fluid bounded by two parallel walls. The simulations reveal propagation of particle-displacement waves, deformation and rearrangements of a particle lattice, propagation of dislocation-like defects in ordered arrays, and transitions between ordered and disordered regions that can coexist for a long time. We argue that ordered motion of the arrays is associated with the dipolar form of the quasi-2D asymptotic far-field flow produced by the particles. We also show that the overall deformation of the arrays can be described using a macroscopic theory where the array is treated as a 2D effective medium. The theory predicts a fingering instability near the array corners, and this instability is confirmed by our microscopic simulations.