(163j) Hydrodynamic Crystals: Collective Dynamics Of Quasi-Two-Dimensional Regular Arrays Of Spherical Particles In Stokes Flow Between Two Parallel Walls

Our accelerated Stokesian-dynamics algorithm for a system of spherical particles suspended in a fluid bounded by two parallel planar walls is used to study motion of quasi-two-dimensional regular arrays of particles in the parallel-wall geometry. The simulations are performed for square arrays of about 1000 particles moving in the center-plane of a channel with wall separation comparable to the particle diameter. Particle motion is produced either by an external Poiseuille flow or by a force parallel to the walls. Our simulations reveal complex collective particle behavior. For example, the particle arrays undergo significant deformations without losing the long-range order. Under some conditions arrays can also develop an instability that is similar to the dislocation in a two-dimensional crystal. After the instability has appeared, ordered and disordered regions in an array coexist for long times. We argue that the ordered array motion is associated with the dipolar form of the quasi-two-dimensional asymptotic far-field flow produced by the particles.