Suspension evolution is described to first order in particle density by a succession of uncorrelated binary collisional events. In our simulations, these finite-concentration effects are included via a Boltzmann Monte-Carlo method. The state of the system is described by an ensemble of particles which are characterized by their vertical position in the channel. The ensemble is then updated by computing a large number of random binary collisions.
We discuss systems where particle-particle and particle-wall interactions are described by a) purely hydrodynamic interactions, and b) via repulsive potentials. For the first class of systems in unbounded domains, binary interactions do not result in particle migration across streamlines. In the presence of a wall, however, we describe a new mechanism of particle migration in which interacting particles swap their vertical positions. This migration is not excluded by the time reversal of Stokes equation and reflection symmetries in the system since swapping particles do not pass each other in the horizontal direction. In the presence of non-hydrodynamic interactions, diffusive behavior is initially observed. However, at later times, layers of higher particle density separated by layers of clean fluid develop. This ordering is driven from initial perturbations in particle density near walls.