A general method for computing the hydrodynamic interactions among an infinite suspension of particles immersed between two infinite plane boundaries, under the condition of vanishing particle Reynolds number, is presented. The method accounts for both near-field particle-particle and particle-boundary lubrication effects as well as dominant many-body effects, which include reflections with both particles and boundaries. Through relative motion of the boundaries, a bulk shear flow can be generated, and the resulting particle motions, as well as the forces exerted by the boundaries on the fluid, computed. Knowledge of the boundary forces allows for the calculation of the suspension viscosity. The simulation method is applied to several example problems; in one, the resuspension of a sediment layer of particles is illustrated. The general method can also be extended to dynamically simulate suspensions immersed in a pressure driven flow between two walls or through a tube.
Exact solution for many-body Hamiltonian of interacting particles with linear spectrum