A theory is developed to predict the motion of N neutrally buoyant spheres suspended in laminar flow between parallel plates. The spheres are at large separation yet nearer each other than the duct walls, and the Reynolds number is small. In this parameter range, viscous interactions are larger than inertial effects, and can be represented in terms of a superposition of ‘strainlets’. Several examples are given to show this viscous interaction effect. Near the leading edge of a front of spheres or near the trailing edge significant lateral migration velocities can occur, being at least one order of magnitude larger than inertially induced migration velocities. This phenomenon may have a negative effect on ‘chromatographic’ separation schemes, affecting particle concentration, recovery and resolution.