On the impact of clusters of rigid balls on the motion of a viscous fluid

We develop a new approach to the problem of the motion of a large number of rigid bodies immersed in a viscous fluid. The leading idea is the concept of cluster - a collection of individual rigid objects that may be grouped or even connected in such a way that their collective impact on the bulk motion of the system is similar to that of a single body. The applications of the new approach include: 1. Improving the critical value of the number of balls of small radius such that their cloud has no impact on the limit system represented by the incompressible Navier–Stokes equations. 2. The balls follow the fluid flow in the asymptotic limit of vanishing radius and increasing number even if a gravitational force is imposed.