A model for suspension of clusters of particle pairs

Abstract

In this paper, we consider $N$ clusters of pairs of particles sedimenting in a viscous fluid. The particles are assumed to be rigid spheres and inertia of both particles and fluid are neglected. The distance between each two particles forming the cluster is comparable to their radii $\frac{1}{N}$ while the minimal distance between the pairs is of order $N^{-1/2}$. We show that, at the mesoscopic level, the dynamics are modelled using a transport-Stokes equation describing the time evolution of the position $x$ and orientation $\xi$ of the clusters. Under the additional assumption that the minimal distance is of order $N^{-1/3}$, we investigate the case where the orientation of the cluster is initially correlated to its position. In this case, a local existence and uniqueness result for the limit model is provided.