A model for suspension of clusters of particle pairs

Mecherbet, Amina

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 5, pp. 1597-1634.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

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 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 ξ 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 each cluster is initially correlated to its position. In this case, a local existence and uniqueness result for the limit model is provided.

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