| Issue |
ESAIM: M2AN
Volume 54, Number 5, September-October 2020
|
|
|---|---|---|
| Page(s) | 1597 - 1634 | |
| DOI | https://doi.org/10.1051/m2an/2020002 | |
| Published online | 28 July 2020 | |
A model for suspension of clusters of particle pairs
1
Sorbonne Universités, Laboratoire Jacques-Louis Lions (UMR 7598), F-75005 Paris, France
2
Université de Paris, Institut de Mathématiques de Jussieu-Paris Rive Gauche (UMR 7586), F-75205 Paris, France
* Corresponding author: mecherbet@ljll.math.upmc.fr
Received:
4
July
2019
Accepted:
2
January
2020
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.
Mathematics Subject Classification: 76T20 / 76D07 / 35Q83 / 35Q70
Key words: Mathematical modelling / suspensions / cluster dynamics / Stokes flow / system of interacting particles
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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