## Abstract

We investigate the dynamics of rigid, spherical particles of radius R sinking in a viscous fluid. Both the inertia of the particles and the fluid are neglected. We are interested in a large number N of particles with average distance d ≫ R. We investigate in which regime (in terms of N and R/d) the particles do not significantly interact and approximately sink like single particles. We rigorously establish the lower bound N_{crit} ≥ C (_{R} ^{d})^{3/2} for the critical number N _{crit} of particles. This lower bound agrees with the heuristically expected N_{crit} in terms of its scaling in R/d. The main difficulty lies in showing that the particles cannot get significantly closer over a relevant time scale. We use the method of reflection for the Stokes operator to bound the strength of the particle interaction.

Original language | English (US) |
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Pages (from-to) | 415-432 |

Number of pages | 18 |

Journal | Communications In Mathematical Physics |

Volume | 250 |

Issue number | 2 |

DOIs | |

State | Published - Sep 2004 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics