## Abstract

A numerical technique for the dynamical simulation of three-dimensional rigid particles in a Newtonian fluid is presented. The key idea is to satisfy the no-slip boundary condition on the particle surface by a localized force-density distribution in an otherwise force-free suspending fluid. The technique is used to model the sedimentation of prolate spheroids of aspect ratio b/a = 5 at Reynolds number 0.3. For a periodic lattice of single spheroids, the ideas of Hasimoto are extended to obtain an estimete forthe finite-size correction to the sedimentation velocity. For a system of several spheroids in periodic arrangement, a maximum of the settling speed is found at the effective volume fraction Φ(b/a)^{2} ≈ 0.4, where Φ is the solid-volume fraction. The occurence of a maximum of the settling speed is partially explained by the competition of two effects: (i) A change in the orientation distribution of the prolate spheroids whose major axes shift from a mostly horizontal orientation (corresponding to small sedimentation speeds) at small Φ to a more uniform orientation at larger Φ, and (ii) a monotonic decrease of the settling speed with increasing solid-volume fraction similar to that predicted by the Richardson-Zaki law α (1 - Φ)^{5}.^{5} for suspensions of spheres.

Original language | English |
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Pages (from-to) | 221-235 |

Number of pages | 15 |

Journal | JOURNAL OF ENGINEERING MATHEMATICS |

Volume | 41 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 1 Nov 2001 |

MoE publication type | A1 Journal article-refereed |

## Keywords

- Ellipsoids
- Fibers
- Finite differences
- Particle scale simulation
- Sedimentation
- Spheroids
- Suspensions