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Computation of particle settling speed and orientation distribution in suspensions of prolate spheroids

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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 estimate for the 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 the settling speed with increasing solid-volume fraction similar to that predicted by the Richardson–Zaki law ∝(1−φ)5⋅5 for suspensions of spheres.

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Authors and Affiliations

  1. Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015, HUT, Espoo, Finland

    Esa Kuusela

  2. Institut für Computeranwendungen 1, Universität Stuttgart, 70569 , Stuttgart, Germany

    Kai Höfler

  3. Institut für Computeranwendungen 1, Universität Stuttgart, 70569 , Stuttgart, Germany

    Stefan Schwarzer

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  1. Esa Kuusela
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  2. Kai Höfler
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  3. Stefan Schwarzer
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Kuusela, E., Höfler, K. & Schwarzer, S. Computation of particle settling speed and orientation distribution in suspensions of prolate spheroids. Journal of Engineering Mathematics 41, 221–235 (2001). https://doi.org/10.1023/A:1011900103361

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