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Sedimentation of Inertialess Particles in Stokes Flows

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Abstract

We investigate the sedimentation of a cloud of rigid, spherical particles of identical radii under gravity in a Stokes fluid. Both inertia and rotation of particles are neglected. We consider the homogenization limit of many small particles in the case of a dilute system in which interactions between particles are still important. In the relevant time scale, we rigorously prove convergence of the dynamics to the solution of a macroscopic equation. This macroscopic equation resembles the Stokes equations for a fluid of variable density subject to gravitation.

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Authors and Affiliations

  1. Institute For Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Richard M. Höfer

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  1. Richard M. Höfer
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Correspondence to Richard M. Höfer.

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Communicated by C. Mouhot

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Höfer, R.M. Sedimentation of Inertialess Particles in Stokes Flows. Commun. Math. Phys. 360, 55–101 (2018). https://doi.org/10.1007/s00220-018-3131-y

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  • DOI: https://doi.org/10.1007/s00220-018-3131-y

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