Sedimentation of particles in Stokes flow

Amina Mecherbet

doi:10.3934/krm.2019038

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2019, Volume 12, Issue 5: 995-1044. Doi: 10.3934/krm.2019038

This issue Previous Article Local sensitivity analysis and spectral convergence of the stochastic Galerkin method for discrete-velocity Boltzmann equations with multi-scales and random inputs Next Article A probabilistic approach for the mean-field limit to the Cucker-Smale model with a singular communication

Sedimentation of particles in Stokes flow

Amina Mecherbet

IMAG, Montpellier University, Place Eugène Bataillon, Montpellier, 34090, France

Received: May 31, 2018

Revised: March 31, 2019

Published: July 2019

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Abstract

In this paper, we consider $ N $ identical spherical particles sedimenting in a uniform gravitational field. Particle rotation is included in the model while fluid and particle inertia are neglected. Using the method of reflections, we extend the investigation of [11] by discussing the threshold beyond which the minimal particle distance is conserved for a short time interval independent of $ N $. We also prove that the particles interact with a singular interaction force given by the Oseen tensor and justify the mean field approximation in the spirit of [8] and [9].

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Mathematics Subject Classification: 35Q70, 76T20, 76D07, 35Q83.

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References

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