Identification of the dilute regime in particle sedimentation

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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 Ncrit ≥ C (R d)3/2 for the critical number N crit of particles. This lower bound agrees with the heuristically expected Ncrit 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 languageEnglish (US)
Pages (from-to)415-432
Number of pages18
JournalCommunications In Mathematical Physics
Volume250
Issue number2
DOIs
StatePublished - Sep 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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