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On the collective effect of a large system of heavy particles immersed in a Newtonian fluid
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We consider the motion of a large number of heavy particles in a Newtonian fluid occupying a bounded spatial domain. When we say "heavy", we mean a particle with a mass density that approaches infinity at an appropriate rate as its radius vanishes. We show that the collective effect of heavy particles on the fluid motion is similar to the Brinkman perturbation of the Navier-Stokes system identified in the homogenization process.
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Cited by 2 Pith papers
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Brinkman's term for the steady-state Navier-Stokes equations with prescribed flux rate or pressure drop in perforated pipes
In the critical dilute regime where particle diameter scales as ε^3 and mutual distance as ε, weak limits of steady Navier-Stokes solutions in a perforated pipe satisfy the Brinkman equation with a friction term, for ...
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