Collective behavior of particles in fluids
Paris, December 14-17, 2020

Richard Höfer (Haussdorff Center for Mathematics, Bonn)

The method of reflections and its applications to mean-field models for sedimenting suspensions

The method of reflections is a method to expand the solution operator to a linear PDE in domains perforated by many disjoint sets in terms of the solution operator when only one of these sets is present. We consider this method for inertialess rigid particles in a Stokes flow. For well-seperated particles with a small volume fraction, the method yields a series expansion that converges with a rate proportional to the particle volume fraction. In the second part of the talk, we discuss how the method of reflections can be used to rigorously derive mean-field limits for sedimenting suspensions when the volume fraction vanishes in the limit. To leading order we obtain a coupled transport-Stokes system. As a first order correction in the volume fraction, we recover the effect of an increased effective viscosity of the suspension. This is joint work with Juan J. L. Velázquez and Richard Schubert.

See slides and record.