Applied Math And Analysis Seminar
Monday, October 3, 2016, 4:30pm, 119 Physics
Athanasios Tzavaras (KAUST)
Kinetic models for the description of sedimenting suspensions

Abstract:

I review some works on modeling and the mathematical theory for dilute suspensions of rigid rods. Such problems appear in modeling sedimentation of suspensions of particles. Similar in spirit models are also used for modeling swimming micro-organisms. Here, we focus on a class of models introduced by Doi and describing suspensions of rod¨Clike molecules in a solvent fluid. They couple a microscopic Fokker-Planck type equation for the probability distribution of rod orientations to a macroscopic Stokes flow. One objective is to compare such models with traditional models used in macoscopic viscoelasticity as the well known Oldroyd model. In particular: For the problem of sedimenting rods under the influence of gravity we discuss the instability of the quiescent flow and the derivation of effective equations describing the collective response. We derive two such effective theories: (i) One ammounts to a classical diffusive limit and produces a Keller-Segel type of model. (ii) A second approach involves the derivation of a moment closure theory and the approximation of moments via a quasi-dynamic approximation. This produces a model that belongs to the class of flux-limited Keller-Segel systems. The two theories are compared numerically with the kinetic equation. (joint work with Christiane Helzel, Univ. Duesseldorf). [video]

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