On the effective viscosity of suspensions

  • Richard Höfer (Universität Bonn)
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Small particles suspended in a fluid are ubiquitous in nature and technology. It is well-known that the particles change the effective viscosity of the fluid. The problem has been addressed by Einstein in his PhD dissertation in 1906. He obtained a quantitative result known as Einstein's law for the effective viscosity for spherical particles to first order in the volume fraction $\phi$ of the particles. Rigorous mathematical results have only been obtained in the last years. I will review these results and present recent improvements where we were able to relax the assumptions on the particle configurations considerably.

This covers physically relevant random distributions of particles. A big challenge consists in the analysis of a dynamic version of Einstein's law. Indeed, the interaction between the particles accounting for Einstein's law is very singular ($1/|x|^3$ in three dimensions), and we presently do not know how to obtain the corresponding mean field-result for fixed volume fraction $\phi$ as we lose control over the interparticle distances. Nevertheless, I will present a perturbative result in the case $\phi \to 0$, that incorporates Einstein's law.

This talk is based on joint works with David Gérard-Varet and Richard Schubert.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 11, 2024 tba with Carlos Román Parra
  • Mar 15, 2024 tba with Esther Bou Dagher
  • Mar 27, 2024 tba with Christian Wagner
  • May 21, 2024 tba with Immanuel Zachhuber