Zusammenfassung für den Vortrag am 04.06.2020 (11:00 Uhr)Arbeitsgemeinschaft ANGEWANDTE ANALYSIS
Richard Höfer (Universität Bonn)
On the effective viscosity of suspensions
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.
One day before the seminar, an announcement with the link will be sent to the mailing list of the AG seminar. If you are not on the mailing list, but still want to join the broadcast, please contact Pavlos Tsatsoulis.