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Einstein's effective viscosity formula

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Authors : Gloria, Antoine (Author of the conference)
CIRM (Publisher )

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Abstract : In 1905, Albert Einstein published two papers that led to an experiment to measure the Avogadro number. The first paper studies the Brownian motion and establishes the Einstein relation in kinetic theory. The second paper studies a Stokes fluid with a suspension of rigid particles, and establishes the Einstein formula for the effective viscosity of this 'complex fluid'. The Avogadro number, which appears in both relations, can then be deduced from two measurements of fluid mechanics. Performed by Jean Perrin in 1907-1909, these experiments confirmed the atomistic nature of matter (for which he was awarded a Nobel prize in 1926) using classical fluid mechanics!
The aim of the talk is to give an elementary and robust proof of Einstein's effective viscosity formula, and to discuss higher-order expansions.
This is a joint work with Mitia Duerinckx (ULB).

Keywords : effective viscosity; homogenization; dilute regime

MSC Codes :
35R60 - PDEs with randomness, stochastic PDE
76M50 - homogenization
76T20 - Suspensions

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 10/05/2022
    Conference Date : 28/04/2022
    Subseries : Research talks
    arXiv category : Analysis of PDEs ; Probability
    Mathematical Area(s) : Analysis and its Applications ; PDE ; Probability & Statistics
    Format : MP4 (.mp4) - HD
    Video Time : 01:03:20
    Targeted Audience : Researchers ; Graduate Students
    Download : https://videos.cirm-math.fr/2022-04-28_Gloria.mp4

Information on the Event

Event Title : Probability/PDE Interactions: Interface Models and Particle Systems / Interactions EDP/Probabilités : interfaces et systèmes de particules
Event Organizers : Duerinckx, Mitia ; Gess, Benjamin ; Fathi, Max ; Guillin, Arnaud ; Simon, Marielle
Dates : 25/04/2022 - 29/04/2022
Event Year : 2022
Event URL : https://conferences.cirm-math.fr/2557.html

Citation Data

DOI : 10.24350/CIRM.V.19909903
Cite this video as: Gloria, Antoine (2022). Einstein's effective viscosity formula. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19909903
URI : http://dx.doi.org/10.24350/CIRM.V.19909903

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