Mild assumptions for the derivation of Einstein's effective viscosity formula

We provide a rigorous derivation of Einstein's formula for the effective viscosity of dilute suspensions of n rigid balls, set in a volume of size 1. So far, most justifications were carried under a strong assumption on the minimal distance between the balls: c > 0. We relax this assumption...

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Bibliographic Details
Published in:Communications in partial differential equations 2021-05, Vol.46 (4), p.611-629
Main Authors: Gérard-Varet, David, Höfer, Richard M.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Derivation
Effective viscosity
homogenization
Mathematics
Stokes equations
suspensions
Viscosity
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Summary:We provide a rigorous derivation of Einstein's formula for the effective viscosity of dilute suspensions of n rigid balls, set in a volume of size 1. So far, most justifications were carried under a strong assumption on the minimal distance between the balls: c > 0. We relax this assumption into a set of two much weaker conditions: one expresses essentially that the balls do not overlap, while the other one gives a control of the number of balls that are close to one another. In particular, our analysis covers the case of suspensions modeled by standard Poisson processes with almost minimal hardcore condition.
ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2020.1850780