This review is devoted to the large-scale rheology of suspensions of rigid particles in Stokes fluid. After describing recent results on the definition of the effective viscosity of such systems in the framework of homogenization theory, we turn to our new results on the asymptotic expansion of the effective viscosity in the dilute regime. This includes a new optimal proof of Einstein’s viscosity formula for the first-order expansion, as well as the continuation of this expansion to higher orders. The essential difficulty originates in the long-range nature of hydrodynamic interactions: suitable renormalizations are needed and are captured by means of diagrammatic expansions.
@article{SLSEDP_2021-2022____A9_0, author = {Mitia Duerinckx and Antoine Gloria}, title = {Effective viscosity of semi-dilute suspensions}, journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications}, note = {talk:3}, pages = {1--14}, publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2021-2022}, doi = {10.5802/slsedp.155}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.155/} }
TY - JOUR AU - Mitia Duerinckx AU - Antoine Gloria TI - Effective viscosity of semi-dilute suspensions JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:3 PY - 2021-2022 SP - 1 EP - 14 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.155/ DO - 10.5802/slsedp.155 LA - en ID - SLSEDP_2021-2022____A9_0 ER -
%0 Journal Article %A Mitia Duerinckx %A Antoine Gloria %T Effective viscosity of semi-dilute suspensions %J Séminaire Laurent Schwartz — EDP et applications %Z talk:3 %D 2021-2022 %P 1-14 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.155/ %R 10.5802/slsedp.155 %G en %F SLSEDP_2021-2022____A9_0
Mitia Duerinckx; Antoine Gloria. Effective viscosity of semi-dilute suspensions. Séminaire Laurent Schwartz — EDP et applications (2021-2022), Talk no. 3, 14 p. doi : 10.5802/slsedp.155. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.155/
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