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Issue ESAIM: Proc.
Volume 28, 2009
CEMRACS 2008 - Modelling and Numerical Simulation of Complex Fluids
Page(s) 55 - 79
DOI http://dx.doi.org/10.1051/proc/2009039
Published online 23 November 2009

ESAIM: Proc., 2009, Vol. 28, pp. 55-79
DOI: 10.1051/proc/2009039

Towards the simulation of dense suspensions: a numerical tool

S. Faure1, S. Martin1, B. Maury1 and T. Takahashi2

1  CNRS & Université Paris-Sud 11, Département de Mathématiques, Bâtiment 425, 91405 Orsay cedex (France)
2  Institut Élie Cartan UMR 7502 (INRIA, Nancy-Université & CNRS), POB 239, 54506 Vandœuvre-lès-Nancy cedex (France) and Team-project CORIDA, INRIA Nancy-Grand Est


Published online: 23 November 2009

Abstract
We present a numerical tool which aims at investigating the rheology of dense suspensions of entities such as spheres, red blood cells, polymer chains, or any kind of rigid or deformable bodies, in a viscous fluid. We shall pay a special attention to the short-range interactions between those entities (contact forces, lubrication forces). As for the fluid itself, our strategy consists in avoiding the direct and costly solution of the Stokes equations by integrating only the interaction forces which are likely to play a significant role in the overall behaviour of the suspension, in the spirit of Stokesian Dynamics. We present some preliminary results for suspensions of spheres, Red Blood Cells, and polymer-like chains.


Résumé
Nous présentons un outil numérique permettant d'étudier la rhéologie de suspensions denses d'entités telles que des sphères, des globules rouges, des chaînes de polymère et, d'une manière générale, des objets rigides ou déformables dans un fluide visqueux. Nous portons une attention particulière aux interactions à courte distance entre ces entités (forces de contact, forces de lubrification). En ce qui concerne le fluide lui-même, notre stratégie consiste à éviter le calcul direct (et coûteux) de la solution des équations de Stokes, en déterminant uniquement les forces d'interaction qui jouent un rôle significatif dans le comportement général de la suspension, dans l'esprit de la méthode dite de Dynamique Stokesienne. Nous présentons quelques résultats préliminaires pour des suspensions de sphères, de globules rouges, et de chaînes de polymère.



© EDP Sciences, ESAIM 2009


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