Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

Aline Lefebvre; Bertrand Maury

doi:10.1016/j.crme.2005.10.007

Fluid–solid interactions: modeling, simulation, bio-mechanical applications

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles
[Viscosité apparente d'un mélange de fluide Newtonien et de particules en interaction]

Aline Lefebvre ¹ ; Bertrand Maury ¹

¹ Laboratoire de mathématiques, université Paris-Sud, 91405 Orsay cedex, France

Comptes Rendus. Mécanique, Fluid-solid interactions: modeling, simulation, bio-mechanical applications, Volume 333 (2005) no. 12, pp. 923-933.

Résumé
Abstract

Nous présentons une étude du comportement global d'un mélange de fluide newtonien et de particules rigides par la simulation directe. Cette approche apporte des éléments d'analyse de l'influence d'inclusions rigides en interaction (comme dans le cas des globules rouges dans le sang) sur le comportement global du mélange complexe. Nous nous sommes concentrés ici sur la viscosité apparente, que nous définissons comme une quantité macroscopique qui caractérise la résistance d'un fluide complexe à un mouvement de cisaillement imposé. Notre objectif principal est d'expliquer les variations non monotones de cette viscosité apparente au cours du temps, lorsque les particules interagissent. Notre analyse se base sur des remarques théoriques préliminaires et sur un certain nombre de calculs de cette viscosité pour des configurations représentatives.

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations.

Publié le : 2005-11-17

DOI : 10.1016/j.crme.2005.10.007

Keywords: Computational fluid mechanics, Apparent viscosity, Fluid–particle flow, Finite element method, Arbitrary Lagrangian Eulerian method
Mots-clés : Mécanique des fluides numérique, Viscosité apparente, Écoulements fluide–particles, Méthode des Éléments Finis, Méthode Arbitraire Lagrange–Euler

Affiliations des auteurs :

Aline Lefebvre ¹ ; Bertrand Maury ¹

¹ Laboratoire de mathématiques, université Paris-Sud, 91405 Orsay cedex, France

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Aline Lefebvre; Bertrand Maury. Apparent viscosity of a mixture of a Newtonian fluid and interacting particles. Comptes Rendus. Mécanique, Fluid-solid interactions: modeling, simulation, bio-mechanical applications, Volume 333 (2005) no. 12, pp. 923-933. doi : 10.1016/j.crme.2005.10.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.10.007/

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