Comptes Rendus
Fluid–solid interactions: modeling, simulation, bio-mechanical applications
Apparent viscosity of a mixture of a Newtonian fluid and interacting particles
Comptes Rendus. Mécanique, Volume 333 (2005) no. 12, pp. 923-933.

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.

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.

Published online:
DOI: 10.1016/j.crme.2005.10.007
Keywords: Computational fluid mechanics, Apparent viscosity, Fluid–particle flow, Finite element method, Arbitrary Lagrangian Eulerian method
Mot clés : Mécanique des fluides numérique, Viscosité apparente, Écoulements fluide–particles, Méthode des Éléments Finis, Méthode Arbitraire Lagrange–Euler

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, 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/

[1] A. Einstein Eine neue Bestimmung der Moleküledimensionen, Ann. Phys. Leipzig, Volume 19 (1906), pp. 289-306

[2] G.K. Batchelor; J.T. Green The hydrodynamic interaction of two small freely moving spheres in a linear flow field, J. Fluid Mech., Volume 56 (1972), pp. 375-400

[3] L.J. Durlofsky; J.F. Brady Dynamic simulation of bounded suspensions of hydrodynamically interacting particles, J. Fluid Mech., Volume 200 (1989), pp. 39-67

[4] S. Haber; H. Brenner Hydrodynamic interaction of spherical particles in quadratic Stokes flows, Int. J. Multiphase Flow, Volume 25 (1999), pp. 1009-1032

[5] R. Glowinski; T.W. Pan; T.I. Hesla; D.D. Joseph A distributed Lagrange multiplier/fictitious domain method for particulate flow, Int. J. Multiphase Flow, Volume 25 (1998), pp. 755-794

[6] R. Glowinski Finite element methods for incompressible viscous flow, Handbook of Numerical Analysis, vol. IX, North-Holland, Amsterdam, 2003, pp. 3-1176

[7] A.A. Johnson; T.E. Tezduyar Simulation of multiple spheres falling in a liquid-filled tube, Comput. Methods Appl. Mech. Engrg., Volume 134 (1996), pp. 351-373

[8] H.H. Hu Direct simulation of flows of solid-liquid mixtures, Int. J. Multiphase Flow, Volume 22 (1996), pp. 335-352

[9] B. Maury Direct simulations of 2D fluid–particle flows in biperiodic domains, J. Comput. Phys., Volume 156 (1999), pp. 325-351

[10] S. Kim; S.J. Karrila Microhydrodynamics: Principles and Selected Applications, Butterworth–Heinemann, Boston, 1991

[11] J.L. Amorós; V. Sanz; A. Gozalbo; B. Beltrán Viscosity of concentrated clay suspensions: effect of solids volume fraction, shear stress, and deflocculant content, British Ceramic Trans., Volume 101 (2002) no. 5, pp. 185-193

[12] L. Berlyand; L. Borcea; A. Panchenko Network approximation for effective viscosity of concentrated suspensions with complex geometry, SIAM J. Math. Anal., Volume 36 (2005) no. 5, pp. 1580-1628

[13] P. Singh; T.I. Hesla; D.D. Joseph Distributed Lagrange multiplier method for particulate flows with collisions, Int. J. Multiphase Flow, Volume 29 (2003), pp. 495-509

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