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Kinetic Theory Microstructure Modeling in Concentrated Suspensions
GeM Institute, Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, 44321 Nantes cedex 3, France
LTN, Polytech'Nantes, La Chantrerie, rue Christian Pauc, BP 50609 44306 Nantes cedex 3, France
Arts et Métiers ParisTech, 2 Boulevard du Ronceray, BP 93525, 49035 Angers cedex 01, France
* Author to whom correspondence should be addressed.
Received: 3 June 2013; in revised form: 6 July 2013 / Accepted: 11 July 2013 / Published: 19 July 2013
Abstract: When suspensions involving rigid rods become too concentrated, standard dilute theories fail to describe their behavior. Rich microstructures involving complex clusters are observed, and no model allows describing its kinematics and rheological effects. In previous works the authors propose a first attempt to describe such clusters from a micromechanical model, but neither its validity nor the rheological effects were addressed. Later, authors applied this model for fitting the rheological measurements in concentrated suspensions of carbon nanotubes (CNTs) by assuming a rheo-thinning behavior at the constitutive law level. However, three major issues were never addressed until now: (i) the validation of the micromechanical model by direct numerical simulation; (ii) the establishment of a general enough multi-scale kinetic theory description, taking into account interaction, diffusion and elastic effects; and (iii) proposing a numerical technique able to solve the kinetic theory description. This paper focuses on these three major issues, proving the validity of the micromechanical model, establishing a multi-scale kinetic theory description and, then, solving it by using an advanced and efficient separated representation of the cluster distribution function. These three aspects, never until now addressed in the past, constitute the main originality and the major contribution of the present paper.
Keywords: kinetic theory; concentrated suspensions; aggregates; Fokker-Planck equation; proper generalized decomposition; micromechanics
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Abisset-Chavanne, E.; Mezher, R.; Le Corre, S.; Ammar, A.; Chinesta, F. Kinetic Theory Microstructure Modeling in Concentrated Suspensions. Entropy 2013, 15, 2805-2832.
Abisset-Chavanne E, Mezher R, Le Corre S, Ammar A, Chinesta F. Kinetic Theory Microstructure Modeling in Concentrated Suspensions. Entropy. 2013; 15(7):2805-2832.
Abisset-Chavanne, Emmanuelle; Mezher, Rabih; Le Corre, Steven; Ammar, Amine; Chinesta, Francisco. 2013. "Kinetic Theory Microstructure Modeling in Concentrated Suspensions." Entropy 15, no. 7: 2805-2832.