Next Article in Journal
Microstructure of Laser Re-Melted AlCoCrCuFeNi High Entropy Alloy Coatings Produced by Plasma Spraying
Next Article in Special Issue
Deformed Exponentials and Applications to Finance
Previous Article in Journal
Non-Linear Canonical Correlation Analysis Using Alpha-Beta Divergence
Previous Article in Special Issue
Statistical Properties of the Foreign Exchange Network at Different Time Scales: Evidence from Detrended Cross-Correlation Coefficient and Minimum Spanning Tree
Entropy 2013, 15(7), 2805-2832; doi:10.3390/e15072805
Article

Kinetic Theory Microstructure Modeling in Concentrated Suspensions

1
, 1
, 2
, 3
 and 1,*
1 GeM Institute, Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, 44321 Nantes cedex 3, France 2 LTN, Polytech'Nantes, La Chantrerie, rue Christian Pauc, BP 50609 44306 Nantes cedex 3, France 3 Arts et M├ętiers ParisTech, 2 Boulevard du Ronceray, BP 93525, 49035 Angers cedex 01, France
* Author to whom correspondence should be addressed.
Received: 3 June 2013 / Revised: 6 July 2013 / Accepted: 11 July 2013 / Published: 19 July 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
Download PDF [4192 KB, uploaded 24 February 2015]

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 kinetic theory; concentrated suspensions; aggregates; Fokker-Planck equation; proper generalized decomposition; micromechanics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Export to BibTeX |
EndNote


MDPI and ACS Style

Abisset-Chavanne, E.; Mezher, R.; Le Corre, S.; Ammar, A.; Chinesta, F. Kinetic Theory Microstructure Modeling in Concentrated Suspensions. Entropy 2013, 15, 2805-2832.

View more citation formats

Article Metrics

Comments

Citing Articles

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert