{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:31:39Z","timestamp":1760243499526,"version":"build-2065373602"},"reference-count":56,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2013,7,19]],"date-time":"2013-07-19T00:00:00Z","timestamp":1374192000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e15072805","type":"journal-article","created":{"date-parts":[[2013,7,19]],"date-time":"2013-07-19T12:12:52Z","timestamp":1374235972000},"page":"2805-2832","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Kinetic Theory Microstructure Modeling in Concentrated Suspensions"],"prefix":"10.3390","volume":"15","author":[{"given":"Emmanuelle","family":"Abisset-Chavanne","sequence":"first","affiliation":[{"name":"GeM Institute, Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, 44321 Nantes cedex 3, France"}]},{"given":"Rabih","family":"Mezher","sequence":"additional","affiliation":[{"name":"GeM Institute, Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, 44321 Nantes cedex 3, France"}]},{"given":"Steven","family":"Le Corre","sequence":"additional","affiliation":[{"name":"LTN, Polytech'Nantes, La Chantrerie, rue Christian Pauc, BP 50609 44306 Nantes cedex 3, France"}]},{"given":"Amine","family":"Ammar","sequence":"additional","affiliation":[{"name":"Arts et M\u00e9tiers ParisTech, 2 Boulevard du Ronceray, BP 93525, 49035 Angers cedex 01, France"}]},{"given":"Francisco","family":"Chinesta","sequence":"additional","affiliation":[{"name":"GeM Institute, Ecole Centrale de Nantes, 1 rue de la Noe, BP 92101, 44321 Nantes cedex 3, France"}]}],"member":"1968","published-online":{"date-parts":[[2013,7,19]]},"reference":[{"key":"ref_1","first-page":"161","article-title":"The motion of ellipsoidal particles immersed in a viscous fluid","volume":"A102","author":"Jeffery","year":"1922","journal-title":"Proc. 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