A closure approximation for nematic liquid crystals based on the canonical distribution subspace theory |
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Authors: | Massimiliano Grosso Pier L Maffettone Francois Dupret |
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Institution: | (1) CESAME Unité de Mécanique Appliquée Université Catholique de Louvain Avenue G. Lemaitre 4-6, B-1348 Louvain La-Neuve Belgium, BE;(2) Dipartimento di Scienza dei Materiali ed Ingegneria Chimica Politecnico di Torino Corso Duca degli Abruzzi 24, I-10129 Torino, Italia e-mail: maffetto@athena.polito.it, |
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Abstract: | A closure approximation for nematic polymers is presented. It approximates the fourth rank order tensor in terms of lower
rank tensors, and is derived in the framework of the canonical distribution subspace theory. This approach requires a choice
of the class of distributions: Here the set of Bingham distributions is chosen, as already introduced by Chaubal and Leal
(1998). The closure is written in a generic frame of reference, and in an explicit form, so that it can be easily implemented.
Such formulation also permits studying the closure approximation with continuation tools, which rather completely describe
the system dynamics. The predictions can then be compared with those obtained with the exact model. The shear flow is considered
as a test, since this flow condition appears to be the most demanding for closure approximations for nematic polymers.
Received: 30 November 1999/Accepted: 30 November 1999 |
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Keywords: | Liquid-crystalline polymers Constitutive equations Bifurcation Orthotropy Shear flow |
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