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Titre :
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Near-equilibrium dynamics of Doi models for liquid crystal polymer flows: catastrophic and regularized behavior
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Auteurs :
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M. Forest ;
Q. Wang
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Type de document :
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article/chapitre/communication
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Année de publication :
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1999
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Format :
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p. 131-150
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Langues:
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= Anglais
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Catégories :
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PHYSIQUE ETAT DE LA MATIERE
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Mots-clés:
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POLYMERE
;
RHEOLOGIE
;
MODELE
;
FLUIDE NON NEWTONIEN
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Résumé :
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Doi models for flows of concentrated solutions of homogeneous liquid crystal polymers (LCPs) are analyzed in the quadratic closure approximation. Our purpose is to clarify a remarkable near-equilibrium behavior of these equations which has apparently gone unnoticed; these results are important for any numerical or experimental interpretations of LCP flows based on Doi models near mechanical and nematic equilibria. To reveal this behavior, we analytically solve the linearized Doi nematodynamic equations; this calculation explicitly captures the coupling between the pure nematic and pure hydrodynamic linearized dynamics. The original Doi model without solvent viscosity is analyzed first: the low concentration (N8/3) prolate nematic phase yield well-posed linearized dynamic; at higher concentration both the isotropic phase (N>3) and the oblate nematic phase (N>3) yield catastrophic linearized dynamics, with exponential growthrates proportional to the amplitude of the wavevector of the linearized disturbance. This result implies that there is unbounded growth in vanishingly small length scales for data near these equilibria.
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Source :
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Journal of Non - Newtonian Fluid Mechanics, vol.83
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