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A molecular kinetic theory of inhomogeneous liquid crystal flow and the small Deborah number limit. (English) Zbl 1131.76010
Summary: The Doi kinetic theory for homogeneous flows of rodlike liquid crystalline polymers (LCPs) is extended to inhomogeneous flows through introducing a nonlocal intermolecular potential. An extra term in the form of an elastic body force comes out as a result of this extension. Systematic asymptotic analysis in the small Deborah number limit is carried out, and the classical Ericksen-Leslie equations are derived in this limit. The Leslie coefficients are derived in terms of molecular parameters, and the Ericksen stress emerges from the body force.

MSC:
76A15 Liquid crystals
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
82D60 Statistical mechanics of polymers
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