Methods and Applications of Analysis

Volume 13 (2006)

Number 2

A Molecular Kinetic Theory of Inhomogeneous Liquid Crystal Flow and the Small Deborah Number Limit

Pages: 181 – 198

DOI: http://dx.doi.org/10.4310/MAA.2006.v13.n2.a5

Authors

Weinan E

Pingwen Zhang

Abstract

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 asympototic 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.

Keywords

Rodlike liquid crystal polymers; Doi equation; Ericksen-Leslie theory; Inhomogeneous flow; Body force

2010 Mathematics Subject Classification

35Q35, 65M12, 76B03

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