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



Weinan E

Pingwen Zhang


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.


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

2010 Mathematics Subject Classification

35Q35, 65M12, 76B03

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