Methods and Applications of Analysis

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

Weinan E and Pingwen Zhang

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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.

Article information

Source
Methods Appl. Anal. Volume 13, Number 2 (2006), 181-198.

Dates
First available in Project Euclid: 18 January 2008

Permanent link to this document
http://projecteuclid.org/euclid.maa/1200694871

Mathematical Reviews number (MathSciNet)
MR2381545

Zentralblatt MATH identifier
1131.76010

Subjects
Primary: 76B03: Existence, uniqueness, and regularity theory [See also 35Q35] 65M12: Stability and convergence of numerical methods 35Q35: PDEs in connection with fluid mechanics

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

Citation

E, Weinan; Zhang, Pingwen. A Molecular Kinetic Theory of Inhomogeneous Liquid Crystal Flow and the Small Deborah Number Limit. Methods Appl. Anal. 13 (2006), no. 2, 181--198. http://projecteuclid.org/euclid.maa/1200694871.


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