Methods and Applications of Analysis
Volume 13 (2006)
A Molecular Kinetic Theory of Inhomogeneous Liquid Crystal Flow and the Small Deborah Number Limit
Pages: 181 – 198
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