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Abstract and Applied Analysis
Volume 2007, Article ID 36267, 15 pages
http://dx.doi.org/10.1155/2007/36267
Research Article

On the Equilibria of the Extended Nematic Polymers under Elongational Flow

1Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA
2Department of Applied Mathematics and Statistics, University of California, Santa Cruz, CA 95064, USA

Received 21 December 2006; Accepted 16 March 2007

Academic Editor: Norimichi Hirano

Copyright © 2007 Hong Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We classify the equilibrium solutions of the Smoluchowski equation for dipolar (extended) rigid nematic polymers under imposed elongational flow. The Smoluchowski equation couples the Maier-Saupe short-range interaction, dipole-dipole interaction, and an external elongational flow. We show that all stable equilibria of rigid, dipolar rod dispersions under imposed uniaxial elongational flow field are axisymmetric. This finding of axisymmetry significantly simplifies any procedure of obtaining experimentally observable equilibria.