Abstract and Applied Analysis
Volume 2007 (2007), Article ID 36267, 15 pages
On the Equilibria of the Extended Nematic Polymers under Elongational Flow
1Department of Applied Mathematics, Naval Postgraduate School, Monterey 93943, CA, USA
2Department of Applied Mathematics and Statistics, University of California, Santa Cruz 95064, CA, 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.
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.