Abstract and Applied Analysis
Volume 2007 (2007), Article ID 36267, 15 pages
doi:10.1155/2007/36267
On the equilibria of the extended nematic polymers under elongational flow
Hong Zhou1
, Lynda Wilson1
and Hongyun Wang3
1Department of Applied Mathematics, Naval Postgraduate School, Monterey 93943, CA, USA
3Department of Applied Mathematics and Statistics, University of California, Santa Cruz 95064, CA, USA
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.