| The Doi equation for the time-dependent orientational distribution function of rodlike molecules in a nematic monodomain is solved for startup of a simple shearing flow with director orientation initially oriented at various angles with respect to the shearing plane, where the shearing plane is defined to be parallel to both the velocity and its gradient. Two numerical solution techniques are used; one is an expansion in spherical harmonic functions, which is a generalization of a technique derived earlier for a director confined to the shearing plane, and the second is a stochastic method that integrates the equations of motion for a large ensemble of molecules. We find that at low and modest shear rates, the director can be attracted either to a time-periodic tumbling orbit that lies in the shearing plane or to an orbit that lies out of the shearing plane. This latter orbit is either a steady log-rolling state with average orientation perpendicular to the shearing plane or a time-periodic kayaking state with an orbit oblique to the shearing plane. The final state of the system depends on the shear rate and the strength of the nematic potential. In some cases both the in-plane tumbling and log-rolling (or kayaking) states are attractors; the final state then depends on the initial director.
for LaTeX users @article{RGLarson1991-24,
author = {R. G. Larson and H. C. \"Ottinger},
title = {Effect of Molecular Elasticity on Out-of-Plane Orientations in Shearing Flows of Liquid-Crystalline Polymers},
journal = {Macromolecules},
volume = {24},
pages = {6270-6282},
year = {1991}
}
\bibitem{RGLarson1991-24} R.G. Larson, H.C. \"Ottinger,
Effect of Molecular Elasticity on Out-of-Plane Orientations in Shearing Flows of Liquid-Crystalline Polymers,
Macromolecules {\bf 24} (1991) 6270-6282.RGLarson1991-24
R.G. Larson, H.C. \"Ottinger
Effect of Molecular Elasticity on Out-of-Plane Orientations in Shearing Flows of Liquid-Crystalline Polymers
Macromolecules,24,1991,6270-6282 |
mk@mat.ethz.ch
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