| Based on a relaxation equation for the alignment tensor characterizing the molecular orientation in liquid crystals under flow we present results for the full orientational dynamics of homogeneous liquid crystals in a shear flow. We extend the analysis of the symmetry-adapted states by Rienäcker and Hess (Physica A 267 [1999] 294), which invoke only 3 of the 5 components of the tensor to full alignment. The steady and transient states of the adapted model are preserved in this more general description, except for log-rolling, which turns out to be unstable in the range of parameters considered. However, the states reported earlier are only stable within a certain range of the parameters and there is a variety of new, symmetry-breaking transient states with the director out of the shear plane, which partially coexist with the in-plane states. The new, out-of-plane states can be divided in two classes: simple periodic and complex orbits. The first class consists of a kayaking-tumbling and a kayaking-wagging state, where the projection of the director onto the shear plane describes a tumbling or wagging motion, respectively. The second class of states, which can be found only in a small parameter range, consists of a variety of either complicated periodic or irregular, chaotic orbits. Both an intermittency route and a period-doubling route to chaos are found.
for LaTeX users @article{GRienäcker2002-315,
author = {G. Rienäcker and M. Kr\"oger and S. Hess},
title = {Chaotic and regular shear-induced orientational dynamics of nematic liquid crystals},
journal = {Physica A},
volume = {315},
pages = {537-568},
year = {2002}
}
\bibitem{GRienäcker2002-315} G. Rienäcker, M. Kr\"oger, S. Hess,
Chaotic and regular shear-induced orientational dynamics of nematic liquid crystals,
Physica A {\bf 315} (2002) 537-568.GRienäcker2002-315
G. Rienäcker, M. Kr\"oger, S. Hess
Chaotic and regular shear-induced orientational dynamics of nematic liquid crystals
Physica A,315,2002,537-568 |
mk@mat.ethz.ch
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