Regular and chaotic flow behavior and orientational dynamics of tumbling nematics

Abstract

We consider liquid crystalline polymers under plane Couette flow and investigate the influence of fluctuating shear rates on the orientational dynamics. With help of phase portraits and time evolution diagrams of the alignment tensor components, we discuss the effect of fluctuations on the flow-aligned, isotropic and periodic solutions. To explore the effect of fluctuations on the chaotic behavior we calculated the greatest Lyapunov exponent for different fluctuation strengths. We found that fluctuations of the shear rate in general have little effect on the dynamics of tumbling nematics. Further we present a new amended potential modeling the isotropic-to-nematic transition. In contrast to the Landau-de Gennes potential our potential has the advantage to restrict the order parameter to physically admissible values. In the end we present some results of the orientational dynamics for a spatially inhomogeneous system. © 2006 American Institute of Physics.