Numerical Analysis of the Rheology of Polymeric Liquid Crystals. (2nd Report, Shear and Extensional Flow Behavior).

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The Doi equations have been directly computed for shear and extensional flow without closure approximations. An extension is imposed on the shear flow plane. It is well-known that for simple shear flow there are three orientation regimes, depending on the magnitude of shear rate; rotational (tumbling), oscillatory (wagging), and stationary (aligning) orientation behaviors. When we add an extension to simple shear flow, the time period of tumbling is increased, while the order parameter in the regime is almost unchanged. In the wagging regime, however, both the time period and the order parameter are increased. Transitions from the tumbling and wagging regimes to the aligning regime are induced when more than a certain magnitude of extension is imposed on a system. An extension has also an effect to make the first normal stress difference positive. Furthermore, motion of individual molecules has been analyzed by integrating the Langevin equation. It is found that the aligning state in shear and extensional flow is due to an approximately stationary behavior of individual molecules, while the aligning state in simple shear flow is an apparently stationary behavior of a group of many rotational molecules.