Numerical Simulation of Flows of Liquid Crystalline Polymers through Contraction-Expansion Geometries

Abstract

Numerical simulations were performed for the flows of liquid crystalline polymers (LCPs) through abrupt contraction-expansion geometries. The constitutive equation used was a modified Doi model. The evolution equation of components of orientational order-parameter tensor was solved by using the method of characteristics and the time step optimum in the Runge-Kutta method.The streamlines for LCPs indicate the flow with a smaller entrance angle and a larger vortex at the contraction region and with a larger exit angle and a smaller vortex at the expansion region than those for the flow of Newtonian fluids. These features in the flow of LCPs are connected with the molecular orientation in the positive and negative elongational flow regions; the molecules prefer to orient in the direction parallel to the streamline in the contraction region and in the direction perpendicular to the streamline at the expansion region. In the region downstream from the expansion, while the distribution of the order parameter recovers to that in the developed flow between parallel plates, the disturbance in the director remains far downstream.