Pressure-driven channel flows of a model liquid-crystalline polymer

Abstract

Shear flows disrupt molecular orientation in liquid-crystalline polymers (LCPs) through director tumbling, and this causes difficulty in controlling the polymer structure and properties in injection molding and extrusion. In this paper we simulate LCP channel flows using the Doi theory. A Bingham closure is used to preserve director tumbling and wagging. The objective is to examine how contractions and expansions in a channel affect LCP orientation and to explore the possibility of using the channel geometry as a means of manipulating LCP order. A finite-element method is used to solve the coupled equations for fluid flow and polymer configuration. Results show that a contraction aligns the director with the streamline and improves molecular order, while an expansion drives the director away from the flow direction and reduces molecular order. If the expansion is strong enough, an instability develops downstream as disturbances in the flow and polymer configuration reinforce each other through the polymer stress. This instability generates a wave that spans roughly the central half of the channel and propagates downstream at the centerline velocity. For abrupt contractions or expansions, disclinations of ±1/2 strength arise in the corner vortex. The numerical results agree qualitatively with experiments when comparisons can be made. In particular, the wavy pattern following a sudden expansion is remarkably similar to previous experimental observations. The simulations suggest that using contractions and expansions may be a feasible strategy for controlling LCP order and morphology in processing.