Three-dimensional flow of liquid crystalline polymers through rectangular channels with abrupt change in geometry

Three-dimensional flows of liquid crystalline polymers (LCPs) in a rectangular 3 to 1 abrupt contraction channel and a rectangular 1 to 3 abrupt expansion channel are numerically analyzed to investigate the molecular orientation behavior of LCPs in complex flows. A modified Doi model is used as a constitutive equation and MAC (marker and cell)-based finite difference method is employed for the numerical technique for solving the basic equations. In the contraction flow, most molecules are aligned in the flow direction near the contraction owing to elongational flow except for a vortex region. Just downstream of the contraction, the velocity overshoot occurs owing to the molecular orientation near the contraction. In the expansion flow, on the other hand, molecules near the mid-plane are aligned perpendicular to the flow direction just downstream of the expansion. This alignment is related to a concave velocity profile appeared in this region. Moreover, the decelerating flow downstream of the expansion causes a three-dimensional structure of directors called a twist structure.