Fluid Dynamics Research 38 (2006) 452 – 468 Three-dimensional ﬂow of liquid crystalline polymers through rectangular channels with abrupt change in geometry Takehiro Yamamoto ∗ , Yasuo Yamasaki, Yusuke Tanaka, Noriyasu Mori Department of Mechanophysics Engineering, Graduate School of Engineering, Osaka University, 2-1,Yamadaoka, Suita, Osaka 565-0871, Japan Received 16 February 2005; received in revised form 22 February 2006; accepted 1 March 2006 Communicated by K. Ishii Abstract 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. © 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved. Keywords: Liquid crystalline polymers; Three-dimensional ﬂow; Contraction channel; Expansion channel; Doi model; Mole- cular orientation; Twist structure ∗ Corresponding author. Fax: +81 06 6879 7308. E-mail address: take@mech.eng.osaka-u.ac.jp (T. Yamamoto). 0169-5983/$30.00 © 2006 The Japan Society of Fluid Mechanics and Elsevier B.V. All rights reserved. doi:10.1016/j.ﬂuiddyn.2006.03.001