Numerical simulation of three-dimensional flows of liquid crystalline polymers in rectangular abrupt contraction and expansion channels

Three-dimensional flows of liquid crystalline polymers in rectangular abrupt contraction and expansion channels were numerically analyzed using a modified Doi model as a constitutive equation. The orientational behavior of molecules was mainly investigated using the director and the orientational order parameter, and the relation between the orientational field and the velocity field was analyzed at several Deborah numbers De. In the contraction flow, flow aligning of molecules occurred in the main flow near the contraction owing to elongational flow. In the expansion flow, molecules near the mid-plane were aligned perpendicular to the flow direction just downstream of the expansion and this alignment related to a concave velocity profile appeared in this region. The order parameter increases just downstream of the expansion and the orientation more slowly relaxes along the flow for larger De. In addition, negative elongational flow downstream of the expansion causes a highly three-dimensional structure of directors called a twist structure.