A CLOSURE APPROXIMATION FOR LIQUID-CRYSTALLINE POLYMER MODELS BASED ON PARAMETRIC DENSITY-ESTIMATION

A new rational closure approximation for the Doi model of liquid-cryst alline polymers (LCPs) is presented and compared with unapproximated r esults. The closure is based upon proposing a parametric form for the orientation distribution function, the Bingham distribution, which is appropriate for the spherical geometry of the configuration space. The closure enjoys the advantage over ad hoc moment closures of always yi elding physical answers; moreover, it is designed to give the exact so lution behavior in a number of limits. Its behavior for steady two-dim ensional flows reveals a range of applicability that extends significa ntly beyond the intended Limits. The main deficiency, a failure to pre dict a flow-aligning transition in simple shear, is shown to be due to the inability to predict skewing of the orientation distribution. Com parisons are also made for a center-gated disk geometry, addressing th e performance in three-dimensional unsteady flow typically seen in pro cessing of LCPs. The Bingham closure shows excellent quantitative agre ement with unapproximated solutions, only underestimating the time sca le of some transient behavior. The approximation is compared with othe r closures in the same vein, and suggestions are made for improvements . (C) 1998 The Society of Rheology.