CLOSURE APPROXIMATIONS FOR THE DOI THEORY - WHICH TO USE IN SIMULATING COMPLEX FLOWS OF LIQUID-CRYSTALLINE POLYMERS

The goal of this article is to determine which closure model should be used in simulating complex flows of liquid-crystalline polymers (LCPs ). We examine the performance of six closure models: the quadratic clo sure, a quadratic closure with finite molecular aspect ratio, the two Hinch-Leal closures, a hybrid between the quadratic and the first Hinc h-Leal closures and a recently proposed Bingham closure. The first par t of the article studies the predictions of the models; in homogeneous flows. We generate their bifurcation diagrams in the (U,Pe) plane, wh ere U is the nematic strength and Pe is the Peclet number, and place s pecial emphasis on the effects of the flow type. These solutions are t hen compared with the ''exact solutions'' of the unapproximated Doi th eory. Results show the Bingham closure to give the best approximation to the Doi theory in terms of reproducing transitions between the dire ctor aligning, wagging and tumbling regimes at the correct values of L i and Re and predicting the arrest of periodic solutions by a mildly e xtensional flow. In the second part of the article, we employ the clos ure models to compute a complex flow in Bn eccentric cylinder geometry . All the models tested predict the same qualitative features of the L CP dynamics. Upon closer inspection of the quantitative differences am ong the solutions, the Bingham closure appears to be the most accurate . Based on these results, we recommend using the Bingham closure in si mulating complex flows of LCPs. (C) 1998 The Society of Rheology.