Closure Approximations for the Doi Theory: Which to Use in Simulating Complex Flows of LCPs

J. Feng , C. V. Chaubal and L. G. Leal

*J. Rheol.* **42**, 1095-1119 (1998)

**Abstract **- The goal of this paper 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 closure, a quadratic closure with finite molecular
aspect ratio, the two Hinch-Leal closures, a hybrid between the quadratic
and the first Hinch-Leal closures and a recently proposed Bingham closure.
The first part of the paper studies the predictions of the models in homogeneous
flows. We generate their bifurcation diagrams in the (U,Pe) plane, where
U is the nematic strength and Pe is the Peclet number, and place special
emphasis on the effects of the flow type. These solutions are then compared
with the "exact solutions" of the unapproximated Doi theory. Results show
the Bingham closure to give the best approximation to the Doi theory in terms
of reproducing transitions between the director aligning, wagging and tumbling
regimes at the correct values of U and Pe and predicting the arrest of periodic
solutions by a mildly extensional flow. In the second part of the paper,
we employ the closure models to compute a complex flow in an eccentric cylinder
geometry. All the models tested predict the same qualitative features of
the LCP dynamics. Upon closer inspection of the quantitative differences
among the solutions, the Bingham closure appears to be the most accurate.
Based on these results, we recommend using the Bingham closure in simulating
complex flows of LCPs.