Rheological phase diagrams for nonhomogeneous flows of rodlike liquid crystalline polymers

The rheological phase diagrams for solutions of rigid rod molecules are computed for planar Couette and Poiseuille flow as a function of Deborah number, initial orientation, and wall separation; this analysis extends the seminal work of Larson and Öttinger [R.G. Larson, H.C. Öttinger, Effect of molecular elasticity on out-of-plane orientations in shearing flows of liquid-crystalline polymers, Macromolecules 24 (1991) 6270–6282] to nonhomogeneous flows. The Doi diffusion equation is solved by using a finite-element discretization of the rod distribution function and Onsager interaction potential. Simulations of planar Couette flow show the familiar logrolling–tumbling–wagging–flow-aligning cascade as Deborah number increases, and the critical Deborah numbers associated with transitions between states vary with wall separation. Defects are caused solely by wall interactions rather than artificial anchoring conditions. Simulations of planar Poiseuille flow show that the system tends toward either logrolling states or composite flow-aligning/logrolling attractors depending on the Deborah number, wall separation, and initial orientation.