Elongational perturbations on nematic liquid crystal polymers under a weak shear

The two-dimensional Smoluchowski equation is employed to study the effect of elongational perturbations on nematic liquid crystal polymers under a weak shear. We use the multiscale asymptotic analysis to show that 1 when the elongational perturbation is small relative to the weak shear, the orientational probability density function pdf tumbles periodically only in an intermediate range of polymer concentration; outside this intermediate range i.e., for very small and very large polymer concentration the orientational pdf converges to a steady state and there is no tumbling. 2 When the elongational perturbation is about 20% of the shear rate or larger, the intermediate range of tumbling disappears and the orientational pdf always converges to a steady state regardless of the polymer concentration. Our theoretical predictions are consistent with various earlier results based on the Leslie–Ericksen theory C. V. Chaubal and L. G. Leal, J. Non-Newtonian Fluid Mech. 82, 22 1999 or analogous 3D numerical simulations M. G. Forest, R. Zhou, and Q. Wang, Phys. Rev. Lett. 93, 088301 2004 ; M. G. Forest, Q. Wang, R. Zhou, and E. Choate, J. Non-Newtonian Fluid Mech. 118, 17 2004 . © 2007 American Institute of Physics. DOI: 10.1063/1.2794002