Elongational perturbations on nematic liquid crystal polymers under a weak shear

Abstract

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 ͑1͒ when the elongational perturbation is small relative to the weak shear, the orientational probability density function ͑pdf͒ tumbles periodically only in an intermediate range of polymer concentration; outside this intermediate range ͑i.e., for very small and very large polymer concentration͒ the orientational pdf converges to a steady state and there is no tumbling. ͑2͒ 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.

Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

“…[118]. Let u = cos sin represent the orientation of rodlike molecules, v = 0 −x be the shear flow, v E = /2 q −y −x be the elongational perturbation.…”

Solução numérica de escoamentos de cristais líquidos nemáticos

“…Essa teoria tem sido utilizada por vários investigadores (ver por exemplo [56,55,144,145]) mas a aplicação dessa teoria a escoamentos em duas dimensões utilizando as equações completas de Doi e Edwards ainda não foi considerada. Mais detalhes sobre a teoria de Doi e Edwards [41] podem ser encontrados em [111,112].…”