均匀剪切流场中液晶聚合物微观结构的无网格模拟  

Simulation of Microstructure for Liquid-crystalline Polymers in Homogenous Shear Flow by Meshfree Methods

作　　者：王晓东[1] 欧阳洁[1] 苏进[1] 

机构地区：[1]西北工业大学应用数学系,西安710129

出　　处：《工程数学学报》2010年第2期194-206,共13页Chinese Journal of Engineering Mathematics

基　　金：国家重点基础研究发展计划(973)项目(2005CB321704);国家自然科学基金(10871159;10590353)~~

摘　　要：采用基于Doi理论的微-宏观双尺度模型研究了液晶聚合物在均匀剪切流场中的微观结构。为保证模拟结果的可靠性,在模型求解中率先使用了高精度、高稳定性的无网格方法,并通过对均匀流场中均质液晶聚合物系统的数值模拟,验证了该方法的有效性。文中着重研究了De数对平板Couette流中液晶聚合物微观结构的影响。模拟得到了液晶聚合物分子四种典型的微观运动结构,即弹性稳态、周期翻转、周期摆动和随流取向。定量分析了De数对两种周期运动的影响,预测了各种结构下分子的有序程度和可能出现的缺陷,并通过对取向角的详细分析,发现了两种边界层效应。The micro-macro dual-scale model based on the Doi theory has been used to study the microstructure of liquid-crystalline polymers in homogenous shear flow. The element free Galerkin （EFG） method with high accuracy and good stability is used to solve the model. The validity of the EFG method has been verified through the simulation of homogenous liquid-crystalline polymers in uniform flow. Four typical microstructures of liquid-crystalline polymers in plane couette flow, say elastic-stability, periodic tumbling, periodic wagging and flow-aligning, have been found by observing the affect of the De number. Moreover, we analyze the influence of the De number on two periodic motions, predict the degree of molecular orders and implied defects, and find the two kinds of boundary effects.

关 键 词：剪切流 液晶 微观结构 双尺度 无网格 

分 类 号：O373[理学—流体力学] O753.2[理学—力学]