Closure approximations for the Doi theory: Which to use in simulating complex flows of liquid-crystalline polymers?
Closure approximations for the Doi theory: Which to use in simulating complex flows of liquid-crystalline polymers?
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DOI：
10.1122/1.550920
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发表时间：
1998-12
影响因子：
3.3
通讯作者：
James J. Feng;Charu V. Chaubal;L. Leal
中科院分区：
文献类型：
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作者：
James J. Feng;Charu V. Chaubal;L. Leal
本文的目的是确定哪种闭合模型应该用于模拟液晶聚合物（lcp）的复杂流动。我们研究了六种闭包模型的性能：二次闭包，具有有限分子长径比的二次闭包，两个Hinch-Leal闭包，二次和第一个Hinch-Leal闭包之间的混合以及最近提出的Bingham闭包。文章的第一部分研究了均匀流中模型的预测。我们在（U,Pe）平面上生成了它们的分岔图，其中U是向列强度，Pe是佩莱特数，并特别强调了流型的影响。然后将这些解与非近似Doi理论的“精确解”进行比较。结果表明，Bingham闭包给出了Doi理论的最佳近似，在正确的U和Pe值上再现了定向对准、摆动和翻滚制度之间的过渡，并预测了周期阻滞。
The goal of this article 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 article 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 period...