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Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow

机译:大幅振荡剪切流动中聚合物取向的傅里叶分解

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In our previous work, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear flow, a flow experiment that has gained a significant following in recent years. We chose rigid dumbbells since these are the simplest molecular model to give higher harmonics in the components of the stress response. We derived the expression for the dumbbell orientation distribution, and then we used this function to calculate the shear stress response, and normal stress difference responses in large-amplitude oscillatory shear flow. In this paper, we deepen our understanding of the polymer motion underlying large-amplitude oscillatory shear flow by decomposing the orientation distribution function into its first five Fourier components (the zeroth, first, second, third, and fourth harmonics). We use three-dimensional images to explore each harmonic of the polymer motion. Our analysis includes the three most important cases: (i) nonlinear steady shear flow (where the Deborah number λ ω is zero and the Weissenberg number λ γ ? 0 is above unity), (ii) nonlinear viscoelasticity (where both λ ω and λ γ ? 0 exceed unity), and (iii) linear viscoelasticity (where λ ω exceeds unity and where λ γ ? 0 approaches zero). We learn that the polymer orientation distribution is spherical in the linear viscoelastic regime, and otherwise tilted and peanut-shaped. We find that the peanut-shaping is mainly caused by the zeroth harmonic, and the tilting, by the second. The first, third, and fourth harmonics of the orientation distribution make only slight contributions to the overall polymer motion.
机译:在我们以前的工作中,我们探讨了刚性哑铃的稀释悬浮液的动态作为大振幅振荡剪切流量的聚合物液体的模型,该流动实验近年来在近年来下降的显着性。我们选择刚性哑铃,因为这些是最简单的分子模型,以在应力反应的组件中提供更高的谐波。我们派生了哑铃取向分布的表达,然后我们使用该功能来计算大幅度振荡剪切流中的剪切应力响应和正常应力差响应。在本文中,我们通过将取向分布函数分解成其前五个傅立叶组分(Zeroth,第一,第二,第三和第四次谐波)来加深了对大幅度振荡剪切流的理解。我们使用三维图像来探索聚合物运动的每个谐波。我们的分析包括三个最重要的情况:(i)非线性稳定剪切流量(其中Deborah编号λω为零,并且Weissenberg编号λγ≤y是高于统一),(ii)非线性粘弹性(其中λω和λ γ≤0超统一),(iii)线性粘弹性(其中λω超过统一,其中λγ≤0接近零)。我们了解到,聚合物取向分布是线性粘弹性状态的球形,以及其他倾斜和花生形状。我们发现花生整形主要是由Zeroth谐波和倾斜的倾斜引起的。定向分布的第一,第三和第四次谐波仅对整体聚合物运动产生轻微贡献。

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