This study examines the simplest relevant molecular model of a polymeric liquid in large-amplitude oscillatory shear (LAOS) flow: rigid dumbbells suspended in a Newtonian solvent. For such suspensions, the viscoelastic response of the polymeric liquid depends exclusively on the dynamics of dumbbell orientation. Previously, the explicit analytical expressions of the zeroth, second, and fourth harmonics of the alternating first normal stress difference response in LAOS have been derived. In this paper, we correct and extend these expressions by seeking an understanding of the next higher harmonic. Specifically, this paper continues a series of studies that shed light on molecular theory as a useful approach in investigating the response of polymeric liquids to oscillatory shear. Following the general method of Bird and Armstrong [“Time-dependent flows of dilute solutions of rodlike macromolecules,” J. Chem. Phys. 56, 3680 (1972)], we derive the expression of the first normal stress coefficient up to and including the sixth harmonic. Our analysis relies on the extension of the orientation distribution function to the sixth power of the shear rate. Our expression is the only one to have been derived from a molecular theory for a sixth harmonic and thus provides the first glimpse of the molecular origins of a first normal stress difference higher than the fourth.

中文翻译：

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振荡剪切流中分子取向的一阶法向应力差的高次谐波模式法

这项研究检查了大振幅振荡剪切 (LAOS) 流中聚合物液体的最简单的相关分子模型：悬浮在牛顿溶剂中的刚性哑铃。对于这种悬浮液，聚合物液体的粘弹性响应完全取决于哑铃取向的动力学。以前，已经导出了 LAOS 中交替第一法向应力差异响应的零次、二次和四次谐波的显式解析表达式。在本文中，我们通过寻求对下一个高次谐波的理解来纠正和扩展这些表达式。具体而言，本文继续进行一系列研究，阐明分子理论是研究聚合物液体对振荡剪切的响应的有用方法。遵循 Bird 和 Armstrong 的一般方法 [“棒状大分子稀溶液的时间相关流动”，J. Chem。物理。56, 3680 (1972)]，我们推导出了直到并包括六次谐波的第一法向应力系数的表达式。我们的分析依赖于方向分布函数对剪切速率的六次方的扩展。我们的表达式是唯一一个源自六次谐波分子理论的表达式，因此提供了高于四次谐波的第一法向应力差的分子起源的第一眼。我们的分析依赖于方向分布函数对剪切速率的六次方的扩展。我们的表达式是唯一一个源自六次谐波分子理论的表达式，因此提供了高于四次谐波的第一法向应力差的分子起源的第一眼。我们的分析依赖于方向分布函数对剪切速率的六次方的扩展。我们的表达式是唯一一个源自六次谐波分子理论的表达式，因此提供了高于四次谐波的第一法向应力差的分子起源的第一眼。