Whereas rigid dumbbell suspensions predict, at least qualitatively, most of the viscoelastic material functions measured in the laboratory, Hookean dumbbells predict few of these. For instance, whereas rigid dumbbells predict a shear-thinning viscosity curve, as they should, Hookean dumbbells yield a constant for the steady shear viscosity. In this paper, we explore the addition of a Hookean spring to the end of a rigid rod, a dumbbell attributed to Fraenkel. In this way, we focus our attention on how macromolecular extensibility affects the configuration distribution in steady shear flow. We arrive at the exact solution to this configuration distribution in steady shear flow at low shear rate and then insert it into the Giesekus expression for the stress tensor to arrive at an exact solution for the zero-shear viscosity and the zero-shear values of the normal stress differences.

中文翻译：

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Fraenkel 哑铃悬浮液的零剪切粘度

刚性哑铃悬架至少可以定性地预测实验室中测量的大部分粘弹性材料功能，而胡克哑铃预测的很少。例如，刚性哑铃预测剪切稀化粘度曲线，正如它们应该的那样，胡克哑铃产生稳定剪切粘度的常数。在本文中，我们探讨了在刚性杆（Fraenkel 设计的哑铃）末端添加胡克弹簧的方法。通过这种方式，我们将注意力集中在大分子延伸性如何影响稳态剪切流中的构型分布上。