Revisit the Elongational Viscosity of FENE Dumbbell Model
Revisit the Elongational Viscosity of FENE Dumbbell Model
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DOI：
10.1678/rheology.45.185
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发表时间：
2017-09
影响因子：
1.3
通讯作者：
H. Watanabe;Yumi Matsumiya
中科院分区：
文献类型：
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作者：
H. Watanabe;Yumi Matsumiya
众所周知，胡克哑铃模型的伸长粘度 η E 随着伸长应变率 ˙ ε 的增大而增大，最终在 ˙ ε 接近 1/2 τ Heq 时发散至无穷大，其中 τ Heq 是胡克哑铃模型的粘弹性弛豫时间，不随 ˙ ε 变化。 η E 的这种散度反映了胡克哑铃的无限扩展性。真实的聚合物链显然具有最大拉伸极限，因此具有有限延展性的哑铃模型在大约半个世纪前就被开发出来，作为强流动下链的模型。该模型表现出强流动下的有限可扩展非线性弹性（FENE）效应，为 η E 提供应变硬化特征，但没有任何发散。这个 FENE 哑铃模型已经过详细的数学分析，现已十分完善。然而，根据天真的预期，FENE 哑铃的硬化可以/应该大大增加粘度。因此，仍然需要在直观的物理基础上解释硬化如何抑制 η E 的发散。从这个角度来看，本研究重点研究FENE哑铃在稳定伸长流下的有效弛豫时间τ F eff 。事实证明，FENE 哑铃的硬化导致 τ Feff 在 ˙ ε > 1/2 τ Heq 处与 ˙ ε -1 成比例减小，并且 τ eff 的减小使得 FENE 哑铃在流动下的有效魏森伯格数 Wi Feff = ˙ ετ Feff 保持在 ~1/2 的临界值以下，即使对于 ˙ ε →∞ 也是如此。 Wi Feff 的有限增加允许 FENE 哑铃稍微改变其构象，即使 ˙ ε 从 1/2 τ Heq 大幅增加到任何更高的值，这自然会导致 η E 缺乏发散。非线性弹性 (FENE) / 哑铃 / 拉伸粘度 / 应变硬化
It is well known that the elongational viscosity η E of the Hookean dumbbell model increases with increasing elongational strain rate ˙ ε and finally diverges to infinite on approach of ˙ ε to 1/2 τ Heq , where τ Heq is the viscoelastic relaxation time of the Hookean dumbbell that does not change with ˙ ε . This divergence of η E reflects infinite extensibility of the Hookean dumbbell. Real polymer chains obviously have the maximum stretch limit, so that the dumbbell model with a finite extensibility was developed almost a half century ago as a model for those chains under strong flow. This model exhibits the finite extensible nonlinear elasticity (FENE) effect under strong flow to provide η E with the strain-hardening feature but without any divergence. This FENE dumbbell model has been mathematically analyzed in detail and is now well established. Nevertheless, in a naive expectation, stiffening of the FENE dumbbell could/should largely increase the viscosity. Thus, it is still desired to explain, on an intuitive physical basis, how the stiffening suppresses the divergence of η E . From this point of view, this study focuses on the effective relaxation time τ F eff of the FENE dumbbell under steady elongational flow. It turned out that the stiffening of the FENE dumbbell leads to a decrease of τ Feff in proportion to ˙ ε −1 at ˙ ε > 1/2 τ Heq , and this decrease of τ eff allows the effective Weissenberg number of the FENE dumbbell under flow, Wi Feff = ˙ ετ Feff , to stay below a critical value of ~1/2 even for ˙ ε →∞. This limited increase of Wi Feff allows the FENE dumbbell to change its conformation just slightly even for a large increase of ˙ ε from 1/2 τ Heq to any higher value, which naturally leads to the lack of divergence of η E . nonlinear elasticity (FENE) / Dumbbell / Elongational viscosity / Strain-hardening