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arXiv 1011.4355cond-mat.softcond-mat.mtrl-sciphysics.flu-dyn
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缠结聚合物中的瞬态剪切带:Rolie-Poly模型的研究

Transient shear banding in entangled polymers: a study using the Rolie-Poly model

J. M. Adams, S. M. Fielding, P. D. Olmsted

摘要:

空间不均匀的剪切流发生在缠结的聚合物溶液,无论是作为稳态剪切带和瞬态后,一个大的步骤应变或在启动到一个稳定的均匀的剪切速率。稳态剪切带是总剪切应力和施加的剪切速率之间具有非单调本构关系的模型的标志,但瞬态条带有时在稳态下不剪切带的流体中看到。我们使用扩散Rolie-Poly模型在牛顿溶剂中模拟这种行为,其本构行为可以是单调或非单调的,取决于对流约束释放(CCR)的程度。我们研究单调本构行为。线性稳定性分析的启动到足够高的剪切速率表明,空间波动是不稳定的,在早期。这种不稳定性和(随时间变化的)本构曲线的负斜率之间存在很强的相关性。如果最不稳定特征值的时间积分足够大,则系统会出现瞬态剪切带,随后在稳态时消失。我们如何扰动,由于波动或不均匀的应力,可以触发这种不稳定性。这种瞬态行为与最近在纠缠聚合物溶液中的观察结果相似

英文摘要:

Spatially inhomogeneous shear flow occurs in entangled polymer solutions, both as steady state shear banding and transiently after a large step strain or during start up to a steady uniform shear rate. Steady state shear banding is a hallmark of models with a non-monotonic constitutive relation between total shear stress and applied shear rate, but transient banding is sometimes seen in fluids that do not shear band at steady state. We model this behavior using the diffusive Rolie-Poly model in a Newtonian solvent, whose constitutive behavior can be monotonic or non-monotonic depending on the degree of convected constraint release (CCR). We study monotonic constitutive behaviour. Linear stability analysis of start up to a sufficiently high shear rate shows that spatial fluctuations are unstable at early times. There is a strong correlation between this instability and the negative slope of the (time dependent) constitutive curve. If the time integral of the most unstable eigenvalue is sufficiently large then the system exhibits transient shear bands that later vanish in steady state. We show how perturbations, due to fluctuations or the inhomogeneous stresses, can trigger this instability. This transient behavior is similar to recent observations in entangled polymer solutions

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