论文标题
稳定剪切流中Fene-P流体的主曲线
Master Curves for FENE-P Fluids in Steady Shear Flow
论文作者
论文摘要
Fene-P（有限延伸的非线性弹性）哑铃本构型方程广泛用于模拟和稳定性分析，并且由于其相对的简单性和准确性在预测稀释聚合物溶液的宏观特性方面的相对简单性和准确性。该模型包含三个独立的材料参数，这些参数以无量纲的形式表示对应于魏森堡的数字（$ \ \ \ textrm {wi} $），即，哑铃放松时间尺度与特征流动时间尺度与有限的可扩展性参数（$ l $）的特征性流动时间尺度的比率相对应的均值均值，与完全延伸的长度相对应 - 平衡条件和溶剂粘度比通常表示$β$。可以使用稳定的简单剪切流中Fene-P模型的流变学预测的确切解决方案[Sureshkumar等人，Phys Fluids（1997）]，但是所得的非线性和嵌套方程组并未容易揭示出在高$ \ textrm {Wi} $的主要剪切物理学，这些物理是由高\ textrm {wi} $ the the Plimite the Plimite the Plyite se saute the Plyite timenite saute the Plyite se sa的限制序列的。在本说明中，我们回顾了一种评估稳定材料功能的简单方法，表征聚合物对剪切应力的非线性演变和随着剪切速率的增加，提供渐近扩展作为$ \ textrm {wi} $的函数，并表明实际上可以为这两种材料函数构建通用曲线以及相应的材料以及对相应的材料的构建构建均可构建的范围。在不同有限伸展性的三个高弹性稀释聚合物溶液上进行的稳定剪切流实验也遵循已识别的主曲线。这些主曲线的无量纲参数为$ \ textrm {wi}/l $，并且仅在强的剪切流中超过$ \ textrm {wi}/l \ gtrsim 1 $ 1 $ 1 $ 1 $ 1 $，这对聚合物链的有限扩展性的效果占据了聚合物应力在流面场中的进化。我们建议在进行稳定性分析或使用Fene-P模型模拟剪切主导的流动时，报告$ \ textrm {Wi}/l $的大小将有助于阐明有限的可扩展性效果。
The FENE-P (Finitely-Extensible Nonlinear Elastic) dumbbell constitutive equation is widely used in simulations and stability analyses of free and wall-bounded viscoelastic shear flows due to its relative simplicity and accuracy in predicting macroscopic properties of dilute polymer solutions. The model contains three independent material parameters, which expressed in dimensionless form correspond to a Weissenberg number ($\textrm{Wi}$), i.e., the ratio of the dumbbell relaxation time scale to a characteristic flow time scale, a finite extensibility parameter ($L$), corresponding to the ratio of the fully extended dumbbell length to the root mean square end-to-end separation of the polymer chain under equilibrium conditions, and a solvent viscosity ratio, commonly denoted $β$. An exact solution for the rheological predictions of the FENE-P model in steady simple shear flow is available [Sureshkumar et al., Phys Fluids (1997)], but the resulting nonlinear and nested set of equations do not readily reveal the key shear-thinning physics that dominates at high $\textrm{Wi}$ as a result of the finite extensibility of the polymer chain. In this note we review a simple way of evaluating the steady material functions characterizing the nonlinear evolution of the polymeric contributions to the shear stress and first normal stress difference as the shear rate increases, provide asymptotic expansions as a function of $\textrm{Wi}$ , and show that it is in fact possible to construct universal master curves for these two material functions as well as the corresponding stress ratio. Steady shear flow experiments on three highly elastic dilute polymer solutions of different finite extensibilities also follow the identified master curves. The governing dimensionless parameter for these master curves is $\textrm{Wi}/L$ and it is only in strong shear flows exceeding $\textrm{Wi}/L \gtrsim 1$ that the effects of finite extensibility of the polymer chains dominate the evolution of polymeric stresses in the flow field. We suggest that reporting the magnitude of $\textrm{Wi}/L$ when performing stability analyses or simulating shear-dominated flows with the FENE-P model will help clarify finite extensibility effects.
