论文标题
稳定剪切和扩展流的启动和停止：仿射线性phan-thien-tanner流体模型的精确分析解决方案
Start-up and cessation of steady shear and extensional flows: Exact analytical solutions for the affine linear Phan-Thien--Tanner fluid model
论文作者
论文摘要
对于仿射线性phan-thien-tanner流体模型，获得了启动和停止流的精确分析解决方案。它们包括启动和停止稳定剪切流的结果，稳定的单轴和双轴伸展流以及稳定的平面伸展流。获得的解决方案表明，在稳定剪切流的启动时，应力经过准周期性的指数降低振荡，同时接近其稳定流量值（因此，存在压力过大）；在稳定的伸展流动的启动时，应力是单调的，而在停止稳定的剪切和延伸流动时，应力会迅速，非指数衰减。还回顾了流体的稳定流动性，这本工作中获得的确切分析解决方案比文献中发现的替代公式更简单。详细研究了稳定和瞬态溶液的特性，包括其低和高魏森堡数量的渐近行为。还讨论了对Phan-Thien-Tanner模型的多模版本的概括。因此，这项工作提供了对启动，停止和剪切和伸展流的启动，停止和稳定制度的仿射线性phan-thien-tanner流体的流变性的完整分析描述。
Exact analytical solutions for start-up and cessation flows are obtained for the affine linear Phan-Thien--Tanner fluid model. They include the results for start-up and cessation of steady shear flows, of steady uniaxial and biaxial extensional flows, and of steady planar extensional flows. The solutions obtained show that at start-up of steady shear flows, the stresses go through quasi-periodic exponentially damped oscillations while approaching their steady-flow values (so that stress overshoots are present); at start-up of steady extensional flows, the stresses grow monotonically, while at cessation of steady shear and extensional flows, the stresses decay quickly and non-exponentially. The steady-flow rheology of the fluid is also reviewed, the exact analytical solutions obtained in this work for steady shear and extensional flows being simpler than the alternative formulas found in the literature. The properties of steady and transient solutions, including their asymptotic behavior at low and high Weissenberg numbers, are investigated in detail. Generalization to the multimode version of the Phan-Thien--Tanner model is also discussed. Thus, this work provides a complete analytical description of the rheology of the affine linear Phan-Thien--Tanner fluid in start-up, cessation, and steady regimes of shear and extensional flows.
