Sudden inception of shearfree flows (also called stress growth in extension) is an extremely useful set of rheological measurement techniques for bringing out fluid nonlinearities. The previous predictions of these departures from linearity employed molecular simulation or finite difference solutions. In this work, we deepen our understanding of the physics of these departures by uncovering the exact solutions to a large and diverse framework of constitutive equations: the Oldroyd 8-constant framework. Specifically, we derive the exact analytical solutions for the first and second elongational viscosities in shearfree flow from the Oldroyd 8-constant framework including (I) uniaxial elongational flow, (II) biaxial stretching flow, and (III) planar elongational flow. We close our work with a worked example on analyzing a highly branched system.

中文翻译：

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来自 Oldroyd 8 常数框架的应力增长无剪切流

无剪切流的突然出现（也称为拉伸应力增长）是一组极其有用的流变测量技术，可用于显示流体非线性。先前对这些偏离线性的预测采用了分子模拟或有限差分解决方案。在这项工作中，我们通过揭示一个庞大而多样的本构方程框架的精确解来加深我们对这些偏离的物理学的理解：Oldroyd 8 常数框架。具体而言，我们从 Oldroyd 8 常数框架（包括（I）单轴拉伸流、（II）双轴拉伸流和（III）平面拉伸流）推导出无剪切流中第一和第二拉伸粘度的精确解析解。我们用一个分析高度分支系统的工作示例来结束我们的工作。