标题： 通过杰弗里-哈姆流测量将流动双折射分析扩展到拉伸剪切组合流 显示英文标题

标题： Extending flow birefringence analysis to combined extensional-shear flows via Jeffery-Hamel flow measurements

摘要： 本研究利用Jeffery-Hamel流动形式探讨了在拉伸-剪切复合流动中相位延迟与应变率之间的关系，该形式给出了一个解析速度解。 使用高速偏振相机测量了1.0 wt$\%$纤维素纳米晶体（CNC）悬浮液的流动双折射。 通过粒子图像测速（PIV）验证了速度场，结果显示与解析解有良好的一致性。 在以剪切或拉伸成分为主的区域，双折射行为与以往的理论和实验结果一致。 在Jeffery-Hamel流动的拉伸-剪切复合区域，双折射幅度遵循剪切和拉伸引起的贡献的平方和平方根（RSS）。 这一观察结果与从莫尔圆推导出的主要应力公式一致，在该公式中，主要应力表示为拉伸和剪切应力的平方和平方根。 这一发现为将应力-双折射分析扩展到同时存在多种变形模式的流动提供了基础。 显示英文摘要

摘要： This study investigates the relationship between phase retardation and strain rates in combined extensional-shear flows using the Jeffery-Hamel flow formalism, which yields an analytical velocity solution. Flow birefringence was measured in a 1.0 wt$\%$ cellulose nanocrystal (CNC) suspension using a high-speed polarization camera. The velocity field was validated via particle image velocimetry (PIV), which showed good agreement with the analytical solution. In regions dominated by either shear or extensional components, the birefringence behavior was consistent with prior theoretical and experimental findings. In the combined extensional-shear regions of the Jeffery-Hamel flow, the birefringence magnitude followed the root-sum-square (RSS) of the shear- and extension-induced contributions. This observation aligns with the principal stress formulation derived from Mohr's circle, in which the principal stress is expressed as the RSS of extensional and shear stresses. This finding provides a basis for extending stress-birefringence analysis to flows with coexisting deformation modes.