Unsteady flows uncover the limits of the stress-optic law

Birefringence induced in complex fluid flows, containing anisotropic microstructures, exhibits vibrant patterns, captivating people perceptually. More practically, it has garnered multidisciplinary expectations on the noninvasive characterization of stress fields in flowing materials based on the stress-optic law established for solid materials, prospecting its in situ and in vitro applications. Here, we question such a paradigm by demonstrating the failure of the law in unsteady flows through laboratory experiments. The latter originates from the relaxation of the microscopic structures, characterized by the Deborah number De, which is a dimensionless number that compares the material's relaxation time and the characteristic time of the applied deformation process. Flow birefringence turns out to represent accumulated fluid deformation only when fluids behave like solids with large De, whereas the anisotropy of the microstructures relaxes for small De, diminishing birefringence. We generalize the formulation of flow birefringence evolution by explicitly decomposing the microscopic and macroscopic contributions to it, providing a unified understanding of flow birefringence based on deep physical interpretations attained through laboratory experiments. Our findings may encourage undertaking a drastic course correction in the future development of flow birefringence as a practical tool for stress quantification based on present-day knowledge, and enlighten its potential usage.