  In this study, the concept of rheo-optics is applied that explores the flow
birefringence caused by stress components along the optical axis of the camera
since it is often overlooked in the traditional theories of photoelastic flow
measurement. A novel aspect of this research is that it involved conducting
polarization measurements on simple shear flows, specifically from a
perspective in which a shear-velocity gradient exists along the camera's
optical axis. A parallel-plate-type rheometer and a polarization camera are
employed for these systematic measurements. The experimental findings for
dilute aqueous cellulose nanocrystal suspensions demonstrates that the flow
birefringence can be expressed as a power law based on the power of the second
invariant of the deformation-rate tensor. This suggests that flow birefringence
can be universally characterized by the coordinate-independent invariants and a
pre-factor determined by the direction of polarization measurement. By
adjusting the nonlinear term in the stress-optic law, its applicability could
be expanded to include three-dimensional fluid stress fields in which the
stress is distributed along the camera's optical axis.
