  This study systematically investigates the flow birefringence of cellulose
nanocrystal (CNC) suspensions. The aim is to clarify the importance of the
stress component along the camera's optical axis in the stress-optic law (SOL),
which describes the relationship between birefringence, the retardation of
transmitted polarized light, and the stress field. More than 100 datasets
pertaining to the retardation of CNC suspensions (concentrations of 0.1, 0.3,
0.5, and 1.0 wt\%) in a laminar flow field within a rectangular channel (aspect
ratios of 0.1, 1, and 3) are systematically obtained. The measured retardation
data are compared with the predictions given by the conventional SOL excluding
the stress component along the camera's optical axis and by the SOL including
these components as second-order terms (2nd-order SOL). The results show that
the 2nd-order SOL gives a significantly better agreement with the measurements.
Based on the 2nd-order SOL, the retardation at the center of the channel, where
the effect of the stress component along the camera's optical axis is most
pronounced, is predicted to be proportional to the square of the flow rate,
which agrees with the experimental data. The results confirm the importance of
considering the stress component along the camera's optical axis in the flow
birefringence of CNC suspensions at high flow rates, even for
quasi-two-dimensional channel flow.
