Three-Dimensional Stress-Measurement Using Flow Birefringence: Revisiting the Stress-Optic Law*

We have developed a novel three-dimensional stress-measurement system. This study systematically investigates the flow birefringence of cellulose nanocrystal (CNC) suspensions to clarify the importance of the stress component along the camera's optical axis in the stress-optic law (SOL). SOL describes the relationship between birefringence, the retardation of transmitted polarized light, and the stress field. Over 100 datasets on the retardation of CNC suspensions (concentrations of 0.1, 0.3, 0.5, and 1.0 wt%) in a laminar flow within a rectangular channel (aspect ratios of 0.1, 1, and 3) were systematically obtained. The measured retardation data were compared with predictions from the conventional SOL excluding the stress component along the camera's optical axis and from the SOL including these components as second-order terms (2nd-order SOL). The results show that the 2nd-order SOL agrees significantly better 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, matching the experimental data. These 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.