Integrated photoelasticity measurements of a three-dimensional laminar flow: second-order stress terms in the stress-optic law

This study experimentally validates a stress-optic law for a three-dimensional flow using integrated photoelasticity. In this stress-optic law, the stress is related to the two photoelastic parameters — the phase retardation Δ and orientation 𝜙 — of elliptically-polarized light. Previous studies have examined the stress-optic law of three-dimensional flows, but the importance of the second-order stress terms in the three-dimensional stress-optic law, i.e., those relating to the stress component along the camera’s optical axis, have not yet been experimentally validated. In this work, we measure the retardation of a steady Newtonian fluid laminar flow (cellulose nanocrystal suspension of 0.5 wt%) in a square channel and compare it with the theoretical prediction. Remarkably, the theoretical result including the second-order stress terms shows good agreement with the experimental result for various flow rates, while the calculation without these terms results in a significant deviation from the measurements. Therefore, proper consideration of the second-order stress terms in the three-dimensional stress-optic law is crucial for integrated photoelasticity measurements of three-dimensional flow fields.