Non-Newtonian effects on flow birefringence under the second-order stress-optic law in Hele-Shaw flow

Determine how non-Newtonian (shear-thinning) constitutive behavior influences the relationship between stress tensor components and measured phase retardation in flow birefringence for Hele-Shaw geometries when interpreted using the second-order stress-optic law, which accounts for stresses along the optical axis.

Background

Flow birefringence links optical anisotropy to fluid stresses and is often analyzed via the stress-optic law (SOL). The conventional, first-order SOL neglects stresses along the optical axis, which become dominant in thin-gap flows like Hele-Shaw cells, motivating the use of a second-order SOL that includes these components.

Prior studies applying the SOL to flow birefringence have largely assumed Newtonian fluids. In Hele-Shaw configurations, detection sensitivity constraints encourage using higher concentrations of birefringent suspensions, which in turn enhance shear-thinning. This raises the unresolved issue of how non-Newtonian rheology affects the interpretation of flow birefringence when the second-order SOL is required to capture optical-axis stresses.