Fig. 4: Mechanism of flow birefringence.
From: Unsteady flows uncover the limits of the stress-optic law
a Illustrative interpretation of temporal evolution of χ, Δn, and \(\dot{\gamma }\) over one oscillatory period To shown in Fig. 2. The evolution of the IE's state over half a cycle is schematized at the top. The oscillatory forcing results in four different phases in one cycle, identified by rotation χ and deformation Δn of the IE. Schematic of the relationship between the macroscopic deformation (parallelograms) and the IE (ellipsoids) for b large De and c small De. Once an oscillatory forcing with large De > 102 is applied, the IE does not recover its original isotropic shape because of negligible relaxation during the one oscillation cycle, i.e., \(\Delta {n}_{\min } > 0\), and the IE immediately reflects macroscopic deformation irrespective of the amplitude of the oscillatory forcing. On the other hand, the IE does not represent macroscopic deformation due to significant relaxation for small De ≤ 102. Steady forcing represents the limiting case as De → 0, where the birefringence Δn∞ emerges due to the equilibrium established between macroscopic forcing and microscopic relaxation in the limit of infinite time.
