Rheo-optics of equilibrium polymer solutions: Wormlike micelles in elongational flow in a microfluidic cross-slot

The rheo-optical analysis of polymer solutions and melts is a critical tool in elucidating their molecular response to flow fields. We therefore evaluate the measurement of flow-induced birefringence (orientation) under extension in microfluidic cross-slots, whose flow kinematics was examined by microparticle image velocimetry. The effects of planar extension on the (non) linear viscoelasticity of wormlike micellar surfactant solutions (comprising either cetyltrimethylammonium bromide or cetylpyridinium chloride in aqueous sodium salicylate) were measured. The effect of wall shear was found to be negligible compared to extension. The birefringence is linear (indicating the validity of the stress-optical rule) for very small extensional Weissenberg numbers, as expected. This rule fails, however, when a sharp birefringence band appears at modest Weissenberg number (indicating the alignment of wormlike micelles along the outflow direction). Experiments that measure average birefringence may misidentify the point of failure of the stress-optical rule. These bands also scatter light and appear in transmittance images, yet with distinctive features. At higher flow rates, the birefringent band broadens after the peak retardation saturates, but the transmittance band remains narrow and eventually the flow becomes asymmetric. This asymmetric transition is elasticity-induced, and no shear banding is observed by particle velocimetry: the velocity profiles remain linear, while the flow becomes asymmetric. These phenomena are common to both fluids studied, but the stress-optical coefficient and the Weissenberg numbers at saturated birefringence differ quantitatively, possibly due to differences in micellar length and scission kinetics, as determined from linear viscoelastic measurements.