Influence of channel size on velocity profiles of shear banding fluids in pressure driven flow*

We investigate the effect of channel dimensions on the velocity profiles of shear banding wormlike micelle solutions in pressure driven microcapillary flow.  Velocity profiles are measured using holographic 3D particle tracking velocimetry on the fluids seeded with microparticles. The velocity profiles at different volumetric flow rates are compared to expected velocity profiles determined from rotational rheometry.  Capillary rheology measurements are performed simultaneously via measurements of flow rate and pressure drop across the capillary. Results from the capillary rheology measurements yield viscosity values consistent with rotational rheometry. Although, we observe deviation between the measured velocity profile and that expected from the global rheology measurements. We attribute the deviation to molecular diffusion, which produces a finite interfacial width between the two shear bands and leads to a rapid decrease in shear rate near the wall. We compare our velocity profile results to theoretical models that include a diffusive terms in the stress balance, which becomes relevant at small channel sizes.