Shear banding and secondary flow in viscoelastic fluids between a cone and plate
This work examines the effects of shear banding on secondary flow of elastic fluid between a cone and a plate. It was motivated by NMR microscopy images depicting shear banding of a surfactant solution in a cone-and-plate rheometer. More precisely, the secondary flow is determined in the cone-and-plate geometry assuming that the rheology in each band is described by Oldroyd-B constitutive equations with different elasticity and viscosity coefficients. Flows with two and three bands are considered. The mathematical approach is to rescale the equations and apply regular perturbation theory assuming that the cone angle is small. In the two-band case it is found that, as the elasticity of the lower band increases relative to the upper, the secondary flow weakens and reverses direction. With respect to viscosity, the secondary flow tends to weaken and become more localized in the less viscous band. For the three-band case it seems that the strength of the secondary flow is controlled by the average elasticity of the bands. These results are then analyzed by the authors particularly within the context of recent studies on stress selection in shear-banding fluids. Comments are also made on possible effects of replacing the infinite cone-and-plate system by a finite system with a free surface. This is a well-written paper with seemingly interesting results, which must now be validated by experiments.
scientific article; zbMATH DE number 1556247