Rheological Characteristics of Shear Banding Flow of Complex Fluids in an Inhomogeneous Shear Field

Abstract

The nominal shear stress versus shear rate curve of the shear banding flow in non-Newtonian complex fluids was investigated for the planer rotating disc and plate geometry of the rheometer. By postulating two discrete values of the viscosity that depends on the local stress, an analytically tractable calculation could be performed and two stress-shear rate curves were obtained depending on the type of the shear banding. By use of this geometry we can specify the initial location (the rim of the disc) of the beginning of the non-Newtonian shear flow without ambiguity. In this way we can eliminate the effect of unexpected fluctuations of shear flow that could occur in homogeneous or almost homogeneous shear rate geometries. The nominal shear stress versus shear rate curve possesses the maximum and minimum values in the case of vorticity banding for shear thinning flow, while the curve becomes a monotonous increasing function for shear thickening flow. In the case of gradient banding, a wedge shaped cross section of the banding pattern was expected only for shear thinning flow and the shear rate stress curve becomes a monotonous increasing function.