Asymptotics of slow flow of very small exponent power-law shear-thinning fluids in a wedge

Abstract

The incompressible slow viscous flow of a power-law shear-thinning fluid in a wedge-shaped region is considered in the specific instance where the stress is a very small power of the strain rate. Asymptotic analysis is used to determine the structure of similarity solutions. The flow is shown to possess an outer region with boundary layers at the walls. The boundary layers have an intricate structure consisting of a transition layer 0 (ɛ) adjoining an inner layer O (ɛlnɛ), which further adjoins an inner-inner layer 0 (ɛ) next to the wall. Explicit solutions are found in all the regions and the existence of ‘dead zones’ in the flow is discussed.