The shear-driven Rayleigh problem for generalised Newtonian fluids

• Self-similar solutions exist for any generalised Newtonian fluid.
• Finite boundary layers are possible for a restricted class of rheologies.
• Shear-thinning and thickening effects on boundary layer thickness are explored.

We consider a variant of the classical ‘Rayleigh problem’ (‘Stokes’s first problem’) in which a semi-infinite region of initially quiescent fluid is mobilised by a shear stress applied suddenly to its boundary. We show that self-similar solutions for the fluid velocity are available for any generalised Newtonian fluid, regardless of its constitutive law. We demonstrate how these solutions may be used to provide insight into some generic questions about the behaviour of unsteady, non-Newtonian boundary layers, and in particular the effect of shear thinning or thickening on the thickness of a boundary layer.