On local solutions to non-Newtonian slow viscous flows

The eigenfunction expansion method is used to obtain local solutions to some non-Newtonian slow viscous flows. The forms of viscosity variation amenable to such analysis are restricted but do include power-law fluids. Power-law flow near a sharp corner between plane boundaries is analysed and results are obtained for the critical corner angle for eddy formation. Flows near a 90° corner with either a moving boundary or a finite flow rate at the corner are also considered. The “stick-slip” behaviour of a power-law fluid at a plane solid boundary is shown to obey a simple law.