Taylor's classical paint scraping problem provides a framework for analyzing wall-driven corner flow induced by the movement of an oblique plane with a fixed velocity U. A study of the dynamics of the inertialess limit of a Carreau fluid in such a system is presented. New perturbation results are obtained both close to, and far from, the corner. When the distance from the corner r is much larger than U Gamma, where Gamma is the relaxation time, a loss of uniformity arises in the solution near the region, where the shear rate becomes zero due to the presence of the two walls. We derive a new boundary layer equation and find two regions of widths r(-n) and r(-2), where r is the distance from the corner and n is the power-law index, where a change in behavior occurs. The shear rate is found to be proportional to the perpendicular distance from the line of zero shear. The point of zero shear moves in the layer of size r(-2). We also find that Carreau effects in the far-field are important for corner angles less than 2.2 rad.