Generalized Newtonian and Herschel-Bulkley yield stress fluids pressure behavior near the tip of a sharp edge in thin film flows

The Letter deals with two-dimensional symmetric and antisymmetric flows of generalized Newtonian and Herschel-Bulkley yield stress fluids close to a sharp edge which, for modeling purposes, is taken to be a geometric singularity. The pressure field is approximated using an asymptotic expansion valid in the tip neighborhood, and its dependence upon the edge angle is studied. For these special flows, the methodology used to obtain the pressure behavior does not require explicit knowledge of the viscosity dependence upon shear rate. Moreover, we prove that whenever the tip angle is such that the edge is hollow shaped, the yield stress fluid behaves solid-like in a neighborhood domain of the tip.