Role of shear thinning in the flow of polymer solutions around a sharp bend

In flows with re-entrant corners, polymeric fluids can exhibit a recirculation region along the wall upstream from the corner. In general, the formation of these vortices is controlled by both the extensional and shear rheology of the material. More importantly, these regions can only form for sufficiently elastic fluids and are often called “lip vortices”. These elastic lip vortices have been observed in the flows of complex fluids in geometries with sharp bends. In this work, we characterize the roles played by elasticity and shear thinning in the formation of the lip vortices. Simulations of the Newtonian, Bird-Carreau, and Oldroyd-B models reveal that elasticity is a necessary element. A systematic study of the White-Metzner, finitely extensible non-linear elastic (FENE-P), Giesekus and Rolie-Poly models shows that the onset and size of the elastic lip vortex is governed by a combination of both the degree of shear thinning and the critical shear rate at which the thinning begins.

(left) Contour plots of velocity magnitude for the FENE-P model showing the decrease in size of the elastic lip vortex as maximum extensibility decreases. (right) Length of the elastic vortex as a function of a modified Carreau number showing a modelindependent effect of the degree and onset of shear thinning.