Corner flow of a suspension of rigid rods

Stress singularities in the neighbourhood of sharp corners can be a source of severe problems in the numerical simulation of non-Newtonian flows leading to loss of convergence with grid refinement (G.G. Lipscombe, R. Kennings and M.M. Denn, J. Non-Newtonian Fluid Mech., 24 (1987) 85 [1]). For Newtonian flows the nature of this singularity is given by the analysis of Dean and Montagnon (W.R. Dean and P.E. Montagnon, Phil. Trans. R. Soc. London, Ser. A., 308 (1949) 199 [2]) in terms of similarity solutions. In this paper we extend this similarity analysis to a suspension of rigid rods. In the limit of nearly full extension the FENE constitutive model has the same behaviour as such a suspension. Our analysis predicts the possibility of lip vortices but their behaviour is somewhat inconsistent with those observed experimentally.