On extensibility effects in the cross-slot flow bifurcation

Viscoelastic flow in a cross-slot geometry are known to give rise to purely-elastic flow instabilities even under inertia-less flow conditions. Here, the flow of the finite extensibility FENE-CR model in a two-dimensional plana cross-slot configuration is studied numerically, using a finite-volume method, with a view to quantifying the influences of the level of extensibility (L-2), concentration parameter (beta) and sharpness of corners (R), on the occurrence of a bifurcated flow pattern. The results show the phenomena to be largely controlled by the elongational properties of the constitutive model, with the critical Deborah number for bifurcation tending to be reduced as extensibility increases, and the sharpness or otherwise of the corners to have only a marginal influence on the triggering mechanism leading to the pitchfork bifurcation, which seems essentially to be restricted to the central, stagnation-point region.