Divergent flow in contractions

This study reports the results of a systematic numerical investigation, using the upper-convected Maxwell (UCM) model, of viscoelastic flow through 'smooth' planar contractions of various contraction ratios with particular emphasis placed on the 'divergent flow' regime. It is shown that both inertia and/or shear-thinning are not required for divergent flow to be predicted in contrast to the existing results in the literature where inertia has always been present when the phenomenon has been observed. Guided by the numerical results a simple explanation is presented for the occurrence of divergent flow and the conditions under which it arises. In addition, above a critical Deborah number, the flow becomes unsteady and we use an analysis based on the scaling laws of McKinley et al. [G.H. McKinley, P. Pakdel, A. Oztekin, Rheological and geometric scaling of purely elastic flow instabilities, J. Non-Newtonian Fluid Mech. 67 (1996) 19-47] for purely elastic instabilities to show that the square of this critical Deborah number varies linearly with contraction ratio in excellent agreement with the numerical results obtained in this study.