On Viscoelastic Flows Through Abrupt Contractions

We show that the quantitative discrepancy between the experimental observation and the theoretical calculation of the vortex growth in viscoelastic flow through abrupt contractions is mainly due to a misunderstanding in the definition of the Weissenberg number. The experimentalists use a relaxation time specified by the shear rate at the wall in the downstream tube while the theoreticians use the low shear rate relaxation time, which is a constant for the fluids used in the experimental programme. We compare two definitions of the Weissenberg number and use them for the analysis of earlier experimental observations and for the theoretical analysis of the flow of a White-Metzner fluid through a 4 : 1 abrupt contraction