Viscoelastic flow transitions in abrupt planar contractions
  We present experimental evidence of global viscoelastic flow transitions in 2:1, 8:1 and 32:1 planar contractions under inertia-less conditions. Light sheet visualization and laser Doppler velocimetry techniques are used to probe spatial structure and time scales associated with the onset of these instabilities. The results are reported in terms of critical Weissenberg numbers characterizing the fluid flow rates. For a given contraction ratio and polymer fluid, a two-dimensional, steady flow with converging streamlines transitions to a two-dimensional pattern with diverging streamlines beyond a critical Weissenberg number. At even higher Weissenberg numbers, spatial transition to three-dimensional flow is observed. A relationship between the upstream Weissenberg number for the onset of this spatial instability and the contraction ratio is derived. For contraction ratios substantially greater than unity, we observe that further increase in the flow rate results in a second temporal transition to a three-dimensional, time-dependent flow. This complex flow arises due to a combination of the effects of stress-curvature interaction and three dimensional perturbations induced by the walls bounding the neutral direction. Comparison with studies on other geometries indicates that boundary shapes deeply influence the sequence and nature of flow transitions. 
Lars Geneiser, Arvind Gopinath, Robert Armstrong and Robert Brown
cond-mat.soft physics.flu-dyn