Some qualitative and quantitative features of die swell

Upper and lower bounds for the die swell ratio are derived for all simple fluids in the presence of surface tension and under the assumptions that the flow remains viscometric up to a finite distance from the exit and that bounds on the shear stress distribution in this length exist. Both circular and plane jets are considered and the bounds so derived depend on the normal stress on the wall in the viscometric region. For Newtonian and power law fluids, this stress can be determined, a priori, from existing theories. However, for viscoelastic liquids, it is an open question at present.