Elongational Effects of Die Flows: Pressure Distribution and Shape Prediction

There are many industrial applications in which shear and extensional behaviors of the material both play a role. This is true, for example, for flows in converging channels or flows in abrupt contractions typical of cable coating, fiber spinning or indeed flows in many plastics and rubber extrusion dies. Viscoelastic flow simulation has made it possible to predict these effects, at least qualitatively. Numerical simulations using a 3-mode PTT model reported here show a good quantitative agreement with experimentally measured pressure drops over a range of flow rates for both a short and a long conical capillary die. While this approach is physically meaningful, convergence at high Weissenberg number remains a challenge for the scientific community. This fact can sometimes justify the call for simpler, qualitative engineering approximations. By adding in the flow equations the dependence of the viscosity function on the third invariant of the rate of deformation tensor, it becomes possible to consider some effects of extensional viscosity in axisymmetric and 3D flows. We observe an increase in the pressure drop and the onset of recirculation patterns. We present numerical simulations of flow in a converging cone capillary and compare the results with available experimental data. We include simulation results for 3D die swell which show the influence of this extensional effect.