Processing Polymer Melts under Rheo-Fluidification Flow Conditions, Part 2: Simple Flow Simulations

The flow equations for melts submitted to conditions of Rheo-Fluidification processing described in Part 1 are determined and solved numerically. The pressure flow from an extruder feed end and drag flow from the modulated rotation of the rotor, i.e., under extrusion conditions with both cross-rotational and oscillatory flow, are combined. The value of pressure, shear stress, and viscosity along the flow path of the melt (a helicoidal motion around a divergent conic surface), for a given throughput and temperature, as the melt is moved through an annular gap of constant thickness are calculated. The simulation is restricted to the simpler case of low throughput where elongational flow can be assumed to be negligible and shear dominates the viscosity expression. The classic lubrication approximation hypothesis applied to a power law fluid is used. This assumption appears justified because of the geometry of the die, which consists of a thin annulus of 2 mm extended over a die length of 570 mm (see Part 1). The viscosity is expressed as a function of strain rate, which is calculated from the contribution of pressure flow, rotational flow, and superposed oscillation. The combined shear rate is calculated assuming a vectorial combination of the individual shear rates, following Cogswell who verified this hypothesis, and according to our own validation of this assumption on the same polymer, using a Couette without vibration.