Steady flow simulation of a polymer‐diluent solution through an abrupt axisymmetric contraction using internally consistent rheological scaling

Abstract

In this work, a new methodology is developed that describes the viscoelastic scaling of a polymerphysical foaming agent (PFA) solution in a detailed and internally consistent manner. The approach is new in that while previous researchers have largely focused on scaling down experimentally obtained high pressure polymer-PFA solution viscosity data onto a master curve for the viscosity of the undiluted polymer melt at a reference temperature and atmospheric pressure, we have generated the shear viscosity data required for our simulations by systematically scaling up the viscosity values obtained from measurements on a pure polymer melt to the desired temperature, pressure, and concentration values characterizing the flow. Simulations have been run for the flow of a polymer-PFA solution through an extrusion foaming die with an abrupt axisymmetric contraction and good qualitative agreement is obtained with experimental pressure drop measurements obtained previously in our laboratory. The pressure drop rates and temperature rise rates have been estimated at the surface of incipient nucleation. Because of the short residence times in the die for the microcellular foaming process, approximating the flow through the die as a single phase flow in our simulations still gives useful insights into the dynamics of the flow.

New challenges in polymer foaming: A review of extrusion processes assisted by supercritical carbon dioxide

“…At the same flow rate, a higher pressure led to a higher pressure drop rate, which plays an important role in determining the cell size and the cell density. A fairly good agreement is obtained between simulated and experimental pressures [74]. The pressure drop decreased with the increase of CO 2 concentration [44], die temperature [29] or inlet melt temperature [74].…”

“…The pressure contours were also obtained. They were found to become flat after a small entrance length in the die, implying that variation in pressure in the radial direction is negligible for all processing conditions studied [74]. A significant temperature increase was observed along and across the die section due to viscous heat dissipation near the wall of the capillary die.…”

“…Moreover, the pressure profile along the capillary was highly nonlinear, the decrease rate being higher at the die entrance [74]. An important implication is that the saturation surface is shifted backwards the die entrance in comparison with a linear profile.…”

“…A significant temperature increase was observed along and across the die section due to viscous heat dissipation near the wall of the capillary die. However, the heat generated near the wall did not have significant time to travel to the centre of the die [74]. The velocity profile assumed a flattened shape characteristic of shear-thinning polymer melts.…”

“…In a first step, the pseudoplastic behavior of the mixture was taken into account by the model of Carreau for each CO 2 concentration [29,44]. Later, the modelling was improved by using an internally consistent viscoelastic scaling approach [74]. In this approach, the temperature, pressure and CO 2 concentration corrections on viscosity were accounted for independently through a combined shift factor, which is the product of the three individual shift factors.…”