In the continuous process for manufacturing microcellular polymer foams, a physical foaming agent is dissolved homogeneously into a polymer melt in an extruder and the homogenized polymer-blowing agent solution is rapidly depressurized by passing it through a die of small cross-section to generate a foamed product with large bubble (cell) density and small bubble size. Cell densities in microcellular foams typically exceed 109 cells/cm3 and cell sizes are typically smaller than 10 µm. A proper knowledge of the rheology of the polymer – blowing agent solution is crucial in correctly predicting the values of the field variables, viz. pressure, temperature and velocity at each point in the die. The knowledge of the field variables at each point in the die combined with an appropriate equation of state allows the determination of the saturation surface as also the point of incipient nucleation in the die. Finally, choice of an appropriate bubble nucleation and bubble growth model, allows the prediction of the final foam morphology.

In this work, we adopt an internally consistent viscoelastic scaling methodology to model the shear viscosity of polystyrene – carbon dioxide solutions. The scaling methodology accounts for temperature, pressure as well as concentrations shifts of the shear viscosity of the polymer – blowing agent solution flowing through the die. CFD simulations have been carried out for mass flow rates of the polymer blowing agent mixture through the axisymmetric extrusion die corresponding to experimental flow rates used previously in our lab1. The experiments (and simulations) cover a broad temperature (140°C to 240°C) and blowing agent concentration (1.0 wt% to 8.0 wt%) range. The simulation predictions are found to agree qualitatively with the experimentally measured total pressure drops across the die length under the processing conditions studied.

Once the values of the field variables are obtained (through simulations) at each point in the die, these values, in conjunction with the Sanchez Lacombe Equation of State (SLEOS) are used to predict the location of the saturation surface in the die. Based on the local values of hydrostatic pressure and temperature in the flow field, bubble nucleation rates are calculated at the binodal using classical nucleation theory. The predicted bubble number density is compared with experimental results. Bubble growth rates corresponding to different streamlines in the die are computed using a modified Newtonian bubble growth model developed by Patel2 to include a variable solution viscosity and diffusivity. Incorporation of local field values of diffusivity and viscosity can have a significant influence on the bubble growth regime. Additionally, exploratory viscoelastic scaling and simulation results for polystyrene nanocomposites with carbon dioxide dissolved in them are presented.

References:

1. Han, X, Koelling, K.W., Tomasko, D.L. and Lee, L.J ; Continuous Microcellular Polystyrene Foam extrusion with Supercritical CO2, Polym. Eng. Sci., 42, pp 2094-2106 (2002) 2. Patel, R.D., Bubble Growth in a Viscous Newtonian Liquid, Chem. Eng. Sci., 35, pp. 2356-2358 (1980)