Theoretical model of the pre-expansion of polystyrene foam
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In the production of expandable polystyrene (EPS) foam, it is desirable to be able to predict the density of the final product by some means other than empirical estimates. Therefore, a theoretical model was developed to predict the bulk density of EPS during a prepuffing expansion. This model was based on the assumption of an isothermal system with mass and momentum transfer processes governing the growth of a cell. Henry's law and the Flory-Hugginâ€™ equation were used in a comparative way to describe the pneuaatogen-polymer melt equilibrium. The polymer melt was assumed to follow power law behavior. The resulting system of nonlinear ordinary differential and partial differential equations was reduced to a system of nonlinear ordinary differential equations by adopting a moment (integral) method- These equations were then solved by the Gear method of IMSL computer library. Considering the shape of cells, a lattice of face-centered cubic packing was chosen, and the cells were assumed to be of equal size. Finally, the bulk density of the complex multicelled EPS beads was estimated from the density of a single cell and was compared with the experimental data from air and helium pre-expansion processes. The influence of some variables (melt viscosity, interfacial tension, diffusion coefficient, gas solubility, concentration of pneumatogen, different expanding atmospheres, and nucleation density) on the bubble growth and the bead den* sity was also discussed.