Modeling of bubble growth behavior in the PS/CO2 batch foaming system using finite element method

Polymeric foams have a cellular structure composed of a polymeric matrix with gaseous cells which achieved by expansion of a blowing agent in polymer melt matrix during a foaming process. In the present study, the bubble expansion step in Polystyrene/CO2 batch foaming process was simulated and compared to the reported experimental results. A single spherical bubble surrounded by an incompressible viscoelastic fluid (upper-convected Maxwell model) was considered. To calculate concentration profile in the shell, mass diffusion equations were solved using finite element method, potential function definition and integral methods. The predicted results show that when the gas concentration profile obtained by finite element method and the concentration gradient near the bubble-shell interface was used to calculate the pressure inside the bubble, the predicted results were in good agreement with the experimental ones which there was less than 1% error at each foaming time. The effects of the thermo-physical and rheological properties on the bubble growth dynamics were also studied and It was found out that increasing the diffusivity coefficient by factor of 10 would increase the bubble size up to 1.5 times, whereas increasing the viscosity by 3 folds would only change the bubble size about 2% showing that the bubble growth step in foaming process was a mass transfer controlled process.