Modelling Nucleation and Cell Size During the Continuous Process of Extrusion Assisted by Supercritical CO 2

Polymer foaming with the process of extrusion assisted by supercritical CO2 is based on the injection of a supercritical fluid, in our case carbon dioxide, in a polymer, which has been previously melted in the barrel of an extruder. Upon depressurisation that happens in the die, nucleated bubbles will appear and grow. Modelling the nucleation and growth is important to better understand and master the process. A suitable and specific mathematical formulation has been implemented to calculate the number and the size of the pores. A methodology consisting in discretizing the space, to bring back to a succession of batch models was the chosen approach and a functional algorithm has been developed. The model will be applied in the foaming process of poly-lactic acid PLA and will be compared to experimental results. INTRODUCTION The process of extrusion assisted by supercritical carbon dioxide (sc-CO2) consists in injecting the pressurised CO2 in the heated barrel of an extruder containing a molten polymer [1]. Physically, different steps occur: sorption and dissolution of gas into molten polymer at elevated pressure before the die, nucleation of bubbles in a supersaturated solution of gas in a molten matrix in the die, growth of bubbles until equilibrium and stabilization of the foam structure by lowering the temperature in and after the die [2]. Shafi et al. [3–6] have developed a model for the nucleation and the growth of the bubbles in batch mode. Only few publications relate to the modelling of extrusion foaming [7]. This is due to the fact that flow induces many changes in the nucleation mechanism and physical properties. In this work, the method of Shimoda et al. [7] will be applied. This approach consists in discretizing the space, to bring back to a succession of batch models. MATHEMATICAL FORMULATION Nucleation The nucleation rate gives information about the number of bubbles nucleated by unit of time and volume. In this work, the choice was to consider a homogeneous nucleation calculated by Equation (1): J t = C! t N! 2γ πm! exp 16πγ! 3k!T P!"!!#$ t − P!"#$%&' t !