The effect of crystallinity on cell growth in semi-crystalline microcellular foams by solid-state process: modeling and numerical simulation

This study establishes a model and simulation scheme to describe the effect of crystallinity as one of the most effective parameters on cell growth phenomena in a solid batch foaming process. The governing model of cell growth dynamics, based on the well-known 'Cell model', is attained in details. To include the effect of crystallinity in the model, the properties of the polymer/gas mixtures (i.e. solubility, diffusivity, surface tension and viscosity) are estimated by modifying relations to consider the effect of crystallinity. A finite element-finite difference (FEFD) method is employed to solve the highly nonlinear and coupled equations of cell growth dynamics. The proposed simulation is able to evaluate all properties of the system at the given process condition and uses them to calculate the cell size, pressure and gas concentration gradient with time. A high-density polyethylene/nitrogen (HDPE/N₂) system is used herein as a case study. Comparing the simulation results with the others works and experimental results verify the accuracy of the simulation scheme. The cell growth is a complicated combination of several phenomena. This study attempted to reach a better understanding of cell growth trend, driving and retarding forces and the effect of crystallinity on them. (paper)