Introduction of the Diffusion Stage into the Bubble Growth Model

This paper deals with the development of a numerical scheme to predict the growth of a bubble within a molten polymer. The model consists of one single bubble which expands through the decomposition of a foaming agent in a limited amount of polymer due to the steadily increasing temperature of the melt. The studied process refers to the foaming during the rotational molding. Through a pressure difference from the gas inside the bubble and the surrounding air, which can be seen as a driving force, the size of the bubble expands. The effects of viscosity and surface tension of the surrounding polymer need to be considered as resisting forces. Due to a gradient of the concentration of gas in the bubble interface a molecular diffusion takes place, which causes the bubble to shrink after the maximum size of the bubble is reached. The equations of momentum and continuity, mass balance and the diffusion-convection equation are solved numerically with the methods of finite elements or finite differences to obtain the resulting radius of the bubble. The numerically determined results are compared with experimental data. The process of the cycle is discussed with the use of different data like the gas pressure inside the bubble or the resulting number of gas molecules. Furthermore, the influence of different material properties is investigated.