Computer Simulation of Bubble-Growth Phenomena in Foaming

Abstract

This paper discusses the research conducted to achieve an accurate bubble-growth model and simulation scheme to describe precisely the bubble-growth phenomena that occur in polymeric foaming. Using the accurately measured thermophysical and rheological properties of polymer/gas mixtures (i.e., the solubility, the diffusivity, the surface tension, the viscosity, and the relaxation time) as the inputs for computer simulation, the growth profiles for bubbles nucleated at different times were predicted and carefully compared to experimentally observed data obtained from batch foaming simulation with online visualization. A polystyrene/carbon dioxide (PS/CO2) system is used herein as a case example. It was verified that the cell-growth model is capable of thoroughly depicting the growth behaviors of bubble nuclei nucleated under varying processing conditions without using any fitting parameter. These results indicate that the established model accounts for most of the physics behind the bubble-growth phenomena. Furthermore, the effects of the aforementioned thermophysical and rheological parameters on the cell-growth dynamics were demonstrated by a series of sensitivity studies.

Numerical simulation of polypropylene foaming process assisted by carbon dioxide: Bubble growth dynamics and stability

“…5a). This is in agreement with reports from other works (Leung et al, 2006;Otsuki and Kanai, 2005). On the other hand, a longer relaxation time indicates a larger elasticity of the material.…”

“…The simulation of bubble growth and stability is based on the well-known cell model (Arefmanesh and Advani, 1991;Leung et al, 2006;Shafi et al, 1996;Venerus et al, 1998;Venerus, 2001;Venerus, 2003;Tuladhar and Mackley, 2004). The cell model approximates the situation in polymer foaming by considering the growth of a single bubble with a shell of polymer-gas solution.…”

Pressure drop threshold in the foaming of low-density polyethylene, polystyrene, and polypropylene using CO2 and N2 as foaming agents

“…Most models of bubble nucleation have been based on the classical nucleation equation established by Blander and Katz [10,11] wherein the bubble nucleation rate per unit volume is related to the minimum work required to form stable bubbles. On the other hand, most models of bubble growth have been based on three fundamental equations: the momentum balance across the bubble interface, the diffusion of dissolved gas molecules in a polymer, and the overall mass balance of the gas in bubbles and the polymer [12,13]. Bubble growth can be quantitatively predicted using accurate properties of the polymer/gas mixtures such as solubility, diffusion coefficient, viscosity, and interfacial tension.…”

An arbitrary Lagrangian–Eulerian method for simulating bubble growth in polymer foaming

“…Numerous 1D models have been developed, which have incorporated non-Newtonian rheology [8,[22][23][24], temperature effects [25] and plasticization [26]. In comparison, 2D computations are scarce.…”