Foaming of thermoplastics is a mature technology facing new challenges. Traditionally, the "blowing agents" are clorine-based gases (e.g., chlorofluorocarbon, CFC) which deplete the ozone layer. The search for environmentally friendly replacements has driven new research into the fundamental physics of the process. With Arkema Group, Inc., our industrial partner, we are investigating the nucleation, growth and burst of bubbles using phase-field simulations. In addition, we have developed an ALE surface tracking scheme to investigate bubble-bubble and bubble-surface interaction during bubble growth. See graphics below.