Aaron Naber, Chun Liu & James J. Feng
AMS Contemp. Math. Ser. Vol. 466, pp. 95-120 (2008)
Abstract - In this paper, we study the nucleation and growth of gas bubbles in a Newtonian fluid. We employ a general energetic variational formulation with a phase-field method, and compare the analytical and numerical predictions of this new formulation with those of classical models. The new approach allows the study of bubble nucleation, growth and coalescence in a unified framework, and has the capability of modeling complex situations in polymer foaming, with multiple-bubble interaction, interaction with an external flow field, complex non-Newtonian rheology and non-Fickian diffusion.