Ripening Kinetics of Bubbles: A Molecular Dynamics Study
  The ripening kinetics of bubbles is studied by performing molecular dynamics simulations. From the time evolution of a system, the growth rates of individual bubbles are determined. At low temperatures, the system exhibits a $t^{1/2}$ law and the growth rate is well described by classical Lifshitz-Slyozov-Wagner (LSW) theory for the reaction-limited case. This is direct evidence that the bubble coarsening at low temperatures is reaction-limited. At high temperatures, although the system exhibits a $t^{1/3}$ law, which suggests that it is diffusion-limited, the accuracy of the growth rate is insufficient to determine whether the form is consistent with the prediction of LSW theory for the diffusion-limited case. The gas volume fraction dependence of the coarsening behavior is also studied. Although the behavior of the system at low temperatures has little sensitivity to the gas volume fraction up to 10%, that at high temperatures deviates from the prediction of LSW theory for the diffusion-limited case as the gas volume fraction increases. These results show that the mean-field-like treatment is valid for a reaction-limited system even with a finite volume fraction, while it becomes inappropriate for a diffusion-limited system since classical LSW theory for the diffusion-limited case is valid at the dilute limit. 
Hiroshi Watanabe, Hajime Inaoka, Nobuyasu Ito
cond-mat.stat-mech