Dynamics of Ostwald ripening in the presence of surfactants

We show that the effect of surfactants on Ostwald ripening can be reduced to the problem of Ostwald ripening with a time-dependent surface tenison. Since the latter can be mapped onto a constant-surface-tension case with a nonlinear time transformation, we can systematically study the effect of surfactants without much difficulty. As a result, we find that the scaled distribution function of droplet size remains the same, but the average domain size no longer obeys the power-law growth ${\mathit{t}}^{1/3}$. Furthermore, we show that the average domain size and the total number of droplets saturate at very late times. The former is inversely proportional to the surfactant density at the interfaces, while the latter is proportional to the square (cube) of the surfactant density at the interfaces in two dimensions (three dimensions). We also find that different growths for different surfactant densities at the interface can be written in a crossover scaling form. These results qualitatively confirm the recent results of Laradji et al. [J. Phys. A 44, L629 (1991)].