The effect of surfactants on the dynamics of phase separation

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Abstract
The dynamics of phase separation in binary systems containing surfactants is investigated by means of a time-dependent Ginzburg-Landau model. The Langevin equations for two scalar fields are solved numerically in two spatial dimensions. One of these fields is the order parameter representing the local difference in the concentrations of the two phase-separating components and the second is the local surfactant concentration. Different conservation laws of the fields, which represent different models for the dynamics of phase separation, are investigated. In all models, the average domain size for intermediate to late times is characterized by anomalously slow dynamics caused by the accumulation of surfactants at the interfaces and by the concomitant decrease in the driving force. Although all models exhibit similar slow growth, the domain structure is found to depend strongly on the nature of the conservation law. Indeed, the structure factor exhibits a peak at k>0 when the order parameter is conserved, whereas the peak is found to lie at k=0 if the order parameter is not conserved. Finally, dynamical scaling in both real- and Fourier-space correlation functions for the order parameter is found during the intermediate time regime.