Lattice-gas simulations of domain growth, saturation, and self-assembly in immiscible fluids and microemulsions

We investigate the growth kinetics of both binary fluid and ternary microemulsion systems in two dimensions using a recently introduced hydrodynamic lattice-gas automaton model of microemulsions. We find that the presence of amphiphile in our simulations reduces the usual oil-water interfacial tension in accord with experiment and consequently affects the nonequilibrium growth of the oil and water domains. As the density of surfactant is increased we observe a crossover from the usual two-dimensional binary fluid scaling laws to a growth that is slow, and we find that, up to a point, this slow growth can be characterized by a logarithmic time scale. With sufficient surfactant in the system we observe that the domains cease to grow beyond a certain point; we find that this final characteristic domain size is inversely proportional to the interfacial surfactant concentration in the system and that a stretch-exponential functional form accurately describes the data across the whole time scale of the simulations in these cases.