Lattice-gas simulations of minority-phase domain growth in binary immiscible and ternary amphiphilic fluids

Abstract

We investigate the growth kinetics of binary immiscible fluids and emulsions in two dimensions using a hydrodynamic lattice-gas model. We perform off-critical quenches in the binary fluid case and find that the domain size within the minority phase grows algebraically with time in accordance with theoretical predictions. In the late-time regime we find a growth exponent $n=0.45\ifmmode\pm\else\textpm\fi{}0.02$ over a wide range of concentrations, in good agreement with other simulations. In the early-time regime we find no universal growth exponent but a strong dependence on the concentration of the minority phase. In the ternary amphiphilic fluid case the kinetics of self-assembly of the droplet phase are studied. At low surfactant concentrations, we find that, after an early algebraic growth, a nucleation regime dominates the late-time kinetics, which is enhanced by an increasing concentration of surfactant. With a further increase in the concentration of surfactant, we see a crossover to logarithmically slow growth, and finally saturation of the oil droplets, which we fit phenomenologically by a stretched-exponential function. Finally, the transition between the droplet and the sponge phase is studied.