Phase separation in two-dimensional binary fluids

Various domain-growth mechanisms in phase-separating binary fluids are discussed. A tube hydrodynamic instability for concentrated mixtures is studied through a linear stability analysis. A quantitative discussion of the three-dimensional linear growth law is given. For two-dimensional concentrated mixtures we argue that domains grow in time with a diffusive growth law $t^{1/2}$. No crossover to a linear growth law is expected, in contrast to d=3. This is in apparent agreement with a molecular-dynamics simulation of a d=2 pure fluid. For two-dimensional dilute mixtures we argue that a $t^{1/2}$ diffusive behavior crosses over to a $t^{1/3}$ Lifshitz-Slyozov growth in the latter stages of phase separation.