Dynamic phase separation: from coarsening to turbulence via structure formation

We investigate some new two-dimensional evolution models belonging to the class of convective Cahn-Hilliard models: (i) a local model with a scalar order parameter, (ii) a nonlocal model with a scalar order parameter, and (iii) a model with a vector order parameter. These models are applicable to phase-separating system where concentration gradients cause hydrodynamic motion due to buoyancy or Marangoni effect. The numerical study of the models shows transition from coarsening, typical of Cahn-Hilliard systems, to spatiotemporally irregular behavior (turbulence), typical of the Kuramoto-Sivashinsky equation, which is obtained in the limit of very strong driving. The transition occurs not in a straightforward way, but through the formation of spatial patterns that emerge for intermediate values of the driving intensity. As in driven one-dimensional models studied before, the mere presence of the driving force, however small, breaks the symmetry between the two separating phases, as well as increases the coarsening rate. With increasing driving, coarsening stops. The dynamics is generally irregular at strong driving, but exhibits specific structural features.