Pattern formation arising from condensation of a homogeneous gas into a binary, phase-separating liquid

We examine the nucleated growth of a binary, immiscible liquid drop within a homogeneous gas. The system couples the growth of the liquid drop with the phase separation of the immiscible components and, thus, can potentially reveal novel pattern formation. To carry out this study, we first characterize the thermodynamic properties of the system in terms of an appropriate Ginzburg-Landau free energy density. By minimizing this free energy, we construct the equilibrium phase diagram for the system. We then use a lattice Boltzmann algorithm to solve the hydrodynamic equations describing the dynamical evolution of the fluid. We observe intriguing tentaclelike structures within the nucleation and growth regime and explore how the formation of these structures depends on the thermodynamic and transport properties of the system. We give scaling laws describing domain growth in both the diffusion- and flow-limited regimes. The results highlight the novel physics that can emerge when there is interplay between the ordering of a density and a concentration field.