Diffusion-Driven Phase Separation of Deeply Quenched Mixtures

In this work, we study the phase separation of deeply quenched mixtures in which the diffusion coefficient depends on the local composition field. In one dimension (1D), the system evolves until it reaches a spatially periodic steady state, with a period that, for instant quenching, coincides with the wavelength of the mode of maximum growth of the linear stability analysis. Similar results are obtained also when the temperature of the system is the solution of the heat equation, but in this case the period of the periodic steady-state solution increases as the heat diffusivity decreases. In 2D the concentration profile, after reaching a periodic configuration similar to the 1D steady state, continues to evolve, forming single-phase domains separated by sharp interfaces, which then thicken as the system tries to minimize its interfacial area. When the quench takes place across, or near, the critical point, the drops merge to form filaments which later coarsen and grow. However, when the quench takes place far from the critical point and near the metastable region of the phase diagram, the length of these filaments decreases as the system becomes a collection of nucleating drops. The composition field within and without these microdomains appears to be nonuniform and time-dependent even after the formation of sharp interfaces, thereby contradicting the commonly accepted assumption of local equilibrium at the late stage of the phase separation process. These results do not depend on the amount and the form of the random noise, while they are strongly influenced by the conditions of the system at the boundaries, as the morphology of phase separation becomes anisotropic and acquires a preferential direction when these conditions are not uniform