Spinodal Decomposition in the Cahn-Hilliard Model

Part of my research has been focused on mathematical models for phase separation in binary alloys, in particular on the phenomenon of spinodal decomposition. Below you can see some movies of simulated phase separation in the Cahn-Hilliard model in two space dimensions, for a variety of values of the total mass $\mu$. Each image links to its movie (MP4 format, about 30 seconds, no sound).

Every simulation starts with an almost homogeneous mixture, which appears as a uniformly colored square. Within a short time, a fine-grained pattern of the two phases emerges, shown in black and light orange, and then slowly coarsens. For $\mu = 0.1$ the two phases form an intertwined, labyrinth-like pattern. As $\mu$ increases, the black phase breaks up into more and more isolated pieces, and for $\mu = 0.6$ it consists of round droplets in a light orange background, which grow larger and fewer over time.