Cahn–Hilliard equation in the context of John W. Cahn

Phase separation is the creation of two distinct phases from a single homogeneous mixture. The most common type of phase separation occurs between two immiscible liquids, such as oil and water. This type of phase separation is known as liquid-liquid equilibrium. Colloids are formed by phase separation, though not all phase separations form colloids - for example, oil and water can form separated layers under gravity rather than remaining as microscopic droplets in suspension.

A common form of spontaneous phase separation is termed spinodal decomposition; Cahn–Hilliard equation describes it. Regions of a phase diagram in which phase separation occurs are called miscibility gaps. There are two boundary curves of note: the binodal coexistence curve and the spinodal curve. On one side of the binodal, mixtures are absolutely stable. In between the binodal and the spinodal, mixtures may be metastable: staying mixed (or unmixed) in the absence of some large disturbance. The region beyond the spinodal curve is absolutely unstable, and (if starting from a mixed state) will spontaneously phase-separate.

Spinodal decomposition is a mechanism by which a single thermodynamic phase spontaneously separates into two phases (without nucleation). Decomposition occurs when there is no thermodynamic barrier to phase separation. As a result, phase separation via decomposition does not require the nucleation events resulting from thermodynamic fluctuations, which normally trigger phase separation.

Spinodal decomposition is observed when mixtures of metals or polymers separate into two co-existing phases, each rich in one species and poor in the other. When the two phases emerge in approximately equal proportion (each occupying about the same volume or area), characteristic intertwined structures are formed that gradually coarsen (see animation). The dynamics of spinodal decomposition is commonly modeled using the Cahn–Hilliard equation.

Reverse diffusion refers to a situation where the transport of particles (atoms or molecules) in a medium occurs towards regions of higher concentration gradients, opposite to that observed during diffusion. This phenomenon occurs during phase separation and is described by the Cahn–Hilliard equation. Reverse diffusion also refers to when water is forced from a region of lower concentration to high. It can occur in osmosis.