Phase separation

[1] The most common type of phase separation is between two immiscible liquids, such as oil and water.

A common form of spontaneous phase separation is termed spinodal decomposition; it is described by the Cahn–Hilliard equation.

In between the binodal and the spinodal, mixtures may be metastable: staying mixed (or unmixed) absent some large disturbance.

The region beyond the spinodal curve is absolutely unstable, and (if starting from a mixed state) will spontaneously phase-separate.

In one case, the enthalpy of mixing is positive, and the temperature is low: the increase in entropy is insufficient to lower the free energy.

In another, considerably more rare case, the entropy of mixing is "unfavorable", that is to say, it is negative.

In this case, even if the change in enthalpy is negative, phase separation will occur unless the temperature is low enough.

It is this second case which gives rise to the idea of the lower critical solution temperature.

A mixture of two helium isotopes (helium-3 and helium-4) in a certain range of temperatures and concentrations separates into parts.

[5] It has been shown experimentally in a two-component ultracold Fermi gas case.