The study of phase equilibria is historically one of the most important sources of information about the nature of intermolecular forces in non-electrolyte liquids and their mixtures. Many of the main features of vapour-liquid and liquid-liquid phase behaviour were already well characterized experimentally during the early part of this century, but the theoretical explanation of phase equilibria for a wide variety of substances and over a large range of pressures and temperatures has lagged far behind. This paper presents theoretical studies of phase equilibria in binary mixtures obeying the van der Waals equation, especially liquid-liquid equilibria that can occur at high pressures. The variety of fluid phase behaviour that occurs in binary mixtures can be qualitatively discussed in terms of the changes in thermodynamic properties near critical points. Upper critical solution temperatures (UCSTs) occur when a heterogeneous (two-phase) system becomes a homogeneous (one-phase) system when the temperature is raised. The maximum temperature along the temperature-mole fraction (
T, x
) coexistence curve for constant pressure is the UCST at this pressure. Lower critical solution temperatures (LCSTs) occur when a homogeneous system becomes a two-phase system when the temperature is increased. The LCST is at the minimum of the
T, x
coexistence curve. Thermodynamic considerations of critical points yield requirements for the curvature of the mixing functions plotted against
x
.
