Mean-field theories, their weaknesses and strength

Within a historical context, an evaluation of mean-field theory is given in its application to fluids and fluid mixtures. The way mean-field equations such as the Van der Waals equation incorporate molecular attraction and repulsion implies neglect of fluctuations. This neglect of both local and long-range structure is an impediment to characterizing liquids and supercritical fluids. In particular, mean-field theory is unable to describe critical behavior properly. This was known around 1900, but has been fully corrected only recently. The simplicity of mean-field equations is also their strong point. By 1905, most complexities of binary fluid phase diagrams known from experiment had been derived from the Van der Waals equation. Efforts to improve this equation have led to pathology in the global phase diagram. Paradoxically, it appears that increased sophistication leads to undesirable features in the phase diagrams.