Maxwell's area rule and lever rule is the proposed modification of van der Waals in critical region. There are two phases corresponding to liquid and gas in the same pressure and the proportions of the phases vary so that the volume varies.
The lever rule used for metal allows allows to explain the mixture but requires that there are two "elements" involved. What the second "element" is in the case of liquid-gas system is poorly understood. TGD suggests the identification of the second "element" as magnetic flux tubes connecting the molecules. Their number per molecule varies and above critical number a phase transition to liquid phase would take place.
Second old problem relates to the numerous anomalies of water (see the web pages of Martin Chaplin). I have discussed these anomalies from TGD viewpoint in (see this). The most well-known anomalies relate to the behavior near freezing point. Below 4 degrees Celsius water expands rather than contracts as temperature is lowered. Also in the freezing an expansion takes place.
A general TGD based explanation for the anomalies of water would be the presence of also dark phases with non-standard value of Planck constant heff/h=n (see this). Combining this idea with the above proposal this would mean that flux tubes associated with hydrogen bonds can have also non-standard value of Planck constant in which case the flux tube length scales like n. The reduction of n would shorten long flexible flux tubes to short and rigid ones. This reduce the motility of molecules and also force them nearer to each other. This would create empty volume and lead to an increase of volume per molecule as temperature is lowered.
Quite generally, the energy for particles with non-standard value of Planck constant is higher than for ordinary ones (see this). In freezing all dark flux tubes would transform to ordinary ones and the surplus energy would be liberated so that the latent heat should be anomalously high for all molecules forming hydrogen bonds. Indeed, for both water and NH3 having hydrogen bonds the latent heat is anomalously high. Hydrogen bonding is possible if molecules have atoms with lone electron pairs (electrons are not assignable to valence bonds). Lone electron pairs could form Cooper pairs at flux tube pairs assignable to hydrogen bonds and carrying the dark proton. Therefore also high Tc superconductivity could be possible.
See the article Maxwell's lever rule and expansion of water in freezing: two poorly understood phenomena or the chapter Quantum Criticality and Dark Matter of "Hyper-finite factors, p-adic length scale hypothesis, and dark matter hierarchy".
For a summary of earlier postings see Latest progress in TGD.