Phe. Meijer et al., ANALYSIS OF THE CRITICAL LINE NETWORK FOR THE VANDERWAALS-EQUATION ATTHE VAN-LAAR POINT, Journal of statistical physics, 71(1-2), 1993, pp. 299-312
The density-density plot of the critical lines of the van der Waals eq
uation at the van Laar point is analyzed through its algebraic propert
ies. It is shown that this curve is an irreducible expression of the f
ifth degree of genus one. In addition, we show the topology of the sec
ond branch, i.e., the T = 0 solution, which will interact with the fir
st branch as soon as the energy parameters are slightly different from
the van Laar values. Finally, we analyze the behavior of the van der
Waals equation near the point at which liquid-liquid separation takes
place.