A. Vanpelt et al., MATHEMATICAL DOUBLE POINTS ACCORDING TO THE SIMPLIFIED-PERTURBED-HARD-CHAIN THEORY, The Journal of chemical physics, 99(12), 1993, pp. 9920-9929
Critical curves of a binary fluid mixture are usually plotted as a fun
ction of pressure and temperature (p, T projection), temperature and c
omposition (T, x projection) or as a function of the reduced densities
of the two components (y1, y2 projection). In these three ways of rep
resentation, we will show the structure of the critical curves around
a mathematical double point. Moreover, it will be shown that mathemati
cal double points can conveniently be divided into two groups: the (me
ta)stable and unstable mathematical double points. To date, the (meta)
stable mathematical double points have not been investigated with a pr
essure-explicit equation of state. In this paper, it will be shown how
the two types of mathematical double points can be calculated. We wil
l digress on the thermodynamic conditions to be obeyed for the calcula
tion of the two types of mathematical double points.