Critical lines for an unequal size of molecules in a binary gas-liquid mixture around the van Laar point using the combination of the Tompa model and the van der Waals equation.

We combine the modified Tompa model with the van der Waals equation to study critical lines for an unequal size of molecules in a binary gas-liquid mixture around the van Laar point. The van Laar point is coined by Meijer and it is the only point at which the mathematical double point curve is stable. It is the intersection of the tricritical point and the double critical end point. We calculate the critical lines as a function of χ(1) and χ(2), the density of type I molecules and the density of type II molecules for various values of the system parameters; hence the global phase diagrams are presented and discussed in the density-density plane. We also investigate the connectivity of critical lines at the van Laar point and its vicinity and discuss these connections according to the Scott and van Konynenburg classifications. It is also found that the critical lines and phase behavior are extremely sensitive to small modifications in the system parameters.