Thermodynamic curvature of the binary van der Waals fluid

The thermodynamic Ricci curvature scalar $R$ has been applied in a number of contexts, mostly for systems characterized by 2D thermodynamic geometries. Calculations of $R$ in thermodynamic geometries of dimension three or greater have been very few, especially in the fluid regime. In this paper, we calculate $R$ for two examples involving binary fluid mixtures: a binary mixture of a van der Waals (vdW) fluid with only repulsive interactions, and a binary vdW mixture with attractive interactions added. In both these examples, we evaluate $R$ for full 3D thermodynamic geometries. Our finding is that basic physical patterns found for $R$ in the pure fluid are reproduced to a large extent for the binary fluid.