Van der Waals introduced the Helmholtz function because its properties could be easily extended to the binary fluid situation. In a binary mixture of vdW fluids the Helmholtz potential is a function of 2 variables, f ( T R , v , x ) , where x is a composition variable, for example x = x 2 so x 1 = 1 − − x . In this case there are three stability conditions ∂ ∂ 2 f ∂ ∂ v 2 > 0 ∂ ∂ 2 f ∂ ∂ x 2 > 0 ∂ ∂ 2 f ∂ ∂ v 2 ∂ ∂ 2 f ∂ ∂ x 2 − − ( ∂ ∂ 2 f ∂ ∂ x ∂ ∂ v ) 2 > 0 and the Helmholtz potential is a surface (of physical interest in the region 0 ≤ ≤ x ≤ ≤ 1 ). The first two stability conditions show that the curvature in each of the directions v and x are both positive for stable states while the third condition indicates that stable states correspond to elliptic points on this surface. Moreover its limit, ∂ ∂ x 2 2 f ∂ ∂ v 2 2 f − − ( ∂ ∂ x v 2 f ) 2 = 0 , is in this case the specification of spinodal points.