Empirical expressions of the pair correlation functions at contact and equation of state of the liquid hard-sphere mixtures at large size ratio

The virial–pressure equation of state of hard-sphere mixtures in the colloidal limit obtained from ad hoc expressions of the contact values of the pair correlation functions and the related question of the fluid–fluid phase separation are revisited. The sensitivity of the location of the binodal to the exponential behaviour of the contact value of the big spheres pair correlation function and its size ratio dependence are analyzed by considering a model for the mean force potential that is used to parameterise the contact value. Agreement with simulation data or accurate integral equations theories is improved when compared with previous approaches based on the virial–pressure equation of state.