Helmholtz free energy for mixing?

[maistral]

TL;DR

Derivation of formula.

Hi, I have been reading a few literature regarding excess Helmholtz energy and I encountered this definition from the paper of Wong and Sandler (apparently, from the mixing rule used in a EOS):

In particular, the ones in the red boxes.

How did these equations come into being? I tried to look for it in books like Tester and SVNA and I still am unable to find where on Earth did these come from. Can someone point me to a reliable resource? Thanks.

 

[Chestermiller]

Check out Smith and Van Ness, Introduction to Chemical Engineering Thermodynamics, Chapters 10 and 11. They work mainly with Gibbs free energy, but you'll get the idea.

It looks like Sanders derived these equations specifically for an Van der Waals gas mixture.