The calculation of free energy of mixing according to the Flory-Huggins theory (and with the assumption of binary interactions) can be easily carried out in a manner similar to the derivation used by Rubinstein & Colby in chapter 4 of their book named:"Polymer Physics, published by: Oxford University Press". the same reasoning used for the binary mixtures in this book is completely applicable for ternary solutions. so far I haven't seen a text explaining the derivation method for the ternary systems, but using this book i hope you can derive it completely and step by step (I have tried it. it's really straight forward).

One must distinguish between the thermodynamic model (e.g., Flory–Huggins) and methods of deriving the phase behaviour from it. If you are primarily interested in the computation of phase diagrams from given models and intheir interpretation, I would recommend the book of Richard J. Sadus or our own (U. Deiters & T. Kraska); if you are more interested in finding suitable models, you should explain what kind of systems you have in mind. Flory–Huggins theory is good for polymer mixtures, but not for small molecules, and it does not describe compression effects well.

Thanks for your point. You are right. My primary interest is not in finding "the proper model". I want to give my students self-study material to learn how they have to deal with ternary solutions. Basically they have to learn to deal with the thermodynamics of ternary solutions. However, it helps a lot when they directly apply to a simple model and Flory-Huggins seems to be a good candidate for this.

Thank you for the clarification. If are interested in phase equilibria at high pressures and not all your phases are incompressible, you will have to use equations of state. The textbooks I mentioned explain how this is done. The book of Sadus contains more examples for ternary mixtures.

Note that both books avoid the so-called gamma–phi approach, which treats coexisting phases by different, often incompatible models. This simplifies the calculations to some extent (so that one can even use a simple model like Flory–Huggins for the liquid), but at the price that some high-pressure phenomena (solubility in the gas phase, critical phenomena) are not predicted well.

The general discussion of phase equilibria can be found in PHASE EQUILIBRIA IN CHEMICAL ENGINEERING by Walas.