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If you have a mixture of 3 (or more) liquids which are "pairwise miscible", but which don't react with each other, does that guarantee that the mixture will only have one layer?
By "pairwise miscible", I mean that for every combination of two substances in the mixture, they are miscible with each other, i.e. soluble in all proportions.
For example, ethanol/water/acetone.
So you want to know whether there is a ternary system with an "island of immiscibility". Well, it turns out that people have thought of this before; such systems have a name ("type 0 systems"), and this paper mentions water/DMSO/THF as an example.
