physical chemistry - Liquid-Liquid phase separation

Consider a container that contains a mixture of many liquids. Can two of these liquids phase separate without having any significant effect on other liquids inside the container? Is there a feasible scenario where the above can actually happen? I am interested in a scenario where the two liquids only separates themselves from each other and not the rest of the mixture.

More precisely: Assume the container contains a mixture of liquids A and B with many other liquids (state 1). Can these two liquids separate (triggered by change in the pressure, temperature, ...) so that at the end (state 2) the liquids in the container are divided into two regions with the following properties:

1. 
   

   The first region does not contain liquid B. It contains liquid A with the exact same mixture of the other liquid (same as state 1).

   
   


2. 
   

   The second region does not contain liquid A. It contains liquid B with the same mixture of other liquids (same as state 1).

   
   
   

Indeed we want other liquids in the container to be neutral to the phase separation of the liquids A and B.

Answer

I don't think what you are asking for is thermodynamically impossible, but I think it is very unlikely. Let's say you start off with a single liquid phase containing molecules A, B, X, Y, and Z.

Let's also say that when temperature changes, two phases form. One phase is mostly A and the other phase is mostly B. Let's call those two phases $a$ and $b$. Your question is, is there some condition where the concentrations of molecules X, Y, and Z in phase $a$ is the same as it is in phase $b$.

In general the distribution of a solute between two phases is governed by a parameter called a partition coefficient or a distribution constant. The distribution of molecule X in phase $a$ vs phase $b$, for example, could be noted as $K_{ab, X}$. For your condition to be satisified, the distribution coefficient of X would have to be 1.0, i.e. it would have an equal preference for both phases. The same would be true of molecules Y and Z, i.e. $K_{ab, X}=K_{ab, Y}=K_{ab, Z}=1$ is required for your condition.

A common type of liquid phase separation is oil and water: they don't mix. I can't think of three molecules that each have an equal preference for water vs. oil. These molecules would be somewhat hydrophobic and somewhat hydrophilic. Feel free to look through a giant compendium of octanol-water partition coefficients published by NIST to look for three molecules X, Y, and Z that all have octanol-water partition coefficients of 1.0 by yourself, though.