What is the reason for phase separation? I have seen phase separation as a phenomenon taking place. However I do not understand why this phenomenon occurs as a counter example to the natural laws of diffusion along the concentration gradient. During phase separation the richer side becomes richer with the atoms which it already has and becomes more and more deficient with the poorer atoms and vice-versa. Similar things will occur in the opposite case as well. How can phase separation be explained in detail, for example with factors like the chemical potential?How do you quantify whether 2 liquid interactions will be unfavorable or not?
The change in Gibbs energy has to be negative for a process to happen (at constant pressure in the absence of work). Gibbs energy is a combination of entropy and enthalpy.


  I do not understand why this phenomenon occurs as a counter example to the natural laws of diffusion along the concentration gradient.


Diffusion is driven by entropy changes, specifically the entropy of mixing (in an ideal solution, the enthalpy of mixing is zero, so the entropy term is the only consideration). The entropy goes up when a solute moves from high to low concentration.

Phase separation occurs when the enthalpy term dominates. If substances A and B are initially mixed and then undergo phase separation, some change occurred (change of temperature, added third component, etc.) so that now phase separation more exothermic (lower energy for [A to interact with A and B interact with B] than [A interacting with B]). Under these circumstances, phase separation can happen.