in a binary two-phase system will the the chemical potential in the two phases differ?
Yes, they will, depending on how you define the "chemical potential of a phase". The chemical potential is a characteristic of a chemical species, ie : a component, not a phase.
But the chemical potential of any given component will be the same in all the phases, if the system is in equilibrium. And this is true of any n-component, m-phase system in equilibrium.
Ok, but in a system such as a detergent system where the same surfactant is in two phases (micelles and lamellar) will the surfactant chemical potential differ, or is the chemical potential associated with the entire micellar domain say?
I can't say I know the chemistry of the specific problem (in this case, the phase diagram of the detergent solution), but going by what I think you mean, I'd have to say the chemical potential of the surfactant will be the same in the two phases, in equilibrium. However, I can not comment on whether or not a detergent is in fact in a meta-stable state.
Also, I'm not sure how you can define a potential for a phase (the micelaar domain) or how that would a useful or sensible quantity.
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