= Chemical potential of a composition field
{title2=$\mu=\delta F/\delta\phi$}
For a composition <free energy> $F=\int[f(\phi)+\kappa|\nabla\phi|^2/2]$, the local chemical potential is the <functional derivative>
$$
\mu=f'(\phi)-\kappa\nabla^2\phi.
$$
At <phase coexistence>, exchanges between the bulk phases require equal <chemical potentials>. Mechanical equilibrium additionally requires equal <pressure> for a flat interface, or a <Young–Laplace equation> pressure jump for a curved interface.
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