  We study a double Cahn-Hilliard type functional related to the
Gross-Pitaevskii energy of two-components Bose-Einstein condensates. In the
case of large but same order intercomponent and intracomponent coupling
strengths, we prove $\Gamma$-convergence to a perimeter minimisation functional
with an inhomogeneous surface tension. We study the asymptotic behavior of the
surface tension as the ratio between the intercomponent and intracomponent
coupling strengths becomes very small or very large. We obtain as a
consequence, symmetry breaking of the minimisers for the harmonic potential
when this radio is sufficiently large.
