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Within Gross-Pitaevskii (GP) theory we derive the interface potential V (l)which describes the interaction between the interface separating two demixedBose-condensed gases and an optical hard wall at a distance l. Previous workrevealed that this interaction gives rise to extraordinary wetting andprewetting phenomena. Calculations that explore non-equilibrium properties byusing l as a constraint provide a thorough explanation for this behavior. Wefind that at bulk two-phase coexistence, V (l) for both complete wetting andpartial wetting is monotonic with exponential decay. Remarkably, at thefirst-order wetting phase transition, V(l) is independent of l. This anomalyexplains the infinite continuous degeneracy of the grand potential reportedearlier. As a physical application, using V(l) we study the three-phase contactline where the interface meets the wall under a contact angle theta. Employingan interface displacement model we calculate the structure of thisinhomogeneity and its line tension tau. Contrary to what happens at a usualfirst-order wetting transition in systems with short-range forces, tau does notapproach a nonzero positive constant for theta going to zero, but insteadapproaches zero (from below) as would be expected for a critical wettingtransition. This hybrid character of tau is a consequence of the absence of abarrier in V(l) at wetting. For a typical V(l) we provide a conjecture for theexact line tension within GP theory.

Interface potential and line tension for Bose-Einstein condensate mixtures near a hard wall