Order of wetting transitions

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Abstract
We present general analytic expressions which permit the determination of the order of wetting transitions in mean-field theory for three systems of current interest: a one-component fluid near a wall, a binary liquid mixture near a wall, and a binary liquid mixture at three-phase coexistence. The underlying atomic forces are taken to be of the realistic long-range van der Waals type. These analytic results are derived by employing the sharp-kink approximation which replaces smooth density profiles by piecewise constant ones. In all those cases in which our analytic predictions can be compared with the numerical results for the full inhomogeneous mean-field equations there is agreement between them.