For a spherical solid particle with a uniform surface at rest in a fluid/fluid interface, it is shown that if the line tension associated with the three-phase contact line around the particle is increased (conceptually), the contact angle between the particle and interface does not change continuously to 0 or 180°. Rather, when a critical value of line tension is attained a discontinuous wetting–drying transition can occur. Such a transition corresponds to the condition where the free energy of the particle at local equilibrium in the interface is equal to that of the particle completely immersed in one of the bulk phases. However, local equilibrium in the interface is possible for line tensions greater than that required for the transition. This means that an ‘activation’ energy is required for the irreversible removal of the particle into one of the bulk phases. Literature values of line tensions span at least five orders of magnitude. If the larger of the reported values operate in systems with the geometry of interest here, interesting wetting phenomena should be apparent for particles with diameters of the order of 1 mm.