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Wetting transitions, in which one liquid wets, or spreads at, the interface between a second liquid and their common vapor, are defined and first- and second-order transitions are distinguished. The mean-field density-functional models of fluid interfaces are recalled. A criterion is noted for determining when the wetting transitions in those models are required to be of first order or may be of second order. It is seen how two examples of such density-functional models that have been treated in the past, one leading to a first-order and the other to a second-order wetting transition, provide examples of the application of the criterion.
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