Line tension at the wetting transition

We ask whether the tension of the line in which three phases meet vanishes at the wetting transition. We answer affirmatively for a simple phenomenological model in which we find that the line tension vanishes proportionally to the contact angle that closes down to 0 at the transition. We show the connection between such line tension and two-dimensional boundary tension at a pre-wetting transition. It is plausible that if the former vanishes at wetting, then so does the latter in the limit where pre-wetting becomes bulk wetting.